CINXE.COM

<!DOCTYPE html> <html class="client-nojs vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-sticky-header-enabled vector-toc-available" lang="en" dir="ltr"> <head> <meta charset="UTF-8"> <title>Capacitor - Wikipedia</title> <script>(function(){var className="client-js vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-sticky-header-enabled vector-toc-available";var cookie=document.cookie.match(/(?:^|; )enwikimwclientpreferences=([^;]+)/);if(cookie){cookie[1].split('%2C').forEach(function(pref){className=className.replace(new RegExp('(^| )'+pref.replace(/-clientpref-\w+$|[^\w-]+/g,'')+'-clientpref-\\w+( |$)'),'$1'+pref+'$2');});}document.documentElement.className=className;}());RLCONF={"wgBreakFrames":false,"wgSeparatorTransformTable":["",""],"wgDigitTransformTable":["",""],"wgDefaultDateFormat":"dmy","wgMonthNames":["","January","February","March","April","May","June","July","August","September","October","November","December"],"wgRequestId":"482ffc0f-c816-421f-b320-f69abb987663","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"Capacitor","wgTitle":"Capacitor","wgCurRevisionId":1281636495,"wgRevisionId":1281636495,"wgArticleId":4932111,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["Webarchive template wayback links","Articles with short description","Short description is different from Wikidata","Use dmy dates from June 2022","All articles with unsourced statements","Articles with unsourced statements from January 2020","Articles with unsourced statements from September 2023","Articles with unsourced statements from October 2020","Articles with unsourced statements from November 2016","Articles containing potentially dated statements from 2010","All articles containing potentially dated statements","All articles with vague or ambiguous time","Vague or ambiguous time from May 2018","Electrical components","Energy storage","Capacitors","Science and technology in the Dutch Republic","Dutch inventions","18th-century inventions","German inventions"],"wgPageViewLanguage":"en","wgPageContentLanguage":"en","wgPageContentModel":"wikitext","wgRelevantPageName":"Capacitor","wgRelevantArticleId":4932111,"wgIsProbablyEditable":true,"wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[],"wgRestrictionMove":[],"wgNoticeProject":"wikipedia","wgCiteReferencePreviewsActive":false,"wgFlaggedRevsParams":{"tags":{"status":{"levels":1}}},"wgMediaViewerOnClick":true,"wgMediaViewerEnabledByDefault":true,"wgPopupsFlags":0,"wgVisualEditor":{"pageLanguageCode":"en","pageLanguageDir":"ltr","pageVariantFallbacks":"en"},"wgMFDisplayWikibaseDescriptions":{"search":true,"watchlist":true,"tagline":false,"nearby":true},"wgWMESchemaEditAttemptStepOversample":false,"wgWMEPageLength":100000,"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q5322","wgCheckUserClientHintsHeadersJsApi":["brands","architecture","bitness","fullVersionList","mobile","model","platform","platformVersion"],"GEHomepageSuggestedEditsEnableTopics":true,"wgGETopicsMatchModeEnabled":false,"wgGELevelingUpEnabledForUser":false}; RLSTATE={"ext.globalCssJs.user.styles":"ready","site.styles":"ready","user.styles":"ready","ext.globalCssJs.user":"ready","user":"ready","user.options":"loading","ext.cite.styles":"ready","ext.math.styles":"ready","mediawiki.page.gallery.styles":"ready","skins.vector.search.codex.styles":"ready","skins.vector.styles":"ready","skins.vector.icons":"ready","jquery.makeCollapsible.styles":"ready","ext.wikimediamessages.styles":"ready","ext.visualEditor.desktopArticleTarget.noscript":"ready","ext.uls.interlanguage":"ready","wikibase.client.init":"ready","ext.wikimediaBadges":"ready"};RLPAGEMODULES=["ext.cite.ux-enhancements","mediawiki.page.gallery","mediawiki.page.media","ext.scribunto.logs","site","mediawiki.page.ready","jquery.makeCollapsible","mediawiki.toc","skins.vector.js","ext.centralNotice.geoIP","ext.centralNotice.startUp","ext.gadget.ReferenceTooltips","ext.gadget.switcher","ext.urlShortener.toolbar","ext.centralauth.centralautologin","mmv.bootstrap","ext.popups","ext.visualEditor.desktopArticleTarget.init","ext.visualEditor.targetLoader","ext.echo.centralauth","ext.eventLogging","ext.wikimediaEvents","ext.navigationTiming","ext.uls.interface","ext.cx.eventlogging.campaigns","ext.cx.uls.quick.actions","wikibase.client.vector-2022","ext.checkUser.clientHints","ext.growthExperiments.SuggestedEditSession"];</script> <script>(RLQ=window.RLQ||[]).push(function(){mw.loader.impl(function(){return["user.options@12s5i",function($,jQuery,require,module){mw.user.tokens.set({"patrolToken":"+\\","watchToken":"+\\","csrfToken":"+\\"}); }];});});</script> <link rel="stylesheet" href="/w/load.php?lang=en&modules=ext.cite.styles%7Cext.math.styles%7Cext.uls.interlanguage%7Cext.visualEditor.desktopArticleTarget.noscript%7Cext.wikimediaBadges%7Cext.wikimediamessages.styles%7Cjquery.makeCollapsible.styles%7Cmediawiki.page.gallery.styles%7Cskins.vector.icons%2Cstyles%7Cskins.vector.search.codex.styles%7Cwikibase.client.init&only=styles&skin=vector-2022"> <script async="" src="/w/load.php?lang=en&modules=startup&only=scripts&raw=1&skin=vector-2022"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=en&modules=site.styles&only=styles&skin=vector-2022"> <meta name="generator" content="MediaWiki 1.44.0-wmf.21"> <meta name="referrer" content="origin"> <meta name="referrer" content="origin-when-cross-origin"> <meta name="robots" content="max-image-preview:standard"> <meta name="format-detection" content="telephone=no"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Capacitors_%287189597135%29.jpg/1200px-Capacitors_%287189597135%29.jpg"> <meta property="og:image:width" content="1200"> <meta property="og:image:height" content="800"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Capacitors_%287189597135%29.jpg/800px-Capacitors_%287189597135%29.jpg"> <meta property="og:image:width" content="800"> <meta property="og:image:height" content="533"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Capacitors_%287189597135%29.jpg/640px-Capacitors_%287189597135%29.jpg"> <meta property="og:image:width" content="640"> <meta property="og:image:height" content="427"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="Capacitor - Wikipedia"> <meta property="og:type" content="website"> <link rel="preconnect" href="//upload.wikimedia.org"> <link rel="alternate" media="only screen and (max-width: 640px)" href="//en.m.wikipedia.org/wiki/Capacitor"> <link rel="alternate" type="application/x-wiki" title="Edit this page" href="/w/index.php?title=Capacitor&action=edit"> <link rel="apple-touch-icon" href="/static/apple-touch/wikipedia.png"> <link rel="icon" href="/static/favicon/wikipedia.ico"> <link rel="search" type="application/opensearchdescription+xml" href="/w/rest.php/v1/search" title="Wikipedia (en)"> <link rel="EditURI" type="application/rsd+xml" href="//en.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://en.wikipedia.org/wiki/Capacitor"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en"> <link rel="alternate" type="application/atom+xml" title="Wikipedia Atom feed" href="/w/index.php?title=Special:RecentChanges&feed=atom"> <link rel="dns-prefetch" href="//meta.wikimedia.org" /> <link rel="dns-prefetch" href="login.wikimedia.org"> </head> <body class="skin--responsive skin-vector skin-vector-search-vue mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject mw-editable page-Capacitor rootpage-Capacitor skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Jump to content</a> <div class="vector-header-container"> <header class="vector-header mw-header"> <div class="vector-header-start"> <nav class="vector-main-menu-landmark" aria-label="Site"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" title="Main menu" > <input type="checkbox" id="vector-main-menu-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-main-menu-dropdown" class="vector-dropdown-checkbox " aria-label="Main menu" > <label id="vector-main-menu-dropdown-label" for="vector-main-menu-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-menu mw-ui-icon-wikimedia-menu"></span> <span class="vector-dropdown-label-text">Main menu</span> </label> <div class="vector-dropdown-content"> <div id="vector-main-menu-unpinned-container" class="vector-unpinned-container"> <div id="vector-main-menu" class="vector-main-menu vector-pinnable-element"> <div class="vector-pinnable-header vector-main-menu-pinnable-header vector-pinnable-header-unpinned" data-feature-name="main-menu-pinned" data-pinnable-element-id="vector-main-menu" data-pinned-container-id="vector-main-menu-pinned-container" data-unpinned-container-id="vector-main-menu-unpinned-container" > <div class="vector-pinnable-header-label">Main menu</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">hide</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Navigation </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage-description" class="mw-list-item"><a href="/wiki/Main_Page" title="Visit the main page [z]" accesskey="z"><span>Main page</span></a></li><li id="n-contents" class="mw-list-item"><a href="/wiki/Wikipedia:Contents" title="Guides to browsing Wikipedia"><span>Contents</span></a></li><li id="n-currentevents" class="mw-list-item"><a href="/wiki/Portal:Current_events" title="Articles related to current events"><span>Current events</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Special:Random" title="Visit a randomly selected article [x]" accesskey="x"><span>Random article</span></a></li><li id="n-aboutsite" class="mw-list-item"><a href="/wiki/Wikipedia:About" title="Learn about Wikipedia and how it works"><span>About Wikipedia</span></a></li><li id="n-contactpage" class="mw-list-item"><a href="//en.wikipedia.org/wiki/Wikipedia:Contact_us" title="How to contact Wikipedia"><span>Contact us</span></a></li> </ul> </div> </div> <div id="p-interaction" class="vector-menu mw-portlet mw-portlet-interaction" > <div class="vector-menu-heading"> Contribute </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-help" class="mw-list-item"><a href="/wiki/Help:Contents" title="Guidance on how to use and edit Wikipedia"><span>Help</span></a></li><li id="n-introduction" class="mw-list-item"><a href="/wiki/Help:Introduction" title="Learn how to edit Wikipedia"><span>Learn to edit</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/Wikipedia:Community_portal" title="The hub for editors"><span>Community portal</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Special:RecentChanges" title="A list of recent changes to Wikipedia [r]" accesskey="r"><span>Recent changes</span></a></li><li id="n-upload" class="mw-list-item"><a href="/wiki/Wikipedia:File_upload_wizard" title="Add images or other media for use on Wikipedia"><span>Upload file</span></a></li><li id="n-specialpages" class="mw-list-item"><a href="/wiki/Special:SpecialPages"><span>Special pages</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Main_Page" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Wikipedia" src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" style="width: 7.5em; height: 1.125em;"> <img class="mw-logo-tagline" alt="The Free Encyclopedia" src="/static/images/mobile/copyright/wikipedia-tagline-en.svg" width="117" height="13" style="width: 7.3125em; height: 0.8125em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/Special:Search" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Search Wikipedia [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Search</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Search Wikipedia" aria-label="Search Wikipedia" autocapitalize="sentences" title="Search Wikipedia [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Special:Search"> </div> <button class="cdx-button cdx-search-input__end-button">Search</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Personal tools"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Appearance" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Appearance</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=en.wikipedia.org&uselang=en" class=""><span>Donate</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Special:CreateAccount&returnto=Capacitor" title="You are encouraged to create an account and log in; however, it is not mandatory" class=""><span>Create account</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Special:UserLogin&returnto=Capacitor" title="You're encouraged to log in; however, it's not mandatory. [o]" accesskey="o" class=""><span>Log in</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Log in and more options" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Personal tools" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Personal tools</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="User menu" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=en.wikipedia.org&uselang=en"><span>Donate</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:CreateAccount&returnto=Capacitor" title="You are encouraged to create an account and log in; however, it is not mandatory"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Create account</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:UserLogin&returnto=Capacitor" title="You're encouraged to log in; however, it's not mandatory. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Log in</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Pages for logged out editors <a href="/wiki/Help:Introduction" aria-label="Learn more about editing"><span>learn more</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Special:MyContributions" title="A list of edits made from this IP address [y]" accesskey="y"><span>Contributions</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Special:MyTalk" title="Discussion about edits from this IP address [n]" accesskey="n"><span>Talk</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Site"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Contents" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Contents</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">hide</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">(Top)</div> </a> </li> <li id="toc-History" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#History"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>History</span> </div> </a> <ul id="toc-History-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Theory_of_operation" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Theory_of_operation"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Theory of operation</span> </div> </a> <button aria-controls="toc-Theory_of_operation-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Theory of operation subsection</span> </button> <ul id="toc-Theory_of_operation-sublist" class="vector-toc-list"> <li id="toc-Overview" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Overview"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Overview</span> </div> </a> <ul id="toc-Overview-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Hydraulic_analogy" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Hydraulic_analogy"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Hydraulic analogy</span> </div> </a> <ul id="toc-Hydraulic_analogy-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Circuit_equivalence_at_short-time_limit_and_long-time_limit" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Circuit_equivalence_at_short-time_limit_and_long-time_limit"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Circuit equivalence at short-time limit and long-time limit</span> </div> </a> <ul id="toc-Circuit_equivalence_at_short-time_limit_and_long-time_limit-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Parallel-plate_capacitor" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Parallel-plate_capacitor"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Parallel-plate capacitor</span> </div> </a> <ul id="toc-Parallel-plate_capacitor-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Interleaved_capacitor" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Interleaved_capacitor"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5</span> <span>Interleaved capacitor</span> </div> </a> <ul id="toc-Interleaved_capacitor-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Energy_stored_in_a_capacitor" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Energy_stored_in_a_capacitor"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.6</span> <span>Energy stored in a capacitor</span> </div> </a> <ul id="toc-Energy_stored_in_a_capacitor-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Current–voltage_relation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Current–voltage_relation"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.7</span> <span>Current–voltage relation</span> </div> </a> <ul id="toc-Current–voltage_relation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-RC_circuits" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#RC_circuits"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.8</span> <span>RC circuits</span> </div> </a> <ul id="toc-RC_circuits-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-AC_circuits" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#AC_circuits"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.9</span> <span>AC circuits</span> </div> </a> <ul id="toc-AC_circuits-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Laplace_circuit_analysis_(s-domain)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Laplace_circuit_analysis_(s-domain)"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.10</span> <span>Laplace circuit analysis (s-domain)</span> </div> </a> <ul id="toc-Laplace_circuit_analysis_(s-domain)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Circuit_analysis" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Circuit_analysis"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.11</span> <span>Circuit analysis</span> </div> </a> <ul id="toc-Circuit_analysis-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Non-ideal_behavior" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Non-ideal_behavior"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Non-ideal behavior</span> </div> </a> <button aria-controls="toc-Non-ideal_behavior-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Non-ideal behavior subsection</span> </button> <ul id="toc-Non-ideal_behavior-sublist" class="vector-toc-list"> <li id="toc-Breakdown_voltage" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Breakdown_voltage"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Breakdown voltage</span> </div> </a> <ul id="toc-Breakdown_voltage-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Equivalent_circuit" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Equivalent_circuit"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Equivalent circuit</span> </div> </a> <ul id="toc-Equivalent_circuit-sublist" class="vector-toc-list"> <li id="toc-Simplified_RLC_series_model" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Simplified_RLC_series_model"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2.1</span> <span>Simplified RLC series model</span> </div> </a> <ul id="toc-Simplified_RLC_series_model-sublist" class="vector-toc-list"> <li id="toc-Q_factor" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Q_factor"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2.1.1</span> <span>Q factor</span> </div> </a> <ul id="toc-Q_factor-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Ripple_current" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ripple_current"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Ripple current</span> </div> </a> <ul id="toc-Ripple_current-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Capacitance_instability" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Capacitance_instability"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4</span> <span>Capacitance instability</span> </div> </a> <ul id="toc-Capacitance_instability-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Current_and_voltage_reversal" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Current_and_voltage_reversal"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.5</span> <span>Current and voltage reversal</span> </div> </a> <ul id="toc-Current_and_voltage_reversal-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Dielectric_absorption" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Dielectric_absorption"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.6</span> <span>Dielectric absorption</span> </div> </a> <ul id="toc-Dielectric_absorption-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Leakage" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Leakage"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.7</span> <span>Leakage</span> </div> </a> <ul id="toc-Leakage-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Electrolytic_failure_from_disuse" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Electrolytic_failure_from_disuse"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.8</span> <span>Electrolytic failure from disuse</span> </div> </a> <ul id="toc-Electrolytic_failure_from_disuse-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Lifespan" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Lifespan"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.9</span> <span>Lifespan</span> </div> </a> <ul id="toc-Lifespan-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Capacitor_types" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Capacitor_types"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Capacitor types</span> </div> </a> <button aria-controls="toc-Capacitor_types-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Capacitor types subsection</span> </button> <ul id="toc-Capacitor_types-sublist" class="vector-toc-list"> <li id="toc-Dielectric_materials" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Dielectric_materials"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Dielectric materials</span> </div> </a> <ul id="toc-Dielectric_materials-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Voltage-dependent_capacitors" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Voltage-dependent_capacitors"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Voltage-dependent capacitors</span> </div> </a> <ul id="toc-Voltage-dependent_capacitors-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Frequency-dependent_capacitors" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Frequency-dependent_capacitors"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Frequency-dependent capacitors</span> </div> </a> <ul id="toc-Frequency-dependent_capacitors-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Styles" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Styles"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>Styles</span> </div> </a> <ul id="toc-Styles-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Capacitor_markings" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Capacitor_markings"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Capacitor markings</span> </div> </a> <button aria-controls="toc-Capacitor_markings-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Capacitor markings subsection</span> </button> <ul id="toc-Capacitor_markings-sublist" class="vector-toc-list"> <li id="toc-Marking_codes_for_larger_parts" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Marking_codes_for_larger_parts"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Marking codes for larger parts</span> </div> </a> <ul id="toc-Marking_codes_for_larger_parts-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Three-/four-character_marking_code_for_small_capacitors" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Three-/four-character_marking_code_for_small_capacitors"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Three-/four-character marking code for small capacitors</span> </div> </a> <ul id="toc-Three-/four-character_marking_code_for_small_capacitors-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Two-character_marking_code_for_small_capacitors" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Two-character_marking_code_for_small_capacitors"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3</span> <span>Two-character marking code for small capacitors</span> </div> </a> <ul id="toc-Two-character_marking_code_for_small_capacitors-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-RKM_code" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#RKM_code"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.4</span> <span>RKM code</span> </div> </a> <ul id="toc-RKM_code-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Historical" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Historical"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.5</span> <span>Historical</span> </div> </a> <ul id="toc-Historical-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Applications" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Applications"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Applications</span> </div> </a> <button aria-controls="toc-Applications-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Applications subsection</span> </button> <ul id="toc-Applications-sublist" class="vector-toc-list"> <li id="toc-Energy_storage" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Energy_storage"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Energy storage</span> </div> </a> <ul id="toc-Energy_storage-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Digital_memory" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Digital_memory"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.2</span> <span>Digital memory</span> </div> </a> <ul id="toc-Digital_memory-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Pulsed_power_and_weapons" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Pulsed_power_and_weapons"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.3</span> <span>Pulsed power and weapons</span> </div> </a> <ul id="toc-Pulsed_power_and_weapons-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Power_conditioning" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Power_conditioning"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.4</span> <span>Power conditioning</span> </div> </a> <ul id="toc-Power_conditioning-sublist" class="vector-toc-list"> <li id="toc-Power-factor_correction" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Power-factor_correction"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.4.1</span> <span>Power-factor correction</span> </div> </a> <ul id="toc-Power-factor_correction-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Suppression_and_coupling" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Suppression_and_coupling"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.5</span> <span>Suppression and coupling</span> </div> </a> <ul id="toc-Suppression_and_coupling-sublist" class="vector-toc-list"> <li id="toc-Signal_coupling" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Signal_coupling"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.5.1</span> <span>Signal coupling</span> </div> </a> <ul id="toc-Signal_coupling-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Decoupling" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Decoupling"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.5.2</span> <span>Decoupling</span> </div> </a> <ul id="toc-Decoupling-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-High-pass_and_low-pass_filters" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#High-pass_and_low-pass_filters"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.5.3</span> <span>High-pass and low-pass filters</span> </div> </a> <ul id="toc-High-pass_and_low-pass_filters-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Noise_suppression,_spikes,_and_snubbers" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Noise_suppression,_spikes,_and_snubbers"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.5.4</span> <span>Noise suppression, spikes, and snubbers</span> </div> </a> <ul id="toc-Noise_suppression,_spikes,_and_snubbers-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Motor_starters" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Motor_starters"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.6</span> <span>Motor starters</span> </div> </a> <ul id="toc-Motor_starters-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Signal_processing" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Signal_processing"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.7</span> <span>Signal processing</span> </div> </a> <ul id="toc-Signal_processing-sublist" class="vector-toc-list"> <li id="toc-Tuned_circuits" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Tuned_circuits"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.7.1</span> <span>Tuned circuits</span> </div> </a> <ul id="toc-Tuned_circuits-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Sensing" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Sensing"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.8</span> <span>Sensing</span> </div> </a> <ul id="toc-Sensing-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Oscillators" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Oscillators"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.9</span> <span>Oscillators</span> </div> </a> <ul id="toc-Oscillators-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Producing_light" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Producing_light"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.10</span> <span>Producing light</span> </div> </a> <ul id="toc-Producing_light-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Hazards_and_safety" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Hazards_and_safety"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Hazards and safety</span> </div> </a> <ul id="toc-Hazards_and_safety-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>References</span> </div> </a> <button aria-controls="toc-References-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle References subsection</span> </button> <ul id="toc-References-sublist" class="vector-toc-list"> <li id="toc-Bibliography" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Bibliography"> <div class="vector-toc-text"> <span class="vector-toc-numb">10.1</span> <span>Bibliography</span> </div> </a> <ul id="toc-Bibliography-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">12</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table of Contents" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Capacitor</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 120 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-120" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">120 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Kapasitor" title="Kapasitor – Afrikaans" lang="af" hreflang="af" data-title="Kapasitor" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Kondensator_(Elektrotechnik)" title="Kondensator (Elektrotechnik) – Alemannic" lang="gsw" hreflang="gsw" data-title="Kondensator (Elektrotechnik)" data-language-autonym="Alemannisch" data-language-local-name="Alemannic" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D9%83%D8%AB%D9%81_(%D9%83%D9%87%D8%B1%D8%A8%D8%A7%D8%A1)" title="مكثف (كهرباء) – Arabic" lang="ar" hreflang="ar" data-title="مكثف (كهرباء)" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Condensador" title="Condensador – Aragonese" lang="an" hreflang="an" data-title="Condensador" data-language-autonym="Aragonés" data-language-local-name="Aragonese" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%A7%E0%A6%BE%E0%A7%B0%E0%A6%95" title="ধাৰক – Assamese" lang="as" hreflang="as" data-title="ধাৰক" data-language-autonym="অসমীয়া" data-language-local-name="Assamese" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Condensador_ll%C3%A9tricu" title="Condensador llétricu – Asturian" lang="ast" hreflang="ast" data-title="Condensador llétricu" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Kondensator_(elektrik)" title="Kondensator (elektrik) – Azerbaijani" lang="az" hreflang="az" data-title="Kondensator (elektrik)" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%AE%D8%A7%D8%B2%D9%86" title="خازن – South Azerbaijani" lang="azb" hreflang="azb" data-title="خازن" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%A7%E0%A6%BE%E0%A6%B0%E0%A6%95" title="ধারক – Bangla" lang="bn" hreflang="bn" data-title="ধারক" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Ti%C4%81n-i%C3%B4ng-kh%C3%AC" title="Tiān-iông-khì – Minnan" lang="nan" hreflang="nan" data-title="Tiān-iông-khì" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%AD%D0%BB%D0%B5%D0%BA%D1%82%D1%80_%D0%BA%D0%BE%D0%BD%D0%B4%D0%B5%D0%BD%D1%81%D0%B0%D1%82%D0%BE%D1%80%D1%8B" title="Электр конденсаторы – Bashkir" lang="ba" hreflang="ba" data-title="Электр конденсаторы" data-language-autonym="Башҡортса" data-language-local-name="Bashkir" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9A%D0%B0%D0%BD%D0%B4%D1%8D%D0%BD%D1%81%D0%B0%D1%82%D0%B0%D1%80" title="Кандэнсатар – Belarusian" lang="be" hreflang="be" data-title="Кандэнсатар" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%9A%D0%B0%D0%BD%D0%B4%D1%8D%D0%BD%D1%81%D0%B0%D1%82%D0%B0%D1%80" title="Кандэнсатар – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Кандэнсатар" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bh mw-list-item"><a href="https://bh.wikipedia.org/wiki/%E0%A4%A7%E0%A4%B0%E0%A4%A8%E0%A5%80" title="धरनी – Bhojpuri" lang="bh" hreflang="bh" data-title="धरनी" data-language-autonym="भोजपुरी" data-language-local-name="Bhojpuri" class="interlanguage-link-target"><span>भोजपुरी</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D0%B4%D0%B5%D0%BD%D0%B7%D0%B0%D1%82%D0%BE%D1%80" title="Кондензатор – Bulgarian" lang="bg" hreflang="bg" data-title="Кондензатор" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bar mw-list-item"><a href="https://bar.wikipedia.org/wiki/Kondensatoa" title="Kondensatoa – Bavarian" lang="bar" hreflang="bar" data-title="Kondensatoa" data-language-autonym="Boarisch" data-language-local-name="Bavarian" class="interlanguage-link-target"><span>Boarisch</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Kondenzator" title="Kondenzator – Bosnian" lang="bs" hreflang="bs" data-title="Kondenzator" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Condensador" title="Condensador – Catalan" lang="ca" hreflang="ca" data-title="Condensador" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Kondenz%C3%A1tor" title="Kondenzátor – Czech" lang="cs" hreflang="cs" data-title="Kondenzátor" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Cynhwysiant_trydanol" title="Cynhwysiant trydanol – Welsh" lang="cy" hreflang="cy" data-title="Cynhwysiant trydanol" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Elektrisk_kondensator" title="Elektrisk kondensator – Danish" lang="da" hreflang="da" data-title="Elektrisk kondensator" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-ary mw-list-item"><a href="https://ary.wikipedia.org/wiki/%D9%83%D9%88%D9%86%D8%AF%D8%A7%D8%B3%D8%A7%D8%AA%D9%88%D8%B1" title="كونداساتور – Moroccan Arabic" lang="ary" hreflang="ary" data-title="كونداساتور" data-language-autonym="الدارجة" data-language-local-name="Moroccan Arabic" class="interlanguage-link-target"><span>الدارجة</span></a></li><li class="interlanguage-link interwiki-de badge-Q17437796 badge-featuredarticle mw-list-item" title="featured article badge"><a href="https://de.wikipedia.org/wiki/Kondensator_(Elektrotechnik)" title="Kondensator (Elektrotechnik) – German" lang="de" hreflang="de" data-title="Kondensator (Elektrotechnik)" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Kondensaator" title="Kondensaator – Estonian" lang="et" hreflang="et" data-title="Kondensaator" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A0%CF%85%CE%BA%CE%BD%CF%89%CF%84%CE%AE%CF%82" title="Πυκνωτής – Greek" lang="el" hreflang="el" data-title="Πυκνωτής" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Condensador_el%C3%A9ctrico" title="Condensador eléctrico – Spanish" lang="es" hreflang="es" data-title="Condensador eléctrico" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Kondensilo" title="Kondensilo – Esperanto" lang="eo" hreflang="eo" data-title="Kondensilo" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Kondentsadore_elektriko" title="Kondentsadore elektriko – Basque" lang="eu" hreflang="eu" data-title="Kondentsadore elektriko" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AE%D8%A7%D8%B2%D9%86" title="خازن – Persian" lang="fa" hreflang="fa" data-title="خازن" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-hif mw-list-item"><a href="https://hif.wikipedia.org/wiki/Capacitor" title="Capacitor – Fiji Hindi" lang="hif" hreflang="hif" data-title="Capacitor" data-language-autonym="Fiji Hindi" data-language-local-name="Fiji Hindi" class="interlanguage-link-target"><span>Fiji Hindi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Condensateur" title="Condensateur – French" lang="fr" hreflang="fr" data-title="Condensateur" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Toilleoir_(leictreonaic)" title="Toilleoir (leictreonaic) – Irish" lang="ga" hreflang="ga" data-title="Toilleoir (leictreonaic)" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Condensador" title="Condensador – Galician" lang="gl" hreflang="gl" data-title="Condensador" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E9%9B%BB%E5%AE%B9" title="電容 – Gan" lang="gan" hreflang="gan" data-title="電容" data-language-autonym="贛語" data-language-local-name="Gan" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%B6%95%EC%A0%84%EA%B8%B0" title="축전기 – Korean" lang="ko" hreflang="ko" data-title="축전기" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B7%D5%AC%D5%A5%D5%AF%D5%BF%D6%80%D5%A1%D5%AF%D5%A1%D5%B6_%D5%AF%D5%B8%D5%B6%D5%A4%D5%A5%D5%B6%D5%BD%D5%A1%D5%BF%D5%B8%D6%80" title="Էլեկտրական կոնդենսատոր – Armenian" lang="hy" hreflang="hy" data-title="Էլեկտրական կոնդենսատոր" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B8%E0%A4%82%E0%A4%A7%E0%A4%BE%E0%A4%B0%E0%A4%BF%E0%A4%A4%E0%A5%8D%E0%A4%B0" title="संधारित्र – Hindi" lang="hi" hreflang="hi" data-title="संधारित्र" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Elektri%C4%8Dni_kondenzator" title="Električni kondenzator – Croatian" lang="hr" hreflang="hr" data-title="Električni kondenzator" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Kondensatoro" title="Kondensatoro – Ido" lang="io" hreflang="io" data-title="Kondensatoro" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Kapasitor" title="Kapasitor – Indonesian" lang="id" hreflang="id" data-title="Kapasitor" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Condensator" title="Condensator – Interlingua" lang="ia" hreflang="ia" data-title="Condensator" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-os mw-list-item"><a href="https://os.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D0%B4%D0%B5%D0%BD%D1%81%D0%B0%D1%82%D0%BE%D1%80" title="Конденсатор – Ossetic" lang="os" hreflang="os" data-title="Конденсатор" data-language-autonym="Ирон" data-language-local-name="Ossetic" class="interlanguage-link-target"><span>Ирон</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Raf%C3%BE%C3%A9ttir" title="Rafþéttir – Icelandic" lang="is" hreflang="is" data-title="Rafþéttir" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Condensatore_(elettrotecnica)" title="Condensatore (elettrotecnica) – Italian" lang="it" hreflang="it" data-title="Condensatore (elettrotecnica)" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A7%D7%91%D7%9C" title="קבל – Hebrew" lang="he" hreflang="he" data-title="קבל" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Kondensator" title="Kondensator – Javanese" lang="jv" hreflang="jv" data-title="Kondensator" data-language-autonym="Jawa" data-language-local-name="Javanese" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%94%E1%83%9A%E1%83%94%E1%83%A5%E1%83%A2%E1%83%A0%E1%83%A3%E1%83%9A%E1%83%98_%E1%83%99%E1%83%9D%E1%83%9C%E1%83%93%E1%83%94%E1%83%9C%E1%83%A1%E1%83%90%E1%83%A2%E1%83%9D%E1%83%A0%E1%83%98" title="ელექტრული კონდენსატორი – Georgian" lang="ka" hreflang="ka" data-title="ელექტრული კონდენსატორი" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%AD%D0%BB%D0%B5%D0%BA%D1%82%D1%80_%D0%BA%D0%BE%D0%BD%D0%B4%D0%B5%D0%BD%D1%81%D0%B0%D1%82%D0%BE%D1%80%D1%8B" title="Электр конденсаторы – Kazakh" lang="kk" hreflang="kk" data-title="Электр конденсаторы" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Kapasita" title="Kapasita – Swahili" lang="sw" hreflang="sw" data-title="Kapasita" data-language-autonym="Kiswahili" data-language-local-name="Swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Kondansat%C3%A8" title="Kondansatè – Haitian Creole" lang="ht" hreflang="ht" data-title="Kondansatè" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/Kondansator" title="Kondansator – Kurdish" lang="ku" hreflang="ku" data-title="Kondansator" data-language-autonym="Kurdî" data-language-local-name="Kurdish" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D0%B4%D0%B5%D0%BD%D1%81%D0%B0%D1%82%D0%BE%D1%80" title="Конденсатор – Kyrgyz" lang="ky" hreflang="ky" data-title="Конденсатор" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Condensatrum" title="Condensatrum – Latin" lang="la" hreflang="la" data-title="Condensatrum" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Kondensators" title="Kondensators – Latvian" lang="lv" hreflang="lv" data-title="Kondensators" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Kondensatorius_(elektra)" title="Kondensatorius (elektra) – Lithuanian" lang="lt" hreflang="lt" data-title="Kondensatorius (elektra)" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Condensator_(elettrotecnica)" title="Condensator (elettrotecnica) – Lombard" lang="lmo" hreflang="lmo" data-title="Condensator (elettrotecnica)" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Kondenz%C3%A1tor_(%C3%A1ramk%C3%B6ri_alkatr%C3%A9sz)" title="Kondenzátor (áramköri alkatrész) – Hungarian" lang="hu" hreflang="hu" data-title="Kondenzátor (áramköri alkatrész)" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D0%B4%D0%B5%D0%BD%D0%B7%D0%B0%D1%82%D0%BE%D1%80" title="Кондензатор – Macedonian" lang="mk" hreflang="mk" data-title="Кондензатор" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Kadobo" title="Kadobo – Malagasy" lang="mg" hreflang="mg" data-title="Kadobo" data-language-autonym="Malagasy" data-language-local-name="Malagasy" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%95%E0%B4%AA%E0%B5%8D%E0%B4%AA%E0%B4%BE%E0%B4%B8%E0%B4%BF%E0%B4%B1%E0%B5%8D%E0%B4%B1%E0%B5%BC" title="കപ്പാസിറ്റർ – Malayalam" lang="ml" hreflang="ml" data-title="കപ്പാസിറ്റർ" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%B8%E0%A4%82%E0%A4%A7%E0%A4%BE%E0%A4%B0%E0%A4%BF%E0%A4%A4%E0%A5%8D%E0%A4%B0" title="संधारित्र – Marathi" lang="mr" hreflang="mr" data-title="संधारित्र" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D8%A7%D9%84%D9%85%D9%83%D8%AB%D9%81" title="المكثف – Egyptian Arabic" lang="arz" hreflang="arz" data-title="المكثف" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-mzn mw-list-item"><a href="https://mzn.wikipedia.org/wiki/%D8%AE%D8%A7%D8%B2%D9%86" title="خازن – Mazanderani" lang="mzn" hreflang="mzn" data-title="خازن" data-language-autonym="مازِرونی" data-language-local-name="Mazanderani" class="interlanguage-link-target"><span>مازِرونی</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Pemuat" title="Pemuat – Malay" lang="ms" hreflang="ms" data-title="Pemuat" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-min mw-list-item"><a href="https://min.wikipedia.org/wiki/Kapasitor" title="Kapasitor – Minangkabau" lang="min" hreflang="min" data-title="Kapasitor" data-language-autonym="Minangkabau" data-language-local-name="Minangkabau" class="interlanguage-link-target"><span>Minangkabau</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D0%B4%D0%B5%D0%BD%D1%81%D0%B0%D1%82%D0%BE%D1%80" title="Конденсатор – Mongolian" lang="mn" hreflang="mn" data-title="Конденсатор" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%9C%E1%80%BB%E1%80%BE%E1%80%95%E1%80%BA%E1%80%9E%E1%80%AD%E1%80%AF" title="လျှပ်သို – Burmese" lang="my" hreflang="my" data-title="လျှပ်သို" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmese" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Condensator" title="Condensator – Dutch" lang="nl" hreflang="nl" data-title="Condensator" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%95%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%AA%E0%A4%BE%E0%A4%B8%E0%A4%BF%E0%A4%9F%E0%A4%B0" title="क्यापासिटर – Nepali" lang="ne" hreflang="ne" data-title="क्यापासिटर" data-language-autonym="नेपाली" data-language-local-name="Nepali" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-new mw-list-item"><a href="https://new.wikipedia.org/wiki/%E0%A4%95%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%AA%E0%A4%BE%E0%A4%B8%E0%A4%BF%E0%A4%A4%E0%A4%B0" title="क्यापासितर – Newari" lang="new" hreflang="new" data-title="क्यापासितर" data-language-autonym="नेपाल भाषा" data-language-local-name="Newari" class="interlanguage-link-target"><span>नेपाल भाषा</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%B3%E3%83%B3%E3%83%87%E3%83%B3%E3%82%B5" title="コンデンサ – Japanese" lang="ja" hreflang="ja" data-title="コンデンサ" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ce mw-list-item"><a href="https://ce.wikipedia.org/wiki/%D0%AD%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%B8%D0%B9%D0%BD_%D0%BA%D0%BE%D0%BD%D0%B4%D0%B5%D0%BD%D1%81%D0%B0%D1%82%D0%BE%D1%80" title="Электрийн конденсатор – Chechen" lang="ce" hreflang="ce" data-title="Электрийн конденсатор" data-language-autonym="Нохчийн" data-language-local-name="Chechen" class="interlanguage-link-target"><span>Нохчийн</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Kondensaator" title="Kondensaator – Northern Frisian" lang="frr" hreflang="frr" data-title="Kondensaator" data-language-autonym="Nordfriisk" data-language-local-name="Northern Frisian" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Kondensator_(elektrisk)" title="Kondensator (elektrisk) – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Kondensator (elektrisk)" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Kondensator" title="Kondensator – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Kondensator" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Condensador" title="Condensador – Occitan" lang="oc" hreflang="oc" data-title="Condensador" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Kaappaasiterii" title="Kaappaasiterii – Oromo" lang="om" hreflang="om" data-title="Kaappaasiterii" data-language-autonym="Oromoo" data-language-local-name="Oromo" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Kondensator_zaryadlanishi" title="Kondensator zaryadlanishi – Uzbek" lang="uz" hreflang="uz" data-title="Kondensator zaryadlanishi" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%B8%E0%A9%B0%E0%A8%A7%E0%A8%BE%E0%A8%B0%E0%A8%BF%E0%A8%A4%E0%A8%B0" title="ਸੰਧਾਰਿਤਰ – Punjabi" lang="pa" hreflang="pa" data-title="ਸੰਧਾਰਿਤਰ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%DA%A9%DB%8C%D9%BE%DB%8C%D8%B3%DB%8C%D9%B9%D8%B1" title="کیپیسیٹر – Western Punjabi" lang="pnb" hreflang="pnb" data-title="کیپیسیٹر" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%DA%A9%D8%A7%D9%86%DA%89%D9%86%D8%B3%D8%B1" title="کانډنسر – Pashto" lang="ps" hreflang="ps" data-title="کانډنسر" data-language-autonym="پښتو" data-language-local-name="Pashto" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Kiapasita" title="Kiapasita – Jamaican Creole English" lang="jam" hreflang="jam" data-title="Kiapasita" data-language-autonym="Patois" data-language-local-name="Jamaican Creole English" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Condensator" title="Condensator – Piedmontese" lang="pms" hreflang="pms" data-title="Condensator" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Kondensater" title="Kondensater – Low German" lang="nds" hreflang="nds" data-title="Kondensater" data-language-autonym="Plattdüütsch" data-language-local-name="Low German" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Kondensator" title="Kondensator – Polish" lang="pl" hreflang="pl" data-title="Kondensator" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Capacitor" title="Capacitor – Portuguese" lang="pt" hreflang="pt" data-title="Capacitor" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Condensator_electric" title="Condensator electric – Romanian" lang="ro" hreflang="ro" data-title="Condensator electric" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D0%B4%D0%B5%D0%BD%D0%B7%D0%B0%D1%82%D0%BE%D1%80" title="Кондензатор – Rusyn" lang="rue" hreflang="rue" data-title="Кондензатор" data-language-autonym="Русиньскый" data-language-local-name="Rusyn" class="interlanguage-link-target"><span>Русиньскый</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%AD%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B8%D0%B9_%D0%BA%D0%BE%D0%BD%D0%B4%D0%B5%D0%BD%D1%81%D0%B0%D1%82%D0%BE%D1%80" title="Электрический конденсатор – Russian" lang="ru" hreflang="ru" data-title="Электрический конденсатор" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Capacitor" title="Capacitor – Scots" lang="sco" hreflang="sco" data-title="Capacitor" data-language-autonym="Scots" data-language-local-name="Scots" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-stq mw-list-item"><a href="https://stq.wikipedia.org/wiki/Kondensatore" title="Kondensatore – Saterland Frisian" lang="stq" hreflang="stq" data-title="Kondensatore" data-language-autonym="Seeltersk" data-language-local-name="Saterland Frisian" class="interlanguage-link-target"><span>Seeltersk</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Kondensatori" title="Kondensatori – Albanian" lang="sq" hreflang="sq" data-title="Kondensatori" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%B0%E0%B7%8F%E0%B6%BB%E0%B7%92%E0%B6%AD%E0%B7%8A%E2%80%8D%E0%B6%BB%E0%B6%9A" title="ධාරිත්‍රක – Sinhala" lang="si" hreflang="si" data-title="ධාරිත්‍රක" data-language-autonym="සිංහල" data-language-local-name="Sinhala" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Capacitor" title="Capacitor – Simple English" lang="en-simple" hreflang="en-simple" data-title="Capacitor" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Kondenz%C3%A1tor_(elektrotechnika)" title="Kondenzátor (elektrotechnika) – Slovak" lang="sk" hreflang="sk" data-title="Kondenzátor (elektrotechnika)" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Kondenzator" title="Kondenzator – Slovenian" lang="sl" hreflang="sl" data-title="Kondenzator" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D0%B4%D0%B5%D0%BD%D0%B7%D0%B0%D1%82%D0%BE%D1%80" title="Кондензатор – Serbian" lang="sr" hreflang="sr" data-title="Кондензатор" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Kondenzator" title="Kondenzator – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Kondenzator" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Kapasitor" title="Kapasitor – Sundanese" lang="su" hreflang="su" data-title="Kapasitor" data-language-autonym="Sunda" data-language-local-name="Sundanese" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Kondensaattori" title="Kondensaattori – Finnish" lang="fi" hreflang="fi" data-title="Kondensaattori" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Kondensator" title="Kondensator – Swedish" lang="sv" hreflang="sv" data-title="Kondensator" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Kapasitor" title="Kapasitor – Tagalog" lang="tl" hreflang="tl" data-title="Kapasitor" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AE%E0%AE%BF%E0%AE%A9%E0%AF%8D%E0%AE%A4%E0%AF%87%E0%AE%95%E0%AF%8D%E0%AE%95%E0%AE%BF" title="மின்தேக்கி – Tamil" lang="ta" hreflang="ta" data-title="மின்தேக்கி" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-shi mw-list-item"><a href="https://shi.wikipedia.org/wiki/Asguday" title="Asguday – Tachelhit" lang="shi" hreflang="shi" data-title="Asguday" data-language-autonym="Taclḥit" data-language-local-name="Tachelhit" class="interlanguage-link-target"><span>Taclḥit</span></a></li><li class="interlanguage-link interwiki-tt badge-Q17437796 badge-featuredarticle mw-list-item" title="featured article badge"><a href="https://tt.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D0%B4%D0%B5%D0%BD%D1%81%D0%B0%D1%82%D0%BE%D1%80" title="Конденсатор – Tatar" lang="tt" hreflang="tt" data-title="Конденсатор" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatar" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%95%E0%B8%B1%E0%B8%A7%E0%B9%80%E0%B8%81%E0%B9%87%E0%B8%9A%E0%B8%9B%E0%B8%A3%E0%B8%B0%E0%B8%88%E0%B8%B8" title="ตัวเก็บประจุ – Thai" lang="th" hreflang="th" data-title="ตัวเก็บประจุ" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D0%B4%D0%B5%D0%BD%D1%81%D0%B0%D1%82%D0%BE%D1%80" title="Конденсатор – Tajik" lang="tg" hreflang="tg" data-title="Конденсатор" data-language-autonym="Тоҷикӣ" data-language-local-name="Tajik" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Kondansat%C3%B6r" title="Kondansatör – Turkish" lang="tr" hreflang="tr" data-title="Kondansatör" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%95%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%B8%D1%87%D0%BD%D0%B8%D0%B9_%D0%BA%D0%BE%D0%BD%D0%B4%D0%B5%D0%BD%D1%81%D0%B0%D1%82%D0%BE%D1%80" title="Електричний конденсатор – Ukrainian" lang="uk" hreflang="uk" data-title="Електричний конденсатор" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%DA%AF%D9%86%D8%AC%D8%A7%D8%A6%D8%B4%D8%AF%D8%A7%D8%B1" title="گنجائشدار – Urdu" lang="ur" hreflang="ur" data-title="گنجائشدار" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-ug mw-list-item"><a href="https://ug.wikipedia.org/wiki/%D9%83%D9%88%D9%86%D8%AF%DB%90%D9%86%D8%B3%D8%A7%D8%AA%D9%88%D8%B1" title="كوندېنساتور – Uyghur" lang="ug" hreflang="ug" data-title="كوندېنساتور" data-language-autonym="ئۇيغۇرچە / Uyghurche" data-language-local-name="Uyghur" class="interlanguage-link-target"><span>ئۇيغۇرچە / Uyghurche</span></a></li><li class="interlanguage-link interwiki-vep mw-list-item"><a href="https://vep.wikipedia.org/wiki/Elektrokondensator" title="Elektrokondensator – Veps" lang="vep" hreflang="vep" data-title="Elektrokondensator" data-language-autonym="Vepsän kel’" data-language-local-name="Veps" class="interlanguage-link-target"><span>Vepsän kel’</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/T%E1%BB%A5_%C4%91i%E1%BB%87n" title="Tụ điện – Vietnamese" lang="vi" hreflang="vi" data-title="Tụ điện" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Kapasitor" title="Kapasitor – Waray" lang="war" hreflang="war" data-title="Kapasitor" data-language-autonym="Winaray" data-language-local-name="Waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wo mw-list-item"><a href="https://wo.wikipedia.org/wiki/Fattalukaay(mb%C3%ABj)" title="Fattalukaay(mbëj) – Wolof" lang="wo" hreflang="wo" data-title="Fattalukaay(mbëj)" data-language-autonym="Wolof" data-language-local-name="Wolof" class="interlanguage-link-target"><span>Wolof</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E7%94%B5%E5%AE%B9%E5%99%A8" title="电容器 – Wu" lang="wuu" hreflang="wuu" data-title="电容器" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%A7%D7%90%D7%A0%D7%93%D7%A2%D7%A0%D7%A1%D7%90%D7%98%D7%90%D7%A8" title="קאנדענסאטאר – Yiddish" lang="yi" hreflang="yi" data-title="קאנדענסאטאר" data-language-autonym="ייִדיש" data-language-local-name="Yiddish" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E9%9B%BB%E5%AE%B9%E5%99%A8" title="電容器 – Cantonese" lang="yue" hreflang="yue" data-title="電容器" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Kondensatuorios" title="Kondensatuorios – Samogitian" lang="sgs" hreflang="sgs" data-title="Kondensatuorios" data-language-autonym="Žemaitėška" data-language-local-name="Samogitian" class="interlanguage-link-target"><span>Žemaitėška</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%94%B5%E5%AE%B9%E5%99%A8" title="电容器 – Chinese" lang="zh" hreflang="zh" data-title="电容器" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q5322#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespaces"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Capacitor" title="View the content page [c]" accesskey="c"><span>Article</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Talk:Capacitor" rel="discussion" title="Discuss improvements to the content page [t]" accesskey="t"><span>Talk</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Change language variant" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">English</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Views"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Capacitor"><span>Read</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Capacitor&action=edit" title="Edit this page [e]" accesskey="e"><span>Edit</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Capacitor&action=history" title="Past revisions of this page [h]" accesskey="h"><span>View history</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Tools" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Tools</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Tools</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">hide</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="More options" > <div class="vector-menu-heading"> Actions </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Capacitor"><span>Read</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Capacitor&action=edit" title="Edit this page [e]" accesskey="e"><span>Edit</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Capacitor&action=history"><span>View history</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> General </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Special:WhatLinksHere/Capacitor" title="List of all English Wikipedia pages containing links to this page [j]" accesskey="j"><span>What links here</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Special:RecentChangesLinked/Capacitor" rel="nofollow" title="Recent changes in pages linked from this page [k]" accesskey="k"><span>Related changes</span></a></li><li id="t-upload" class="mw-list-item"><a href="//en.wikipedia.org/wiki/Wikipedia:File_Upload_Wizard" title="Upload files [u]" accesskey="u"><span>Upload file</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Capacitor&oldid=1281636495" title="Permanent link to this revision of this page"><span>Permanent link</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Capacitor&action=info" title="More information about this page"><span>Page information</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Special:CiteThisPage&page=Capacitor&id=1281636495&wpFormIdentifier=titleform" title="Information on how to cite this page"><span>Cite this page</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Special:UrlShortener&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FCapacitor"><span>Get shortened URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Special:QrCode&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FCapacitor"><span>Download QR code</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Print/export </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Special:DownloadAsPdf&page=Capacitor&action=show-download-screen" title="Download this page as a PDF file"><span>Download as PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Capacitor&printable=yes" title="Printable version of this page [p]" accesskey="p"><span>Printable version</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> In other projects </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Capacitor" hreflang="en"><span>Wikimedia Commons</span></a></li><li class="wb-otherproject-link wb-otherproject-wikibooks mw-list-item"><a href="https://en.wikibooks.org/wiki/A-level_Physics_(Advancing_Physics)/Capacitors" hreflang="en"><span>Wikibooks</span></a></li><li class="wb-otherproject-link wb-otherproject-wikiversity mw-list-item"><a href="https://en.wikiversity.org/wiki/Electronics/Capacitors" hreflang="en"><span>Wikiversity</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q5322" title="Structured data on this page hosted by Wikidata [g]" accesskey="g"><span>Wikidata item</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Appearance</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">hide</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Passive two-terminal electronic component that stores electrical energy in an electric field</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">This article is about the electronic component. For the physical phenomenon, see <a href="/wiki/Capacitance" title="Capacitance">Capacitance</a>. For an overview of types, see <a href="/wiki/Capacitor_types" title="Capacitor types">Capacitor types</a>.</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">"Capacitive" redirects here. For the term used when referring to touchscreens, see <a href="/wiki/Capacitive_sensing" title="Capacitive sensing">Capacitive sensing</a>.</div> <p class="mw-empty-elt"> </p> <style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox"><caption class="infobox-title">Capacitor</caption><tbody><tr><td colspan="2" class="infobox-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:Capacitors_(7189597135).jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Capacitors_%287189597135%29.jpg/220px-Capacitors_%287189597135%29.jpg" decoding="async" width="220" height="147" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Capacitors_%287189597135%29.jpg/330px-Capacitors_%287189597135%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Capacitors_%287189597135%29.jpg/440px-Capacitors_%287189597135%29.jpg 2x" data-file-width="1500" data-file-height="1000" /></a></span></td></tr><tr><th scope="row" class="infobox-label">Type</th><td class="infobox-data"><a href="/wiki/Passivity_(engineering)" title="Passivity (engineering)">Passive</a></td></tr><tr><th scope="row" class="infobox-label"><span class="nowrap">Working principle<span style="visibility:hidden; color:transparent; padding-left:2px">‍</span></span></th><td class="infobox-data"><a href="/wiki/Capacitance" title="Capacitance">Capacitance</a></td></tr><tr><th scope="row" class="infobox-label">Inventor</th><td class="infobox-data"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style><div class="plainlist"><ul><li><a href="/wiki/Ewald_Georg_von_Kleist" title="Ewald Georg von Kleist">Ewald Georg von Kleist</a></li><li><a href="/wiki/Pieter_van_Musschenbroek" title="Pieter van Musschenbroek">Pieter van Musschenbroek</a></li></ul></div></td></tr><tr><th scope="row" class="infobox-label">Invention year</th><td class="infobox-data">1745<span class="noprint">; 280 years ago</span><span style="display:none"> (<span class="bday dtstart published updated">1745</span>)</span></td></tr><tr><th scope="row" class="infobox-label">Number of <a href="/wiki/Terminal_(electronics)" title="Terminal (electronics)">terminals</a></th><td class="infobox-data">2</td></tr><tr><th colspan="2" class="infobox-header"><a href="/wiki/Electronic_symbol" title="Electronic symbol">Electronic symbol</a></th></tr><tr><td colspan="2" class="infobox-full-data"><div class="skin-invert-image"><span class="skin-invert-image" typeof="mw:File"><a href="/wiki/File:Types_of_capacitor.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Types_of_capacitor.svg/230px-Types_of_capacitor.svg.png" decoding="async" width="230" height="106" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Types_of_capacitor.svg/345px-Types_of_capacitor.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Types_of_capacitor.svg/460px-Types_of_capacitor.svg.png 2x" data-file-width="489" data-file-height="226" /></a></span></div></td></tr></tbody></table> <p>In <a href="/wiki/Electrical_engineering" title="Electrical engineering">electrical engineering</a>, a <b>capacitor</b> is a device that stores <a href="/wiki/Electrical_energy" title="Electrical energy">electrical energy</a> by accumulating <a href="/wiki/Electric_charge" title="Electric charge">electric charges</a> on two closely spaced surfaces that are insulated from each other. The capacitor was originally known as the <b>condenser</b>,<sup id="cite_ref-duff_1-0" class="reference"><a href="#cite_note-duff-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> a term still encountered in a few compound names, such as the <i><a href="/wiki/Condenser_microphone" class="mw-redirect" title="Condenser microphone">condenser microphone</a></i>. It is a <a href="/wiki/Passivity_(engineering)" title="Passivity (engineering)">passive</a> <a href="/wiki/Electronic_component" title="Electronic component">electronic component</a> with two <a href="/wiki/Terminal_(electronics)" title="Terminal (electronics)">terminals</a>. </p><p>The utility of a capacitor depends on its <a href="/wiki/Capacitance" title="Capacitance">capacitance</a>. While some capacitance exists between any two electrical conductors in proximity in a <a href="/wiki/Electric_circuit" class="mw-redirect" title="Electric circuit">circuit</a>, a capacitor is a component designed specifically to add capacitance to some part of the circuit. </p><p>The physical form and construction of practical capacitors vary widely and many <a href="/wiki/Capacitor_types" title="Capacitor types">types of capacitor</a> are in common use. Most capacitors contain at least two <a href="/wiki/Electrical_conductor" title="Electrical conductor">electrical conductors</a>, often in the form of metallic plates or surfaces separated by a <a href="/wiki/Dielectric" title="Dielectric">dielectric</a> medium. A conductor may be a foil, thin film, <a href="/wiki/Sintered" class="mw-redirect" title="Sintered">sintered</a> bead of metal, or an <a href="/wiki/Electrolyte" title="Electrolyte">electrolyte</a>. The nonconducting dielectric acts to increase the capacitor's charge capacity. Materials commonly used as dielectrics include <a href="/wiki/Glass" title="Glass">glass</a>, <a href="/wiki/Ceramic" title="Ceramic">ceramic</a>, <a href="/wiki/Plastic_film" title="Plastic film">plastic film</a>, <a href="/wiki/Paper" title="Paper">paper</a>, <a href="/wiki/Mica" title="Mica">mica</a>, air, and <a href="/wiki/Oxide" title="Oxide">oxide layers</a>. When an <a href="/wiki/Electric_potential" title="Electric potential">electric potential</a> difference (a <a href="/wiki/Voltage" title="Voltage">voltage</a>) is applied across the terminals of a capacitor, for example when a capacitor is connected across a battery, an <a href="/wiki/Electric_field" title="Electric field">electric field</a> develops across the dielectric, causing a net positive <a href="/wiki/Electric_charge" title="Electric charge">charge</a> to collect on one plate and net negative charge to collect on the other plate. No current actually flows through a <a href="/wiki/Perfect_dielectric" class="mw-redirect" title="Perfect dielectric">perfect dielectric</a>. However, there is a flow of charge through the source circuit. If the condition is maintained sufficiently long, the current through the source circuit ceases. If a time-varying voltage is applied across the leads of the capacitor, the source experiences an ongoing current due to the charging and discharging cycles of the capacitor. </p><p>Capacitors are widely used as parts of <a href="/wiki/Electrical_circuit" class="mw-redirect" title="Electrical circuit">electrical circuits</a> in many common electrical devices. Unlike a <a href="/wiki/Resistor" title="Resistor">resistor</a>, an ideal capacitor does not dissipate energy, although real-life capacitors do dissipate a small amount (see <a href="#Non-ideal_behavior">Non-ideal behavior</a>). </p><p>The earliest forms of capacitors were created in the 1740s, when European experimenters discovered that electric charge could be stored in water-filled glass jars that came to be known as <a href="/wiki/Leyden_jar" title="Leyden jar">Leyden jars</a>. Today, capacitors are widely used in <a href="/wiki/Electronic_circuit" title="Electronic circuit">electronic circuits</a> for blocking <a href="/wiki/Direct_current" title="Direct current">direct current</a> while allowing <a href="/wiki/Alternating_current" title="Alternating current">alternating current</a> to pass. In <a href="/wiki/Analog_filter" class="mw-redirect" title="Analog filter">analog filter</a> networks, they smooth the output of <a href="/wiki/Power_supply" title="Power supply">power supplies</a>. In <a href="/wiki/LC_circuit" title="LC circuit">resonant circuits</a> they tune <a href="/wiki/Radio" title="Radio">radios</a> to particular <a href="/wiki/Frequency" title="Frequency">frequencies</a>. In <a href="/wiki/Electric_power_transmission" title="Electric power transmission">electric power transmission</a> systems, they stabilize voltage and power flow.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> The property of energy storage in capacitors was exploited as dynamic memory in early digital computers,<sup id="cite_ref-floyd_3-0" class="reference"><a href="#cite_note-floyd-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> and still is in modern <a href="/wiki/DRAM" class="mw-redirect" title="DRAM">DRAM</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=1" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Leyden_jar" title="Leyden jar">Leyden jar</a></div> <p>Natural capacitors have existed since prehistoric times. The most common example of natural capacitance are the static charges accumulated between clouds in the sky and the surface of the Earth, where the air between them serves as the dielectric. This results in bolts of <a href="/wiki/Lightning" title="Lightning">lightning</a> when the breakdown voltage of the air is exceeded.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Leidse_flessen_Museum_Boerhave_december_2003_2.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Leidse_flessen_Museum_Boerhave_december_2003_2.jpg/180px-Leidse_flessen_Museum_Boerhave_december_2003_2.jpg" decoding="async" width="180" height="240" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Leidse_flessen_Museum_Boerhave_december_2003_2.jpg/270px-Leidse_flessen_Museum_Boerhave_december_2003_2.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/22/Leidse_flessen_Museum_Boerhave_december_2003_2.jpg/360px-Leidse_flessen_Museum_Boerhave_december_2003_2.jpg 2x" data-file-width="400" data-file-height="533" /></a><figcaption>Battery of four <a href="/wiki/Leyden_jar" title="Leyden jar">Leyden jars</a> in <a href="/wiki/Museum_Boerhaave" title="Museum Boerhaave">Museum Boerhaave</a>, <a href="/wiki/Leiden" title="Leiden">Leiden</a>, the <a href="/wiki/Netherlands" title="Netherlands">Netherlands</a></figcaption></figure> <p>In October 1745, <a href="/wiki/Ewald_Georg_von_Kleist" title="Ewald Georg von Kleist">Ewald Georg von Kleist</a> of <a href="/wiki/Pomerania" title="Pomerania">Pomerania</a>, Germany, found that <a href="/wiki/Electric_charge" title="Electric charge">charge</a> could be stored by connecting a high-voltage <a href="/wiki/Electrostatic_generator" title="Electrostatic generator">electrostatic generator</a> by a wire to a volume of water in a hand-held glass jar.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Von Kleist's hand and the water acted as conductors and the jar as a <a href="/wiki/Dielectric" title="Dielectric">dielectric</a> (although details of the mechanism were incorrectly identified at the time). Von Kleist found that touching the wire resulted in a powerful spark, much more painful than that obtained from an electrostatic machine. The following year, the Dutch physicist <a href="/wiki/Pieter_van_Musschenbroek" title="Pieter van Musschenbroek">Pieter van Musschenbroek</a> invented a similar capacitor, which was named the <a href="/wiki/Leyden_jar" title="Leyden jar">Leyden jar</a>, after the <a href="/wiki/Leiden_University" title="Leiden University">University of Leiden</a> where he worked.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> He also was impressed by the power of the shock he received, writing, "I would not take a second shock for the kingdom of France."<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Daniel_Gralath" title="Daniel Gralath">Daniel Gralath</a> was the first to combine several jars in parallel to increase the charge storage capacity.<sup id="cite_ref-Benjamin1895_8-0" class="reference"><a href="#cite_note-Benjamin1895-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Benjamin_Franklin" title="Benjamin Franklin">Benjamin Franklin</a> investigated the <a href="/wiki/Leyden_jar" title="Leyden jar">Leyden jar</a> and came to the conclusion that the charge was stored on the glass, not in the water as others had assumed. He also adopted the term "battery",<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> (denoting the increase of power with a row of similar units as in a <a href="/wiki/Artillery_battery" title="Artillery battery">battery of cannon</a>), subsequently applied to <a href="/wiki/Battery_(electricity)" class="mw-redirect" title="Battery (electricity)">clusters of electrochemical cells</a>.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> In 1747, Leyden jars were made by coating the inside and outside of jars with metal foil, leaving a space at the mouth to prevent arcing between the foils.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> The earliest unit of capacitance was the <a href="/wiki/Jar_(unit)" title="Jar (unit)">jar</a>, equivalent to about 1.11 <a href="/wiki/Farad#Definition" title="Farad">nanofarads</a>.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p><p>Leyden jars or more powerful devices employing flat glass plates alternating with foil conductors were used exclusively up until about 1900, when the invention of <a href="/wiki/Wireless_telegraphy" title="Wireless telegraphy">wireless</a> (<a href="/wiki/Radio" title="Radio">radio</a>) created a demand for standard capacitors, and the steady move to higher <a href="/wiki/Frequency" title="Frequency">frequencies</a> required capacitors with lower <a href="/wiki/Inductance" title="Inductance">inductance</a>. More compact construction methods began to be used, such as a flexible dielectric sheet (like oiled paper) sandwiched between sheets of metal foil, rolled or folded into a small package. </p><p><span class="anchor" id="Condenser"></span> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Radio_Times_-_1923-12-28_-_page_39_-_Dubilier.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/5/57/Radio_Times_-_1923-12-28_-_page_39_-_Dubilier.png" decoding="async" width="255" height="518" class="mw-file-element" data-file-width="255" data-file-height="518" /></a><figcaption>Advert from the 28 December 1923 edition of <a href="/wiki/The_Radio_Times" class="mw-redirect" title="The Radio Times">The Radio Times</a> for Dubilier condensers, for use in wireless receiving sets</figcaption></figure> <p>Early capacitors were known as <i>condensers</i>, a term that is still occasionally used today, particularly in high power applications, such as automotive systems. The term <i>condensatore</i> was used by <a href="/wiki/Alessandro_Volta" title="Alessandro Volta">Alessandro Volta</a> in 1780 to refer to a device, similar to his <a href="/wiki/Electrophorus" title="Electrophorus">electrophorus</a>, he developed to measure electricity, and translated in 1782 as <i>condenser</i>,<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> where the name referred to the device's ability to store a higher density of electric charge than was possible with an isolated conductor.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-duff_1-1" class="reference"><a href="#cite_note-duff-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> The term became deprecated because of the ambiguous meaning of <a href="/wiki/Steam_condenser" class="mw-redirect" title="Steam condenser">steam condenser</a>, with <i>capacitor</i> becoming the recommended term in the UK from 1926,<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> while the change occurred considerably later in the United States. </p><p>Since the beginning of the study of <a href="/wiki/Electricity" title="Electricity">electricity</a>, non-conductive materials like <a href="/wiki/Glass" title="Glass">glass</a>, <a href="/wiki/Porcelain" title="Porcelain">porcelain</a>, <a href="/wiki/Paper" title="Paper">paper</a> and <a href="/wiki/Mica" title="Mica">mica</a> have been used as <a href="/wiki/Insulator_(electricity)" title="Insulator (electricity)">insulators</a>. Decades later, these materials were also well-suited for use as the dielectric for the first capacitors. Paper capacitors, made by sandwiching a strip of impregnated paper between strips of metal and rolling the result into a cylinder, were commonly used in the late 19th century; their manufacture started in 1876,<sup id="cite_ref-Boggs_17-0" class="reference"><a href="#cite_note-Boggs-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> and they were used from the early 20th century as <a href="/wiki/Decoupling_capacitor" title="Decoupling capacitor">decoupling capacitors</a> in <a href="/wiki/Telephony" title="Telephony">telephony</a>. </p><p>Porcelain was used in the first <a href="/wiki/Ceramic_capacitor" title="Ceramic capacitor">ceramic capacitors</a>. In the early years of <a href="/wiki/Marconi" class="mw-redirect" title="Marconi">Marconi</a>'s wireless transmitting apparatus, porcelain capacitors were used for high voltage and high frequency application in the <a href="/wiki/Transmitter" title="Transmitter">transmitters</a>. On the receiver side, smaller <a href="/wiki/Silver_mica_capacitor" title="Silver mica capacitor">mica capacitors</a> were used for <a href="/wiki/LC_circuit" title="LC circuit">resonant circuits</a>. Mica capacitors were invented in 1909 by William Dubilier. Prior to World War II, mica was the most common dielectric for capacitors in the United States.<sup id="cite_ref-Boggs_17-1" class="reference"><a href="#cite_note-Boggs-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p><p>Charles Pollak (born <a href="/wiki/Karol_Pollak" title="Karol Pollak">Karol Pollak</a>), the inventor of the first <a href="/wiki/Electrolytic_capacitor" title="Electrolytic capacitor">electrolytic capacitors</a>, found out that the oxide layer on an aluminum anode remained stable in a neutral or alkaline <a href="/wiki/Electrolyte" title="Electrolyte">electrolyte</a>, even when the power was switched off. In 1896 he was granted U.S. Patent No. 672,913 for an "Electric liquid capacitor with aluminum electrodes". Solid electrolyte <a href="/wiki/Tantalum_capacitor" title="Tantalum capacitor">tantalum capacitors</a> were invented by <a href="/wiki/Bell_Laboratories" class="mw-redirect" title="Bell Laboratories">Bell Laboratories</a> in the early 1950s as a miniaturized and more reliable low-voltage support capacitor to complement their newly invented <a href="/wiki/Transistor" title="Transistor">transistor</a>. </p><p>With the development of plastic materials by organic chemists during the <a href="/wiki/Second_World_War" class="mw-redirect" title="Second World War">Second World War</a>, the capacitor industry began to replace paper with thinner polymer films. One very early development in <a href="/wiki/Film_capacitor" title="Film capacitor">film capacitors</a> was described in British Patent 587,953 in 1944.<sup id="cite_ref-Boggs_17-2" class="reference"><a href="#cite_note-Boggs-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p><p>Electric double-layer capacitors (now <a href="/wiki/Supercapacitor" title="Supercapacitor">supercapacitors</a>) were invented in 1957 when H. Becker developed a "Low voltage electrolytic capacitor with porous carbon electrodes".<sup id="cite_ref-Boggs_17-3" class="reference"><a href="#cite_note-Boggs-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> He believed that the energy was stored as a charge in the carbon pores used in his capacitor as in the pores of the etched foils of electrolytic capacitors. Because the double layer mechanism was not known by him at the time, he wrote in the patent: "It is not known exactly what is taking place in the component if it is used for energy storage, but it leads to an extremely high capacity." </p><p>The MOS capacitor was later widely adopted as a storage capacitor in <a href="/wiki/Memory_chip" class="mw-redirect" title="Memory chip">memory chips</a>, and as the basic building block of the <a href="/wiki/Charge-coupled_device" title="Charge-coupled device">charge-coupled device</a> (CCD) in <a href="/wiki/Image_sensor" title="Image sensor">image sensor</a> technology.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> In 1966, Dr. <a href="/wiki/Robert_Dennard" class="mw-redirect" title="Robert Dennard">Robert Dennard</a> invented modern DRAM architecture, combining a single MOS transistor per capacitor.<sup id="cite_ref-ibm100_21-0" class="reference"><a href="#cite_note-ibm100-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Theory_of_operation">Theory of operation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=2" title="Edit section: Theory of operation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Capacitance" title="Capacitance">Capacitance</a></div> <div class="mw-heading mw-heading3"><h3 id="Overview">Overview</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=3" title="Edit section: Overview"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size skin-invert-image" typeof="mw:File/Thumb"><a href="/wiki/File:Capacitor_schematic_with_dielectric.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Capacitor_schematic_with_dielectric.svg/180px-Capacitor_schematic_with_dielectric.svg.png" decoding="async" width="180" height="198" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Capacitor_schematic_with_dielectric.svg/270px-Capacitor_schematic_with_dielectric.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Capacitor_schematic_with_dielectric.svg/360px-Capacitor_schematic_with_dielectric.svg.png 2x" data-file-width="430" data-file-height="473" /></a><figcaption>Charge separation in a parallel-plate capacitor causes an internal electric field. A dielectric (orange) reduces the field and increases the capacitance.</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Plattenkondensator_hg.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d3/Plattenkondensator_hg.jpg/180px-Plattenkondensator_hg.jpg" decoding="async" width="180" height="152" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d3/Plattenkondensator_hg.jpg/270px-Plattenkondensator_hg.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d3/Plattenkondensator_hg.jpg/360px-Plattenkondensator_hg.jpg 2x" data-file-width="2168" data-file-height="1828" /></a><figcaption>A simple demonstration capacitor made of two parallel metal plates, using an air gap as the dielectric</figcaption></figure> <p>A capacitor consists of two <a href="/wiki/Electrical_conductor" title="Electrical conductor">conductors</a> separated by a non-conductive region.<sup id="cite_ref-FOOTNOTEUlaby1999168_23-0" class="reference"><a href="#cite_note-FOOTNOTEUlaby1999168-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> The non-conductive region can either be a <a href="/wiki/Vacuum" title="Vacuum">vacuum</a> or an electrical insulator material known as a <a href="/wiki/Dielectric" title="Dielectric">dielectric</a>. Examples of dielectric media are glass, air, paper, plastic, ceramic, and even a <a href="/wiki/Semiconductor" title="Semiconductor">semiconductor</a> <a href="/wiki/Depletion_region" title="Depletion region">depletion region</a> chemically identical to the conductors. From <a href="/wiki/Coulomb%27s_law" title="Coulomb's law">Coulomb's law</a> a charge on one conductor will exert a force on the <a href="/wiki/Charge_carrier" title="Charge carrier">charge carriers</a> within the other conductor, attracting opposite polarity charge and repelling like polarity charges, thus an opposite polarity charge will be induced on the surface of the other conductor. The conductors thus hold equal and opposite charges on their facing surfaces,<sup id="cite_ref-FOOTNOTEUlaby1999157_24-0" class="reference"><a href="#cite_note-FOOTNOTEUlaby1999157-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> and the dielectric develops an electric field. </p><p>An ideal capacitor is characterized by a constant <a href="/wiki/Capacitance" title="Capacitance">capacitance</a> <i>C</i>, in <a href="/wiki/Farad" title="Farad">farads</a> in the <a href="/wiki/SI" class="mw-redirect" title="SI">SI</a> system of units, defined as the ratio of the positive or negative charge <i>Q</i> on each conductor to the voltage <i>V</i> between them:<sup id="cite_ref-FOOTNOTEUlaby1999168_23-1" class="reference"><a href="#cite_note-FOOTNOTEUlaby1999168-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C={\frac {Q}{V}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>Q</mi> <mi>V</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C={\frac {Q}{V}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/69c105c2c94d7e78f0556c93c3632186ec717d89" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:7.539ex; height:5.509ex;" alt="{\displaystyle C={\frac {Q}{V}}}" /></span> A capacitance of one <a href="/wiki/Farad" title="Farad">farad</a> (F) means that one <a href="/wiki/Coulomb" title="Coulomb">coulomb</a> of charge on each conductor causes a voltage of one <a href="/wiki/Volt" title="Volt">volt</a> across the device.<sup id="cite_ref-FOOTNOTEUlaby199969_25-0" class="reference"><a href="#cite_note-FOOTNOTEUlaby199969-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> Because the conductors (or plates) are close together, the opposite charges on the conductors attract one another due to their electric fields, allowing the capacitor to store more charge for a given voltage than when the conductors are separated, yielding a larger capacitance. </p><p>In practical devices, charge build-up sometimes affects the capacitor mechanically, causing its capacitance to vary. In this case, capacitance is defined in terms of incremental changes: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C={\frac {\mathrm {d} Q}{\mathrm {d} V}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>Q</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>V</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C={\frac {\mathrm {d} Q}{\mathrm {d} V}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d7dc78cc4edfe43ba739c59f62796c1a3c3240c8" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:8.832ex; height:5.509ex;" alt="{\displaystyle C={\frac {\mathrm {d} Q}{\mathrm {d} V}}}" /></span> </p> <div class="mw-heading mw-heading3"><h3 id="Hydraulic_analogy">Hydraulic analogy</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=4" title="Edit section: Hydraulic analogy"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Capacitor-animation.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/94/Capacitor-animation.gif/250px-Capacitor-animation.gif" decoding="async" width="220" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/94/Capacitor-animation.gif/330px-Capacitor-animation.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/94/Capacitor-animation.gif/500px-Capacitor-animation.gif 2x" data-file-width="1200" data-file-height="220" /></a><figcaption>In the <a href="/wiki/Hydraulic_analogy" title="Hydraulic analogy">hydraulic analogy</a>, a capacitor is analogous to an elastic diaphragm within a pipe. This animation shows a diaphragm being stretched and un-stretched, which is analogous to a capacitor being charged and discharged.</figcaption></figure> <p>In the <a href="/wiki/Hydraulic_analogy" title="Hydraulic analogy">hydraulic analogy</a>, voltage is analogous to water pressure and electrical current through a wire is analogous to water flow through a pipe. A capacitor is like an elastic diaphragm within the pipe. Although water cannot pass through the diaphragm, it moves as the diaphragm stretches or un-stretches. </p> <ul><li>Capacitance is analogous to diaphragm <a href="/wiki/Elasticity_(physics)" title="Elasticity (physics)">elasticity</a>. In the same way that the ratio of charge differential to voltage would be greater for a larger capacitance value (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C=Q/V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mo>=</mo> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C=Q/V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/865af670ac05c87761922dc6685480d11f616622" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.653ex; height:2.843ex;" alt="{\displaystyle C=Q/V}" /></span>), the ratio of water displacement to pressure would be greater for a diaphragm that flexes more readily.</li> <li>In an AC circuit, a capacitor behaves like a diaphragm in a pipe, allowing the charge to move on both sides of the dielectric while no electrons actually pass through. For DC circuits, a capacitor is analogous to a <a href="/wiki/Hydraulic_accumulator" title="Hydraulic accumulator">hydraulic accumulator</a>, storing the energy until pressure is released. Similarly, they can be used to smooth the flow of electricity in <a href="/wiki/Rectifier" title="Rectifier">rectified</a> DC circuits in the same way an accumulator damps surges from a hydraulic pump.</li> <li>Charged capacitors and stretched diaphragms both store <a href="/wiki/Potential_energy" title="Potential energy">potential energy</a>. The more a capacitor is charged, the higher the voltage across the plates (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V=Q/C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo>=</mo> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V=Q/C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6cdd8702406140ef98d434fbf6d86771d133e1f7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.653ex; height:2.843ex;" alt="{\displaystyle V=Q/C}" /></span>). Likewise, the greater the displaced water volume, the greater the elastic potential energy.</li> <li>Electrical current affects the charge differential across a capacitor just as the flow of water affects the volume differential across a diaphragm.</li> <li>Just as capacitors experience <a href="/wiki/Dielectric_breakdown" class="mw-redirect" title="Dielectric breakdown">dielectric breakdown</a> when subjected to high voltages, diaphragms burst under extreme pressures.</li> <li>Just as capacitors block DC while passing AC, diaphragms displace no water unless there is a change in pressure.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Circuit_equivalence_at_short-time_limit_and_long-time_limit">Circuit equivalence at short-time limit and long-time limit</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=5" title="Edit section: Circuit equivalence at short-time limit and long-time limit"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In a circuit, a capacitor can behave differently at different time instants. However, it is usually easy to think about the short-time limit and long-time limit: </p> <ul><li>In the long-time limit, after the charging/discharging current has saturated the capacitor, no current would come into (or get out of) either side of the capacitor; Therefore, the long-time equivalence of capacitor is an open circuit.</li> <li>In the short-time limit, if the capacitor starts with a certain voltage V, since the voltage drop on the capacitor is known at this instant, we can replace it with an ideal voltage source of voltage V. Specifically, if V=0 (capacitor is uncharged), the short-time equivalence of a capacitor is a short circuit.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Parallel-plate_capacitor">Parallel-plate capacitor</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=6" title="Edit section: Parallel-plate capacitor"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size skin-invert-image" typeof="mw:File/Thumb"><a href="/wiki/File:Parallel_plate_capacitor.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/Parallel_plate_capacitor.svg/250px-Parallel_plate_capacitor.svg.png" decoding="async" width="180" height="144" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/Parallel_plate_capacitor.svg/270px-Parallel_plate_capacitor.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/35/Parallel_plate_capacitor.svg/360px-Parallel_plate_capacitor.svg.png 2x" data-file-width="250" data-file-height="200" /></a><figcaption>Parallel plate capacitor model consists of two conducting plates, each of area <i>A</i>, separated by a gap of thickness <i>d</i> containing a dielectric.</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Big_SMD_capacitor_2.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/29/Big_SMD_capacitor_2.jpg/180px-Big_SMD_capacitor_2.jpg" decoding="async" width="180" height="131" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/29/Big_SMD_capacitor_2.jpg/270px-Big_SMD_capacitor_2.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/29/Big_SMD_capacitor_2.jpg/360px-Big_SMD_capacitor_2.jpg 2x" data-file-width="3292" data-file-height="2404" /></a><figcaption>A surface-mount capacitor. The plates, not visible, are layered horizontally between ceramic dielectric layers, and connect alternately to either end-cap, which are visible.</figcaption></figure> <p>The simplest model of a capacitor consists of two thin parallel conductive plates each with an area of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" /></span> separated by a uniform gap of thickness <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e85ff03cbe0c7341af6b982e47e9f90d235c66ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.216ex; height:2.176ex;" alt="{\displaystyle d}" /></span> filled with a dielectric of <a href="/wiki/Permittivity" title="Permittivity">permittivity</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varepsilon }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ε</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varepsilon }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a30c89172e5b88edbd45d3e2772c7f5e562e5173" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.083ex; height:1.676ex;" alt="{\displaystyle \varepsilon }" /></span>. It is assumed the gap <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e85ff03cbe0c7341af6b982e47e9f90d235c66ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.216ex; height:2.176ex;" alt="{\displaystyle d}" /></span> is much smaller than the dimensions of the plates. This model applies well to many practical capacitors which are constructed of metal sheets separated by a thin layer of insulating dielectric, since manufacturers try to keep the dielectric very uniform in thickness to avoid thin spots which can cause failure of the capacitor. </p><p>Since the separation between the plates is uniform over the plate area, the electric field between the plates <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}" /></span> is constant, and directed perpendicularly to the plate surface, except for an area near the edges of the plates where the field decreases because the electric field lines "bulge" out of the sides of the capacitor. This "fringing field" area is approximately the same width as the plate separation, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e85ff03cbe0c7341af6b982e47e9f90d235c66ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.216ex; height:2.176ex;" alt="{\displaystyle d}" /></span>, and assuming <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e85ff03cbe0c7341af6b982e47e9f90d235c66ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.216ex; height:2.176ex;" alt="{\displaystyle d}" /></span> is small compared to the plate dimensions, it is small enough to be ignored. Therefore, if a charge of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle +Q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>+</mo> <mi>Q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle +Q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/50207f58f170206fc2b7f7117b09c91b36d9cd26" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.646ex; height:2.509ex;" alt="{\displaystyle +Q}" /></span> is placed on one plate and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -Q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mi>Q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -Q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3ff459062914e488a99e0f453ee6fe6b1315a34d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.646ex; height:2.509ex;" alt="{\displaystyle -Q}" /></span> on the other plate (the situation for unevenly charged plates is discussed below), the charge on each plate will be spread evenly in a <a href="/wiki/Surface_charge#Conductors" title="Surface charge">surface charge</a> layer of constant <a href="/wiki/Charge_density" title="Charge density">charge density</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma =\pm Q/A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>σ</mi> <mo>=</mo> <mo>±</mo> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma =\pm Q/A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1939061b8487aa1be2eb3153f07ca2e3bb966a87" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.98ex; height:2.843ex;" alt="{\displaystyle \sigma =\pm Q/A}" /></span> coulombs per square meter, on the inside surface of each plate. From <a href="/wiki/Gauss%27s_law" title="Gauss's law">Gauss's law</a> the magnitude of the electric field between the plates is <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E=\sigma /\varepsilon }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>ε</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=\sigma /\varepsilon }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a457d458a637415f8b6fd47bf32fd0b3105c9cc0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.45ex; height:2.843ex;" alt="{\displaystyle E=\sigma /\varepsilon }" /></span>. The voltage(difference) <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}" /></span> between the plates is defined as the <a href="/wiki/Line_integral" title="Line integral">line integral</a> of the electric field over a line (in the z-direction) from one plate to another <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V=\int _{0}^{d}E(z)\,\mathrm {d} z=Ed={\frac {\sigma }{\varepsilon }}d={\frac {Qd}{\varepsilon A}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> </mrow> </msubsup> <mi>E</mi> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>z</mi> <mo>=</mo> <mi>E</mi> <mi>d</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>σ</mi> <mi>ε</mi> </mfrac> </mrow> <mi>d</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>Q</mi> <mi>d</mi> </mrow> <mrow> <mi>ε</mi> <mi>A</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V=\int _{0}^{d}E(z)\,\mathrm {d} z=Ed={\frac {\sigma }{\varepsilon }}d={\frac {Qd}{\varepsilon A}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5757f0216de0316500783c2e9f9c252a123bd21f" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:35.829ex; height:6.343ex;" alt="{\displaystyle V=\int _{0}^{d}E(z)\,\mathrm {d} z=Ed={\frac {\sigma }{\varepsilon }}d={\frac {Qd}{\varepsilon A}}}" /></span> The capacitance is defined as <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C=Q/V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mo>=</mo> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C=Q/V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/865af670ac05c87761922dc6685480d11f616622" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.653ex; height:2.843ex;" alt="{\displaystyle C=Q/V}" /></span>. Substituting <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}" /></span> above into this equation </p> <div class="equation-box" style="margin: 0 0 0 1.6em;padding: 5px; border-width:1px; border-style: solid; border-color: black; color: inherit;text-align: center; display: table"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C={\frac {\varepsilon A}{d}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>ε</mi> <mi>A</mi> </mrow> <mi>d</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C={\frac {\varepsilon A}{d}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/322c7f05d61cb28486028820649f631f3587e342" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:8.528ex; height:5.509ex;" alt="{\displaystyle C={\frac {\varepsilon A}{d}}}" /></span> </p> </div> <p>Therefore, in a capacitor the highest capacitance is achieved with a high <a href="/wiki/Permittivity" title="Permittivity">permittivity</a> dielectric material, large plate area, and small separation between the plates. </p><p>Since the area <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" /></span> of the plates increases with the square of the linear dimensions and the separation <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e85ff03cbe0c7341af6b982e47e9f90d235c66ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.216ex; height:2.176ex;" alt="{\displaystyle d}" /></span> increases linearly, the capacitance scales with the linear dimension of a capacitor (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C\varpropto L}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mo>∝</mo> <mi>L</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C\varpropto L}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8e79c1460da8bb069d12b5593f9b9f35150af217" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.448ex; height:2.176ex;" alt="{\displaystyle C\varpropto L}" /></span>), or as the cube root of the volume. </p><p>A parallel plate capacitor can only store a finite amount of energy before <a href="/wiki/Dielectric_breakdown" class="mw-redirect" title="Dielectric breakdown">dielectric breakdown</a> occurs. The capacitor's dielectric material has a <a href="/wiki/Dielectric_strength" title="Dielectric strength">dielectric strength</a> <i>U</i><sub>d</sub> which sets the <a class="mw-selflink-fragment" href="#Breakdown_voltage">capacitor's breakdown voltage</a> at <span class="texhtml"><i>V</i> = <i>V</i><sub>bd</sub> = <i>U</i><sub>d</sub><i>d</i></span>. The maximum energy that the capacitor can store is therefore <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E={\frac {1}{2}}CV^{2}={\frac {1}{2}}{\frac {\varepsilon A}{d}}\left(U_{d}d\right)^{2}={\frac {1}{2}}\varepsilon AdU_{d}^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>C</mi> <msup> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>ε</mi> <mi>A</mi> </mrow> <mi>d</mi> </mfrac> </mrow> <msup> <mrow> <mo>(</mo> <mrow> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> </mrow> </msub> <mi>d</mi> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>ε</mi> <mi>A</mi> <mi>d</mi> <msubsup> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E={\frac {1}{2}}CV^{2}={\frac {1}{2}}{\frac {\varepsilon A}{d}}\left(U_{d}d\right)^{2}={\frac {1}{2}}\varepsilon AdU_{d}^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f19772390e42d7cee49594224e4195ecf0ccada" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:39.164ex; height:5.509ex;" alt="{\displaystyle E={\frac {1}{2}}CV^{2}={\frac {1}{2}}{\frac {\varepsilon A}{d}}\left(U_{d}d\right)^{2}={\frac {1}{2}}\varepsilon AdU_{d}^{2}}" /></span> </p><p>The maximum energy is a function of dielectric volume, <a href="/wiki/Permittivity" title="Permittivity">permittivity</a>, and <a href="/wiki/Dielectric_strength" title="Dielectric strength">dielectric strength</a>. Changing the plate area and the separation between the plates while maintaining the same volume causes no change of the maximum amount of energy that the capacitor can store, so long as the distance between plates remains much smaller than both the length and width of the plates. In addition, these equations assume that the electric field is entirely concentrated in the dielectric between the plates. In reality there are fringing fields outside the dielectric, for example between the sides of the capacitor plates, which increase the effective capacitance of the capacitor. This is sometimes called <a href="/wiki/Parasitic_capacitance" title="Parasitic capacitance">parasitic capacitance</a>. For some simple capacitor geometries this additional capacitance term can be calculated analytically.<sup id="cite_ref-Pillai1970_26-0" class="reference"><a href="#cite_note-Pillai1970-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> It becomes negligibly small when the ratios of plate width to separation and length to separation are large. </p><p>For unevenly charged plates: </p> <ul><li>If one plate is charged with <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a8ea6463cb36d8278ff71214fb4d13127039ae53" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.893ex; height:2.509ex;" alt="{\displaystyle Q_{1}}" /></span> while the other is charged with <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b86e8bff64d5e62fc8f45a35875e78bc9bef74a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.893ex; height:2.509ex;" alt="{\displaystyle Q_{2}}" /></span>, and if both plates are separated from other materials in the environment, then the inner surface of the first plate will have <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle {\frac {Q_{1}-Q_{2}}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle {\frac {Q_{1}-Q_{2}}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5658cc5467c73da6f955430ebf360405b7a1bf16" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:6.378ex; height:4.009ex;" alt="{\textstyle {\frac {Q_{1}-Q_{2}}{2}}}" /></span>, and the inner surface of the second plated will have <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle -{\frac {Q_{1}-Q_{2}}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle -{\frac {Q_{1}-Q_{2}}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6643063542c6298ebdc711a12d11a7d359b723b5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:8.186ex; height:4.009ex;" alt="{\textstyle -{\frac {Q_{1}-Q_{2}}{2}}}" /></span> charge.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (January 2020)">citation needed</span></a></i>]</sup> Therefore, the voltage <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}" /></span> between the plates is <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle V={\frac {Q_{1}-Q_{2}}{2C}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>V</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <mn>2</mn> <mi>C</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle V={\frac {Q_{1}-Q_{2}}{2C}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f115664981209fbbebef47ccd7b61fb2423dc87e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:11.263ex; height:4.176ex;" alt="{\textstyle V={\frac {Q_{1}-Q_{2}}{2C}}}" /></span>. Note that the outer surface of both plates will have <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle {\frac {Q_{1}+Q_{2}}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle {\frac {Q_{1}+Q_{2}}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/457d7c70f6cc6e099979d464f7468917e1488e02" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:6.378ex; height:4.009ex;" alt="{\textstyle {\frac {Q_{1}+Q_{2}}{2}}}" /></span>, but those charges do not affect the voltage between the plates.</li> <li>If one plate is charged with <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a8ea6463cb36d8278ff71214fb4d13127039ae53" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.893ex; height:2.509ex;" alt="{\displaystyle Q_{1}}" /></span> while the other is charged with <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b86e8bff64d5e62fc8f45a35875e78bc9bef74a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.893ex; height:2.509ex;" alt="{\displaystyle Q_{2}}" /></span>, and if the second plate is connected to ground, then the inner surface of the first plate will have <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a8ea6463cb36d8278ff71214fb4d13127039ae53" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.893ex; height:2.509ex;" alt="{\displaystyle Q_{1}}" /></span>, and the inner surface of the second plated will have <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -Q_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -Q_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7b9db04e84bb87eedaf885f20a7c632ebffb9b54" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.701ex; height:2.509ex;" alt="{\displaystyle -Q_{1}}" /></span>. Therefore, the voltage <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}" /></span> between the plates is <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle V={\frac {Q_{1}}{C}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>V</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mi>C</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle V={\frac {Q_{1}}{C}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d769cf40dffc2c1b6b5dea79b72bc2deed82352e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:7.853ex; height:4.176ex;" alt="{\textstyle V={\frac {Q_{1}}{C}}}" /></span>. Note that the outer surface of both plates will have zero charge.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Interleaved_capacitor">Interleaved capacitor</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=7" title="Edit section: Interleaved capacitor"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size skin-invert-image" typeof="mw:File/Thumb"><a href="/wiki/File:Interleaved_Capacitor.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/26/Interleaved_Capacitor.jpg/250px-Interleaved_Capacitor.jpg" decoding="async" width="220" height="298" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/2/26/Interleaved_Capacitor.jpg 1.5x" data-file-width="286" data-file-height="388" /></a><figcaption>The interleaved capacitor can be seen as a combination of several parallel connected capacitors.</figcaption></figure> <p>For <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}" /></span> number of plates in a capacitor, the total capacitance would be <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C=\varepsilon _{o}{\frac {A}{d}}(n-1)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mo>=</mo> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>o</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>A</mi> <mi>d</mi> </mfrac> </mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C=\varepsilon _{o}{\frac {A}{d}}(n-1)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8cc81aa7faa4c126d227da44b3469e15a3b680a8" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:16.764ex; height:5.509ex;" alt="{\displaystyle C=\varepsilon _{o}{\frac {A}{d}}(n-1)}" /></span> where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C=\varepsilon _{o}A/d}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mo>=</mo> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>o</mi> </mrow> </msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>d</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C=\varepsilon _{o}A/d}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e462b839f4c16c04ee63980dd69e602d104b1629" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.099ex; height:2.843ex;" alt="{\displaystyle C=\varepsilon _{o}A/d}" /></span> is the capacitance for a single plate and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}" /></span> is the number of interleaved plates. </p><p>As shown to the figure on the right, the interleaved plates can be seen as parallel plates connected to each other. Every pair of adjacent plates acts as a separate capacitor; the number of pairs is always one less than the number of plates, hence the <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (n-1)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>n</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (n-1)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/df88c6333caaf6471cf277f24b802ff9931b133e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.207ex; height:2.843ex;" alt="{\displaystyle (n-1)}" /></span> multiplier. </p> <div class="mw-heading mw-heading3"><h3 id="Energy_stored_in_a_capacitor">Energy stored in a capacitor</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=8" title="Edit section: Energy stored in a capacitor"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>To increase the charge and voltage on a capacitor, <a href="/wiki/Work_(thermodynamics)" title="Work (thermodynamics)">work</a> must be done by an external power source to move charge from the negative to the positive plate against the opposing force of the electric field.<sup id="cite_ref-Purcell_27-0" class="reference"><a href="#cite_note-Purcell-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Serway_28-0" class="reference"><a href="#cite_note-Serway-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> If the voltage on the capacitor is <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}" /></span>, the work <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle dW}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>W</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dW}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e3a511937b90a98ab09ea7e06c16b184394f529c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.651ex; height:2.176ex;" alt="{\displaystyle dW}" /></span> required to move a small increment of charge <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle dq}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dq}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/212a4169ef66be3955464b7b64e185e2b78ef365" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.285ex; height:2.509ex;" alt="{\displaystyle dq}" /></span> from the negative to the positive plate is <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle dW=Vdq}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>W</mi> <mo>=</mo> <mi>V</mi> <mi>d</mi> <mi>q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dW=Vdq}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a59b930a030c30b969748c27c8333a2f20016f76" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.822ex; height:2.509ex;" alt="{\displaystyle dW=Vdq}" /></span>. The energy is stored in the increased electric field between the plates. The total energy <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle W}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>W</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/54a9c4c547f4d6111f81946cad242b18298d70b7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.435ex; height:2.176ex;" alt="{\displaystyle W}" /></span> stored in a capacitor (expressed in <a href="/wiki/Joule" title="Joule">joules</a>) is equal to the total work done in establishing the electric field from an uncharged state.<sup id="cite_ref-Hammond2013_29-0" class="reference"><a href="#cite_note-Hammond2013-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Serway_28-1" class="reference"><a href="#cite_note-Serway-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Purcell_27-1" class="reference"><a href="#cite_note-Purcell-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle W=\int _{0}^{Q}V(q)\,\mathrm {d} q=\int _{0}^{Q}{\frac {q}{C}}\,\mathrm {d} q={\frac {1}{2}}{\frac {Q^{2}}{C}}={\frac {1}{2}}VQ={\frac {1}{2}}CV^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>W</mi> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>Q</mi> </mrow> </msubsup> <mi>V</mi> <mo stretchy="false">(</mo> <mi>q</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>q</mi> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>Q</mi> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>q</mi> <mi>C</mi> </mfrac> </mrow> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>q</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>C</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>V</mi> <mi>Q</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>C</mi> <msup> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W=\int _{0}^{Q}V(q)\,\mathrm {d} q=\int _{0}^{Q}{\frac {q}{C}}\,\mathrm {d} q={\frac {1}{2}}{\frac {Q^{2}}{C}}={\frac {1}{2}}VQ={\frac {1}{2}}CV^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d8fa812ddd1fed2c3a80f4d6b099f67cd1266899" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:57.549ex; height:6.343ex;" alt="{\displaystyle W=\int _{0}^{Q}V(q)\,\mathrm {d} q=\int _{0}^{Q}{\frac {q}{C}}\,\mathrm {d} q={\frac {1}{2}}{\frac {Q^{2}}{C}}={\frac {1}{2}}VQ={\frac {1}{2}}CV^{2}}" /></span> where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8752c7023b4b3286800fe3238271bbca681219ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}" /></span> is the charge stored in the capacitor, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}" /></span> is the voltage across the capacitor, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4fc55753007cd3c18576f7933f6f089196732029" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}" /></span> is the capacitance. This potential energy will remain in the capacitor until the charge is removed. If charge is allowed to move back from the positive to the negative plate, for example by connecting a circuit with resistance between the plates, the charge moving under the influence of the electric field will do work on the external circuit. </p><p>If the gap between the capacitor plates <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e85ff03cbe0c7341af6b982e47e9f90d235c66ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.216ex; height:2.176ex;" alt="{\displaystyle d}" /></span> is constant, as in the parallel plate model above, the electric field between the plates will be uniform (neglecting fringing fields) and will have a constant value <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E=V/d}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>d</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=V/d}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/41f15e903d7ebd822c0d45550f96434c328ddb5a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.04ex; height:2.843ex;" alt="{\displaystyle E=V/d}" /></span>. In this case the stored energy can be calculated from the electric field strength <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle W={\frac {1}{2}}CV^{2}={\frac {1}{2}}{\frac {\varepsilon A}{d}}\left(Ed\right)^{2}={\frac {1}{2}}\varepsilon AdE^{2}={\frac {1}{2}}\varepsilon E^{2}({\text{volume of electric field}})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>W</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>C</mi> <msup> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>ε</mi> <mi>A</mi> </mrow> <mi>d</mi> </mfrac> </mrow> <msup> <mrow> <mo>(</mo> <mrow> <mi>E</mi> <mi>d</mi> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>ε</mi> <mi>A</mi> <mi>d</mi> <msup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>ε</mi> <msup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>volume of electric field</mtext> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W={\frac {1}{2}}CV^{2}={\frac {1}{2}}{\frac {\varepsilon A}{d}}\left(Ed\right)^{2}={\frac {1}{2}}\varepsilon AdE^{2}={\frac {1}{2}}\varepsilon E^{2}({\text{volume of electric field}})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6f8dbafddafe46befc92d3aa9dfb83019551af9a" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:72.194ex; height:5.509ex;" alt="{\displaystyle W={\frac {1}{2}}CV^{2}={\frac {1}{2}}{\frac {\varepsilon A}{d}}\left(Ed\right)^{2}={\frac {1}{2}}\varepsilon AdE^{2}={\frac {1}{2}}\varepsilon E^{2}({\text{volume of electric field}})}" /></span> The last formula above is equal to the energy density per unit volume in the electric field multiplied by the volume of field between the plates, confirming that the energy in the capacitor is stored in its electric field. </p> <div class="mw-heading mw-heading3"><h3 id="Current–voltage_relation"><span id="Current.E2.80.93voltage_relation"></span>Current–voltage relation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=9" title="Edit section: Current–voltage relation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size skin-invert-image" typeof="mw:File/Thumb"><a href="/wiki/File:Capacitor-positive-voltage-and-current-functions-of-time.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/17/Capacitor-positive-voltage-and-current-functions-of-time.svg/180px-Capacitor-positive-voltage-and-current-functions-of-time.svg.png" decoding="async" width="180" height="239" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/17/Capacitor-positive-voltage-and-current-functions-of-time.svg/270px-Capacitor-positive-voltage-and-current-functions-of-time.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/17/Capacitor-positive-voltage-and-current-functions-of-time.svg/360px-Capacitor-positive-voltage-and-current-functions-of-time.svg.png 2x" data-file-width="94" data-file-height="125" /></a><figcaption>Schematic showing polarity of voltage and direction of current for this current–voltage relation</figcaption></figure> <p>The current <i>I</i>(<i>t</i>) through any component in an electric circuit is defined as the rate of flow of a charge <i>Q</i>(<i>t</i>) passing through it. Actual charges – electrons – cannot pass through the dielectric of an <i>ideal</i> capacitor.<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>note 1<span class="cite-bracket">]</span></a></sup> Rather, one electron accumulates on the negative plate for each one that leaves the positive plate, resulting in an electron depletion and consequent positive charge on one electrode that is equal and opposite to the accumulated negative charge on the other. Thus the charge on the electrodes is equal to the <a href="/wiki/Integral" title="Integral">integral</a> of the current as well as proportional to the voltage, as discussed above. As with any <a href="/wiki/Antiderivative" title="Antiderivative">antiderivative</a>, a <a href="/wiki/Constant_of_integration" title="Constant of integration">constant of integration</a> is added to represent the initial voltage <i>V</i>(<i>t</i><sub>0</sub>). This is the integral form of the capacitor equation:<sup id="cite_ref-FOOTNOTEDorfSvoboda2001263_31-0" class="reference"><a href="#cite_note-FOOTNOTEDorfSvoboda2001263-31"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V(t)={\frac {Q(t)}{C}}=V(t_{0})+{\frac {1}{C}}\int _{t_{0}}^{t}I(\tau )\,\mathrm {d} \tau }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>Q</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mi>C</mi> </mfrac> </mrow> <mo>=</mo> <mi>V</mi> <mo stretchy="false">(</mo> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>C</mi> </mfrac> </mrow> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msubsup> <mi>I</mi> <mo stretchy="false">(</mo> <mi>τ</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>τ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V(t)={\frac {Q(t)}{C}}=V(t_{0})+{\frac {1}{C}}\int _{t_{0}}^{t}I(\tau )\,\mathrm {d} \tau }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/114522dd9081ecade516f956dc536c14a2f867b1" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:38.019ex; height:6.509ex;" alt="{\displaystyle V(t)={\frac {Q(t)}{C}}=V(t_{0})+{\frac {1}{C}}\int _{t_{0}}^{t}I(\tau )\,\mathrm {d} \tau }" /></span> </p><p>Taking the derivative of this and multiplying by <i>C</i> yields the derivative form:<sup id="cite_ref-FOOTNOTEDorfSvoboda2001260_32-0" class="reference"><a href="#cite_note-FOOTNOTEDorfSvoboda2001260-32"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I(t)={\frac {\mathrm {d} Q(t)}{\mathrm {d} t}}=C{\frac {\mathrm {d} V(t)}{\mathrm {d} t}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>Q</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>V</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I(t)={\frac {\mathrm {d} Q(t)}{\mathrm {d} t}}=C{\frac {\mathrm {d} V(t)}{\mathrm {d} t}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8db8944be32d696afb8cb8be351586afe18cd89d" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:24.965ex; height:5.843ex;" alt="{\displaystyle I(t)={\frac {\mathrm {d} Q(t)}{\mathrm {d} t}}=C{\frac {\mathrm {d} V(t)}{\mathrm {d} t}}}" /></span> for <span class="texhtml mvar" style="font-style:italic;">C</span> independent of time, voltage and electric charge. </p><p>The <a href="/wiki/Duality_(electrical_circuits)" title="Duality (electrical circuits)">dual</a> of the capacitor is the <a href="/wiki/Inductor" title="Inductor">inductor</a>, which stores energy in a <a href="/wiki/Magnetic_field" title="Magnetic field">magnetic field</a> rather than an electric field. Its current-voltage relation is obtained by exchanging current and voltage in the capacitor equations and replacing <span class="texhtml mvar" style="font-style:italic;">C</span> with the inductance <span class="texhtml mvar" style="font-style:italic;">L</span>. </p> <div class="mw-heading mw-heading3"><h3 id="RC_circuits">RC circuits</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=10" title="Edit section: RC circuits"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/RC_circuit" title="RC circuit">RC circuit</a></div> <figure class="mw-default-size skin-invert-image" typeof="mw:File/Thumb"><a href="/wiki/File:RC_switch.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/90/RC_switch.svg/220px-RC_switch.svg.png" decoding="async" width="220" height="121" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/90/RC_switch.svg/330px-RC_switch.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/90/RC_switch.svg/440px-RC_switch.svg.png 2x" data-file-width="2014" data-file-height="1109" /></a><figcaption>A simple resistor–capacitor circuit demonstrates charging of a capacitor.</figcaption></figure> <p>A series circuit containing only a <a href="/wiki/Resistor" title="Resistor">resistor</a>, a capacitor, a switch and a constant DC source of voltage <span class="texhtml"><i>V</i><sub>0</sub></span> is known as a <i>charging circuit</i>.<sup id="cite_ref-ChargingCircuit_33-0" class="reference"><a href="#cite_note-ChargingCircuit-33"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> If the capacitor is initially uncharged while the switch is open, and the switch is closed at <span class="texhtml"><i>t</i> = 0</span>, it follows from <a href="/wiki/Kirchhoff%27s_voltage_law" class="mw-redirect" title="Kirchhoff's voltage law">Kirchhoff's voltage law</a> that <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{0}=v_{\text{resistor}}(t)+v_{\text{capacitor}}(t)=i(t)R+{\frac {1}{C}}\int _{t_{0}}^{t}i(\tau )\,\mathrm {d} \tau }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>resistor</mtext> </mrow> </msub> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>+</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>capacitor</mtext> </mrow> </msub> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>i</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mi>R</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>C</mi> </mfrac> </mrow> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msubsup> <mi>i</mi> <mo stretchy="false">(</mo> <mi>τ</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>τ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{0}=v_{\text{resistor}}(t)+v_{\text{capacitor}}(t)=i(t)R+{\frac {1}{C}}\int _{t_{0}}^{t}i(\tau )\,\mathrm {d} \tau }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4f45415029d9dacbf018a9ea050506e7d18ceb44" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:52.698ex; height:6.509ex;" alt="{\displaystyle V_{0}=v_{\text{resistor}}(t)+v_{\text{capacitor}}(t)=i(t)R+{\frac {1}{C}}\int _{t_{0}}^{t}i(\tau )\,\mathrm {d} \tau }" /></span> </p><p>Taking the derivative and multiplying by <i>C</i>, gives a <a href="/wiki/First-order_differential_equation" class="mw-redirect" title="First-order differential equation">first-order differential equation</a>: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle RC{\frac {\mathrm {d} i(t)}{\mathrm {d} t}}+i(t)=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>i</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mi>i</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle RC{\frac {\mathrm {d} i(t)}{\mathrm {d} t}}+i(t)=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cb010f1c4559365a1f0accd3807feacc043aede9" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:19.663ex; height:5.843ex;" alt="{\displaystyle RC{\frac {\mathrm {d} i(t)}{\mathrm {d} t}}+i(t)=0}" /></span> </p><p>At <span class="texhtml"><i>t</i> = 0</span>, the voltage across the capacitor is zero and the voltage across the resistor is <i>V</i><sub>0</sub>. The initial current is then <span class="texhtml"><i>I</i>(0) = <i>V</i><sub>0</sub>/<i>R</i></span>. With this assumption, solving the differential equation yields <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}I(t)&={\frac {V_{0}}{R}}e^{-t/\tau _{0}}\\V(t)&=V_{0}\left(1-e^{-t/\tau _{0}}\right)\\Q(t)&=CV_{0}\left(1-e^{-t/\tau _{0}}\right)\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>I</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mi>R</mi> </mfrac> </mrow> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </msup> </mtd> </mtr> <mtr> <mtd> <mi>V</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mtd> <mtd> <mi></mi> <mo>=</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </msup> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>Q</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>C</mi> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </msup> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}I(t)&={\frac {V_{0}}{R}}e^{-t/\tau _{0}}\\V(t)&=V_{0}\left(1-e^{-t/\tau _{0}}\right)\\Q(t)&=CV_{0}\left(1-e^{-t/\tau _{0}}\right)\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4e985d0a7526d56480e62ad8f0f270f8129d1bd9" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -7.005ex; width:25.238ex; height:15.176ex;" alt="{\displaystyle {\begin{aligned}I(t)&={\frac {V_{0}}{R}}e^{-t/\tau _{0}}\\V(t)&=V_{0}\left(1-e^{-t/\tau _{0}}\right)\\Q(t)&=CV_{0}\left(1-e^{-t/\tau _{0}}\right)\end{aligned}}}" /></span> where <span class="texhtml"><i>τ</i><sub>0</sub> = <i>RC</i></span> is the <i><a href="/wiki/Time_constant" title="Time constant">time constant</a></i> of the system. As the capacitor reaches equilibrium with the source voltage, the voltages across the resistor and the current through the entire circuit <a href="/wiki/Exponential_decay" title="Exponential decay">decay exponentially</a>. In the case of a <i>discharging</i> capacitor, the capacitor's initial voltage (<span class="texhtml"><i>V</i><sub>Ci</sub></span>) replaces <span class="texhtml"><i>V</i><sub>0</sub></span>. The equations become <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}I(t)&={\frac {V_{Ci}}{R}}e^{-t/\tau _{0}}\\V(t)&=V_{Ci}\,e^{-t/\tau _{0}}\\Q(t)&=C\,V_{Ci}\,e^{-t/\tau _{0}}\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>I</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> <mi>i</mi> </mrow> </msub> <mi>R</mi> </mfrac> </mrow> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </msup> </mtd> </mtr> <mtr> <mtd> <mi>V</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mtd> <mtd> <mi></mi> <mo>=</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> <mi>i</mi> </mrow> </msub> <mspace width="thinmathspace"></mspace> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </msup> </mtd> </mtr> <mtr> <mtd> <mi>Q</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>C</mi> <mspace width="thinmathspace"></mspace> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> <mi>i</mi> </mrow> </msub> <mspace width="thinmathspace"></mspace> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </msup> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}I(t)&={\frac {V_{Ci}}{R}}e^{-t/\tau _{0}}\\V(t)&=V_{Ci}\,e^{-t/\tau _{0}}\\Q(t)&=C\,V_{Ci}\,e^{-t/\tau _{0}}\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/93d81411954c8f7d3633f7210659119d5d400f67" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.505ex; width:19.842ex; height:12.176ex;" alt="{\displaystyle {\begin{aligned}I(t)&={\frac {V_{Ci}}{R}}e^{-t/\tau _{0}}\\V(t)&=V_{Ci}\,e^{-t/\tau _{0}}\\Q(t)&=C\,V_{Ci}\,e^{-t/\tau _{0}}\end{aligned}}}" /></span> </p> <div class="mw-heading mw-heading3"><h3 id="AC_circuits">AC circuits</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=11" title="Edit section: AC circuits"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Reactance_(electronics)" class="mw-redirect" title="Reactance (electronics)">reactance (electronics)</a> and <a href="/wiki/Electrical_impedance#Deriving_the_device-specific_impedances" title="Electrical impedance">electrical impedance § Deriving the device-specific impedances</a></div> <p><a href="/wiki/Electrical_impedance" title="Electrical impedance">Impedance</a>, the vector sum of <a href="/wiki/Electrical_reactance" title="Electrical reactance">reactance</a> and <a href="/wiki/Electrical_resistance" class="mw-redirect" title="Electrical resistance">resistance</a>, describes the phase difference and the ratio of amplitudes between sinusoidally varying voltage and sinusoidally varying current at a given frequency. <a href="/wiki/Fourier_analysis" title="Fourier analysis">Fourier analysis</a> allows any signal to be constructed from a <a href="/wiki/Spectrum" title="Spectrum">spectrum</a> of frequencies, whence the circuit's reaction to the various frequencies may be found. The reactance and impedance of a capacitor are respectively <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}X&=-{\frac {1}{\omega C}}=-{\frac {1}{2\pi fC}}\\Z&={\frac {1}{j\omega C}}=-{\frac {j}{\omega C}}=-{\frac {j}{2\pi fC}}\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>X</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>ω</mi> <mi>C</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>π</mi> <mi>f</mi> <mi>C</mi> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>Z</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>j</mi> <mi>ω</mi> <mi>C</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>j</mi> <mrow> <mi>ω</mi> <mi>C</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>j</mi> <mrow> <mn>2</mn> <mi>π</mi> <mi>f</mi> <mi>C</mi> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}X&=-{\frac {1}{\omega C}}=-{\frac {1}{2\pi fC}}\\Z&={\frac {1}{j\omega C}}=-{\frac {j}{\omega C}}=-{\frac {j}{2\pi fC}}\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e5028804b60761fe9cac8610a018b1fce63db85" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.101ex; margin-bottom: -0.237ex; width:31.073ex; height:11.843ex;" alt="{\displaystyle {\begin{aligned}X&=-{\frac {1}{\omega C}}=-{\frac {1}{2\pi fC}}\\Z&={\frac {1}{j\omega C}}=-{\frac {j}{\omega C}}=-{\frac {j}{2\pi fC}}\end{aligned}}}" /></span> where <span class="texhtml"><i>j</i></span> is the <a href="/wiki/Imaginary_unit" title="Imaginary unit">imaginary unit</a> and <span class="texhtml mvar" style="font-style:italic;">ω</span> is the <a href="/wiki/Angular_frequency" title="Angular frequency">angular frequency</a> of the sinusoidal signal. The <span class="texhtml">−<i>j</i></span> phase indicates that the AC voltage <span class="texhtml"><i>V</i> = <i>ZI</i></span> lags the AC current by 90°: the positive current phase corresponds to increasing voltage as the capacitor charges; zero current corresponds to instantaneous constant voltage, etc. </p><p>Impedance decreases with increasing capacitance and increasing frequency.<sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> This implies that a higher-frequency signal or a larger capacitor results in a lower voltage amplitude per current amplitude – an AC "short circuit" or <a href="/wiki/AC_coupling" class="mw-redirect" title="AC coupling">AC coupling</a>. Conversely, for very low frequencies, the reactance is high, so that a capacitor is nearly an open circuit in AC analysis – those frequencies have been "filtered out". </p><p>Capacitors are different from resistors and inductors in that the impedance is <i>inversely</i> proportional to the defining characteristic; i.e., <a href="/wiki/Capacitance" title="Capacitance">capacitance</a>. </p><p>A capacitor connected to an alternating voltage source has a displacement current to flowing through it. In the case that the voltage source is <i>V</i><sub>0</sub>cos(ωt), the displacement current can be expressed as: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I=C{\frac {{\text{d}}V}{{\text{d}}t}}=-\omega {C}{V_{0}}\sin(\omega t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> <mo>=</mo> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>d</mtext> </mrow> <mi>V</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>d</mtext> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ω</mi> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I=C{\frac {{\text{d}}V}{{\text{d}}t}}=-\omega {C}{V_{0}}\sin(\omega t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c72f83d1ec3d05872b38faca49aafacd99808651" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:27.818ex; height:5.509ex;" alt="{\displaystyle I=C{\frac {{\text{d}}V}{{\text{d}}t}}=-\omega {C}{V_{0}}\sin(\omega t)}" /></span> </p><p>At <span class="texhtml">sin(<i>ωt</i>) = −1</span>, the capacitor has a maximum (or peak) current whereby <span class="texhtml"><i>I</i><sub>0</sub> = <i>ωCV</i><sub>0</sub></span>. The ratio of peak voltage to peak current is due to <a href="/wiki/Electrical_reactance#Capacitive_reactance" title="Electrical reactance">capacitive reactance</a> (denoted X<sub>C</sub>). <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X_{C}={\frac {V_{0}}{I_{0}}}={\frac {V_{0}}{\omega CV_{0}}}={\frac {1}{\omega C}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <mi>ω</mi> <mi>C</mi> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>ω</mi> <mi>C</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X_{C}={\frac {V_{0}}{I_{0}}}={\frac {V_{0}}{\omega CV_{0}}}={\frac {1}{\omega C}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b18f2e56afbedae3f19a7f23936fe16c5185ad7" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:26.453ex; height:5.843ex;" alt="{\displaystyle X_{C}={\frac {V_{0}}{I_{0}}}={\frac {V_{0}}{\omega CV_{0}}}={\frac {1}{\omega C}}}" /></span> </p><p>X<sub>C</sub> approaches zero as <span class="texhtml mvar" style="font-style:italic;">ω</span> approaches infinity. If X<sub>C</sub> approaches 0, the capacitor resembles a short wire that strongly passes current at high frequencies. X<sub>C</sub> approaches infinity as ω approaches zero. If X<sub>C</sub> approaches infinity, the capacitor resembles an open circuit that poorly passes low frequencies. </p><p>The current of the capacitor may be expressed in the form of cosines to better compare with the voltage of the source: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I=-I_{0}\sin({\omega t})=I_{0}\cos({\omega t}+{90^{\circ }})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> <mo>=</mo> <mo>−</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> <mi>t</mi> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> <mi>t</mi> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mn>90</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I=-I_{0}\sin({\omega t})=I_{0}\cos({\omega t}+{90^{\circ }})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/df902d1277c056fbe293cb0bba34af840da2428f" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:34.481ex; height:2.843ex;" alt="{\displaystyle I=-I_{0}\sin({\omega t})=I_{0}\cos({\omega t}+{90^{\circ }})}" /></span> </p><p>In this situation, the current is out of <a href="/wiki/Phase_(waves)" title="Phase (waves)">phase</a> with the voltage by +π/2 radians or +90 degrees, i.e. the current leads the voltage by 90°. </p> <div class="mw-heading mw-heading3"><h3 id="Laplace_circuit_analysis_(s-domain)"><span id="Laplace_circuit_analysis_.28s-domain.29"></span>Laplace circuit analysis (s-domain)</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=12" title="Edit section: Laplace circuit analysis (s-domain)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>When using the <a href="/wiki/Laplace_transform" title="Laplace transform">Laplace transform</a> in circuit analysis, the impedance of an ideal capacitor with no initial charge is represented in the <span class="texhtml mvar" style="font-style:italic;">s</span> domain by: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z(s)={\frac {1}{sC}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Z</mi> <mo stretchy="false">(</mo> <mi>s</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>s</mi> <mi>C</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z(s)={\frac {1}{sC}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/752defe15d6b794bf37204dcc0cfc76428a62c1c" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:11.372ex; height:5.343ex;" alt="{\displaystyle Z(s)={\frac {1}{sC}}}" /></span> where </p> <ul><li><span class="texhtml mvar" style="font-style:italic;">C</span> is the capacitance, and</li> <li><span class="texhtml mvar" style="font-style:italic;">s</span> is the complex frequency.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Circuit_analysis">Circuit analysis</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=13" title="Edit section: Circuit analysis"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Series_and_parallel_circuits" title="Series and parallel circuits">Series and parallel circuits</a></div> <div class="skin-invert-image"><style data-mw-deduplicate="TemplateStyles:r1273380762/mw-parser-output/.tmulti">.mw-parser-output .tmulti .multiimageinner{display:flex;flex-direction:column}.mw-parser-output .tmulti .trow{display:flex;flex-direction:row;clear:left;flex-wrap:wrap;width:100%;box-sizing:border-box}.mw-parser-output .tmulti .tsingle{margin:1px;float:left}.mw-parser-output .tmulti .theader{clear:both;font-weight:bold;text-align:center;align-self:center;background-color:transparent;width:100%}.mw-parser-output .tmulti .thumbcaption{background-color:transparent}.mw-parser-output .tmulti .text-align-left{text-align:left}.mw-parser-output .tmulti .text-align-right{text-align:right}.mw-parser-output .tmulti .text-align-center{text-align:center}@media all and (max-width:720px){.mw-parser-output .tmulti .thumbinner{width:100%!important;box-sizing:border-box;max-width:none!important;align-items:center}.mw-parser-output .tmulti .trow{justify-content:center}.mw-parser-output .tmulti .tsingle{float:none!important;max-width:100%!important;box-sizing:border-box;text-align:center}.mw-parser-output .tmulti .tsingle .thumbcaption{text-align:left}.mw-parser-output .tmulti .trow>.thumbcaption{text-align:center}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .tmulti .multiimageinner span:not(.skin-invert-image):not(.skin-invert):not(.bg-transparent) img{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .tmulti .multiimageinner span:not(.skin-invert-image):not(.skin-invert):not(.bg-transparent) img{background-color:white}}</style><div class="thumb tmulti tright"><div class="thumbinner multiimageinner" style="width:204px;max-width:204px"><div class="trow"><div class="tsingle" style="width:202px;max-width:202px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Capacitors_in_parallel.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Capacitors_in_parallel.svg/200px-Capacitors_in_parallel.svg.png" decoding="async" width="200" height="94" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Capacitors_in_parallel.svg/300px-Capacitors_in_parallel.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Capacitors_in_parallel.svg/400px-Capacitors_in_parallel.svg.png 2x" data-file-width="512" data-file-height="241" /></a></span></div><div class="thumbcaption">Several capacitors in parallel</div></div></div><div class="trow"><div class="tsingle" style="width:202px;max-width:202px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Kondensator_C1_plus_C2.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Kondensator_C1_plus_C2.svg/250px-Kondensator_C1_plus_C2.svg.png" decoding="async" width="200" height="95" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Kondensator_C1_plus_C2.svg/330px-Kondensator_C1_plus_C2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Kondensator_C1_plus_C2.svg/500px-Kondensator_C1_plus_C2.svg.png 2x" data-file-width="505" data-file-height="241" /></a></span></div><div class="thumbcaption">The parallel connection of two capacitors</div></div></div></div></div></div> <dl><dt>Capacitors in parallel</dt> <dd>Capacitors in a parallel configuration each have the same applied voltage. Their capacitance values add up. Charge is apportioned among them by capacitance value. Using the schematic diagram to visualize parallel plates, it is apparent that each capacitor contributes to the total surface area. <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C_{\mathrm {eq} }=\sum _{i=1}^{n}C_{i}=C_{1}+C_{2}+\cdots +C_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">q</mi> </mrow> </mrow> </msub> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{\mathrm {eq} }=\sum _{i=1}^{n}C_{i}=C_{1}+C_{2}+\cdots +C_{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/703b552010fcfe02ae1c454740b4b08ff65d23a4" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:35.461ex; height:6.843ex;" alt="{\displaystyle C_{\mathrm {eq} }=\sum _{i=1}^{n}C_{i}=C_{1}+C_{2}+\cdots +C_{n}}" /></span> <div style="clear:both;" class=""></div></dd></dl> <div class="skin-invert-image"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1273380762/mw-parser-output/.tmulti" /><div class="thumb tmulti tright"><div class="thumbinner multiimageinner" style="width:204px;max-width:204px"><div class="trow"><div class="tsingle" style="width:202px;max-width:202px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Capacitors_in_series.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/75/Capacitors_in_series.svg/200px-Capacitors_in_series.svg.png" decoding="async" width="200" height="44" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/75/Capacitors_in_series.svg/300px-Capacitors_in_series.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/75/Capacitors_in_series.svg/400px-Capacitors_in_series.svg.png 2x" data-file-width="937" data-file-height="208" /></a></span></div><div class="thumbcaption">Several capacitors in series</div></div></div><div class="trow"><div class="tsingle" style="width:202px;max-width:202px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Kondensator_C1_C2_Reihe.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/01/Kondensator_C1_C2_Reihe.svg/250px-Kondensator_C1_C2_Reihe.svg.png" decoding="async" width="200" height="95" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/01/Kondensator_C1_C2_Reihe.svg/330px-Kondensator_C1_C2_Reihe.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/01/Kondensator_C1_C2_Reihe.svg/500px-Kondensator_C1_C2_Reihe.svg.png 2x" data-file-width="505" data-file-height="241" /></a></span></div><div class="thumbcaption">The serial connection of two capacitors</div></div></div></div></div></div> <dl><dt>For capacitors in series</dt> <dd>Connected in series, the schematic diagram reveals that the separation distance, not the plate area, adds up. The capacitors each store instantaneous charge build-up equal to that of every other capacitor in the series. The total voltage difference from end to end is apportioned to each capacitor according to the inverse of its capacitance. The entire series acts as a capacitor <i>smaller</i> than any of its components. <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C_{\mathrm {eq} }=\left(\sum _{i=1}^{n}{\frac {1}{C_{i}}}\right)^{-1}=\left({1 \over C_{1}}+{1 \over C_{2}}+{1 \over C_{3}}+\dots +{1 \over C_{n}}\right)^{-1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">q</mi> </mrow> </mrow> </msub> <mo>=</mo> <msup> <mrow> <mo>(</mo> <mrow> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>=</mo> <msup> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mfrac> </mrow> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{\mathrm {eq} }=\left(\sum _{i=1}^{n}{\frac {1}{C_{i}}}\right)^{-1}=\left({1 \over C_{1}}+{1 \over C_{2}}+{1 \over C_{3}}+\dots +{1 \over C_{n}}\right)^{-1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3c2c5e388b15e5c2a0afd67d00d2fbef733843a0" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:56.966ex; height:8.009ex;" alt="{\displaystyle C_{\mathrm {eq} }=\left(\sum _{i=1}^{n}{\frac {1}{C_{i}}}\right)^{-1}=\left({1 \over C_{1}}+{1 \over C_{2}}+{1 \over C_{3}}+\dots +{1 \over C_{n}}\right)^{-1}}" /></span></dd> <dd>Capacitors are combined in series to achieve a higher working voltage, for example for smoothing a high voltage power supply. The voltage ratings, which are based on plate separation, add up, if capacitance and leakage currents for each capacitor are identical. In such an application, on occasion, series strings are connected in parallel, forming a matrix. The goal is to maximize the energy storage of the network without overloading any capacitor. For high-energy storage with capacitors in series, some safety considerations must be applied to ensure one capacitor failing and leaking current does not apply too much voltage to the other series capacitors.</dd> <dd>Series connection is also sometimes used to adapt polarized <a href="/wiki/Electrolytic_capacitor" title="Electrolytic capacitor">electrolytic capacitors</a> for bipolar AC use. <div style="clear:both;" class=""></div></dd> <dt>Voltage distribution in parallel-to-series networks.</dt> <dd>To model the distribution of voltages from a single charged capacitor <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(A\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mi>A</mi> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(A\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/152cb9c4035201d875275fd6d2c381731b6d0c1d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.552ex; height:2.843ex;" alt="{\displaystyle \left(A\right)}" /></span> connected in parallel to a chain of capacitors in series <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(B_{\text{n}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>n</mtext> </mrow> </msub> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(B_{\text{n}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9c9af1ff617b8d2eafbd21e0febdb66d8473e6d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.72ex; height:2.843ex;" alt="{\displaystyle \left(B_{\text{n}}\right)}" /></span>: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}{\text{(volts)}}A_{\mathrm {eq} }&=A\left(1-{\frac {1}{n+1}}\right)\\{\text{(volts)}}B_{\text{1..n}}&={\frac {A}{n}}\left(1-{\frac {1}{n+1}}\right)\\A-B&=0\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mtext>(volts)</mtext> </mrow> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">q</mi> </mrow> </mrow> </msub> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>A</mi> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mtext>(volts)</mtext> </mrow> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>1..n</mtext> </mrow> </msub> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>A</mi> <mi>n</mi> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>A</mi> <mo>−</mo> <mi>B</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mn>0</mn> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}{\text{(volts)}}A_{\mathrm {eq} }&=A\left(1-{\frac {1}{n+1}}\right)\\{\text{(volts)}}B_{\text{1..n}}&={\frac {A}{n}}\left(1-{\frac {1}{n+1}}\right)\\A-B&=0\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d839242befd85c00935f8a3fcbd960d0bcb51e2" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -7.171ex; width:31.788ex; height:15.509ex;" alt="{\displaystyle {\begin{aligned}{\text{(volts)}}A_{\mathrm {eq} }&=A\left(1-{\frac {1}{n+1}}\right)\\{\text{(volts)}}B_{\text{1..n}}&={\frac {A}{n}}\left(1-{\frac {1}{n+1}}\right)\\A-B&=0\end{aligned}}}" /></span></dd> <dd><b>Note:</b> This is only correct if all capacitance values are equal.</dd> <dd>The power transferred in this arrangement is: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P={\frac {1}{R}}\cdot {\frac {1}{n+1}}A_{\text{volts}}\left(A_{\text{farads}}+B_{\text{farads}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>R</mi> </mfrac> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> </mrow> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>volts</mtext> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>farads</mtext> </mrow> </msub> <mo>+</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>farads</mtext> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P={\frac {1}{R}}\cdot {\frac {1}{n+1}}A_{\text{volts}}\left(A_{\text{farads}}+B_{\text{farads}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/80ebe7a1fe393959ca320417028b5e0f4654af6d" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:38.483ex; height:5.343ex;" alt="{\displaystyle P={\frac {1}{R}}\cdot {\frac {1}{n+1}}A_{\text{volts}}\left(A_{\text{farads}}+B_{\text{farads}}\right)}" /></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Non-ideal_behavior">Non-ideal behavior</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=14" title="Edit section: Non-ideal behavior"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><span class="anchor" id="Non-ideal_behavior"></span> In practice, capacitors deviate from the ideal capacitor equation in several aspects. Some of these, such as leakage current and parasitic effects are linear, or can be analyzed as nearly linear, and can be accounted for by adding virtual components to form <a class="mw-selflink-fragment" href="#Equivalent_circuit">an equivalent circuit</a>. The usual methods of <a href="/wiki/Network_analysis_(electrical_circuits)" title="Network analysis (electrical circuits)">network analysis</a> can then be applied.<sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> In other cases, such as with breakdown voltage, the effect is non-linear and ordinary (normal, e.g., linear) network analysis cannot be used, the effect must be considered separately. Yet another group of artifacts may exist, including temperature dependence, that may be linear but invalidates the assumption in the analysis that capacitance is a constant. Finally, combined parasitic effects such as inherent inductance, resistance, or dielectric losses can exhibit non-uniform behavior at varying frequencies of operation. </p> <div class="mw-heading mw-heading3"><h3 id="Breakdown_voltage"><span class="anchor" id="sparking"></span>Breakdown voltage</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=15" title="Edit section: Breakdown voltage"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Breakdown_voltage" title="Breakdown voltage">Breakdown voltage</a></div> <p>Above a particular electric field strength, known as the dielectric strength <i>E<sub>ds</sub></i>, the dielectric in a capacitor becomes conductive. The voltage at which this occurs is called the breakdown voltage of the device, and is given by the product of the dielectric strength and the separation between the conductors,<sup id="cite_ref-FOOTNOTEUlaby1999170_36-0" class="reference"><a href="#cite_note-FOOTNOTEUlaby1999170-36"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{\text{bd}}=E_{\text{ds}}d}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>bd</mtext> </mrow> </msub> <mo>=</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ds</mtext> </mrow> </msub> <mi>d</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{\text{bd}}=E_{\text{ds}}d}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d2425ee406f69eb4a4bae3d403bb1bd097eb2687" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.239ex; height:2.509ex;" alt="{\displaystyle V_{\text{bd}}=E_{\text{ds}}d}" /></span> </p><p>The maximum energy that can be stored safely in a capacitor is limited by the breakdown voltage. Exceeding this voltage can result in a short circuit between the plates, which can often cause permanent damage to the dielectric, plates, or both. Due to the scaling of capacitance and breakdown voltage with dielectric thickness, all capacitors made with a particular dielectric have approximately equal maximum <a href="/wiki/Energy_density" title="Energy density">energy density</a>, to the extent that the dielectric dominates their volume.<sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> </p><p>For air dielectric capacitors the breakdown field strength is of the order 2–5 MV/m (or kV/mm); for <a href="/wiki/Mica" title="Mica">mica</a> the breakdown is 100–300 MV/m; for oil, 15–25 MV/m; it can be much less when other materials are used for the dielectric.<sup id="cite_ref-38" class="reference"><a href="#cite_note-38"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> The dielectric is used in very thin layers and so absolute breakdown voltage of capacitors is limited. Typical ratings for capacitors used for general <a href="/wiki/Electronics" title="Electronics">electronics</a> applications range from a few volts to 1 kV. As the voltage increases, the dielectric must be thicker, making high-voltage capacitors larger per capacitance than those rated for lower voltages. </p><p>The breakdown voltage is critically affected by factors such as the geometry of the capacitor conductive parts; sharp edges or points increase the electric field strength at that point and can lead to a local breakdown. Once this starts to happen, the breakdown quickly tracks through the dielectric until it reaches the opposite plate, leaving carbon behind and causing a short (or relatively low resistance) circuit. The results can be explosive, as the short in the capacitor draws current from the surrounding circuitry and dissipates the energy.<sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> However, in capacitors with particular dielectrics<sup id="cite_ref-40" class="reference"><a href="#cite_note-40"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> and thin metal electrodes, shorts are not formed after breakdown. It happens because a metal melts or evaporates in a breakdown vicinity, isolating it from the rest of the capacitor.<sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-43" class="reference"><a href="#cite_note-43"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> </p><p>The usual breakdown route is that the field strength becomes large enough to pull electrons in the dielectric from their atoms thus causing conduction. Other scenarios are possible, such as impurities in the dielectric, and, if the dielectric is of a crystalline nature, imperfections in the crystal structure can result in an <a href="/wiki/Avalanche_breakdown" title="Avalanche breakdown">avalanche breakdown</a> as seen in semi-conductor devices. Breakdown voltage is also affected by pressure, humidity and temperature.<sup id="cite_ref-44" class="reference"><a href="#cite_note-44"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Equivalent_circuit">Equivalent circuit</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=16" title="Edit section: Equivalent circuit"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size skin-invert-image" typeof="mw:File/Thumb"><a href="/wiki/File:Real_capacitor_model_adding_inductance_and_series_and_parallel_resistance.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/44/Real_capacitor_model_adding_inductance_and_series_and_parallel_resistance.svg/260px-Real_capacitor_model_adding_inductance_and_series_and_parallel_resistance.svg.png" decoding="async" width="260" height="152" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/44/Real_capacitor_model_adding_inductance_and_series_and_parallel_resistance.svg/390px-Real_capacitor_model_adding_inductance_and_series_and_parallel_resistance.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/44/Real_capacitor_model_adding_inductance_and_series_and_parallel_resistance.svg/520px-Real_capacitor_model_adding_inductance_and_series_and_parallel_resistance.svg.png 2x" data-file-width="166" data-file-height="97" /></a><figcaption>Real capacitor model that adds an inductance and resistance in series and a conductance in parallel to its capacitance. Its total impedance is: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}Z_{\Sigma }&{=}Z_{\text{ESL}}+R_{\text{lead}}+(Z_{\text{C}}\parallel G_{\text{dielectric}})\\&{=}j\omega \cdot {\text{ESL}}+R_{\text{lead}}+{\frac {1}{j\omega \cdot C+G_{\text{dielectric}}}}.\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Σ</mi> </mrow> </msub> </mtd> <mtd> <mi></mi> <mrow class="MJX-TeXAtom-ORD"> <mo>=</mo> </mrow> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ESL</mtext> </mrow> </msub> <mo>+</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>lead</mtext> </mrow> </msub> <mo>+</mo> <mo stretchy="false">(</mo> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>C</mtext> </mrow> </msub> <mo>∥</mo> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>dielectric</mtext> </mrow> </msub> <mo stretchy="false">)</mo> </mtd> </mtr> <mtr> <mtd></mtd> <mtd> <mi></mi> <mrow class="MJX-TeXAtom-ORD"> <mo>=</mo> </mrow> <mi>j</mi> <mi>ω</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>ESL</mtext> </mrow> <mo>+</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>lead</mtext> </mrow> </msub> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>j</mi> <mi>ω</mi> <mo>⋅</mo> <mi>C</mi> <mo>+</mo> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>dielectric</mtext> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>.</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}Z_{\Sigma }&{=}Z_{\text{ESL}}+R_{\text{lead}}+(Z_{\text{C}}\parallel G_{\text{dielectric}})\\&{=}j\omega \cdot {\text{ESL}}+R_{\text{lead}}+{\frac {1}{j\omega \cdot C+G_{\text{dielectric}}}}.\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/18fc30d575ac51ab1e02d315da6c98388ea1316d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.629ex; margin-bottom: -0.209ex; width:43.3ex; height:8.843ex;" alt="{\displaystyle {\begin{aligned}Z_{\Sigma }&{=}Z_{\text{ESL}}+R_{\text{lead}}+(Z_{\text{C}}\parallel G_{\text{dielectric}})\\&{=}j\omega \cdot {\text{ESL}}+R_{\text{lead}}+{\frac {1}{j\omega \cdot C+G_{\text{dielectric}}}}.\end{aligned}}}" /></span></figcaption></figure> <p>An ideal capacitor only stores and releases electrical energy, without dissipation. In practice, capacitors have imperfections within the capacitor's materials that result in the following parasitic components:<sup id="cite_ref-45" class="reference"><a href="#cite_note-45"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{ESL}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>ESL</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{ESL}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1ca47fd3b03cf6612a1281b873c6f50597eaf6cf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.328ex; height:2.176ex;" alt="{\displaystyle {\text{ESL}}}" /></span>, the <i><a href="/wiki/Equivalent_series_inductance" title="Equivalent series inductance">equivalent series inductance</a>,</i> due to the leads. This is usually significant only at relatively high frequencies.</li> <li>Two resistances that add a <a href="/wiki/Real_number" title="Real number">real-valued</a> component to the total impedance, which wastes power: <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{\text{lead}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>lead</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{\text{lead}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b19a95c3b0453bb4f1c27e83f91b5bdab7cb45eb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.92ex; height:2.509ex;" alt="{\displaystyle R_{\text{lead}}}" /></span>, a small series resistance in the <a href="/wiki/Lead_(electronics)" title="Lead (electronics)">leads</a>. Becomes more relevant as frequency increases.</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G_{\text{dielectric}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>dielectric</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G_{\text{dielectric}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fbf403a637d56b7802b6047d4f1cc8d4e67b1da8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.549ex; height:2.509ex;" alt="{\displaystyle G_{\text{dielectric}}}" /></span>, a small <a href="/wiki/Electrical_Conductance" class="mw-redirect" title="Electrical Conductance">conductance</a> (or reciprocally, a large resistance) in parallel with the capacitance, to account for imperfect dielectric material. This causes a small leakage current across the dielectric (see <a href="#Leakage">§ Leakage</a>)<sup id="cite_ref-FOOTNOTEUlaby1999169_46-0" class="reference"><a href="#cite_note-FOOTNOTEUlaby1999169-46"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> that slowly discharges the capacitor over time. This conductance dominates the total resistance at very low frequencies. Its value varies greatly depending on the capacitor material and quality.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="Probably should find citation giving numbers for different types of capacitors. (September 2023)">citation needed</span></a></i>]</sup></li></ul></li></ul> <div class="mw-heading mw-heading4"><h4 id="Simplified_RLC_series_model">Simplified RLC series model</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=17" title="Edit section: Simplified RLC series model"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size skin-invert-image" typeof="mw:File/Thumb"><a href="/wiki/File:ESL_ESR_capacitor_model.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/ESL_ESR_capacitor_model.svg/220px-ESL_ESR_capacitor_model.svg.png" decoding="async" width="220" height="62" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/ESL_ESR_capacitor_model.svg/330px-ESL_ESR_capacitor_model.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/72/ESL_ESR_capacitor_model.svg/440px-ESL_ESR_capacitor_model.svg.png 2x" data-file-width="150" data-file-height="42" /></a><figcaption>Simplified <a href="/wiki/RLC_circuit#Series_circuit" title="RLC circuit">RLC series</a> capacitor model. Its total equivalent impedance is: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle j\omega \cdot {\text{ESL}}+{\text{ESR}}-{\frac {j}{\omega \cdot C}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>j</mi> <mi>ω</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>ESL</mtext> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>ESR</mtext> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>j</mi> <mrow> <mi>ω</mi> <mo>⋅</mo> <mi>C</mi> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle j\omega \cdot {\text{ESL}}+{\text{ESR}}-{\frac {j}{\omega \cdot C}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d5e1470c7feaadb07d6ded50eb4efcb6e7b5dd0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; margin-left: -0.027ex; width:25.079ex; height:5.509ex;" alt="{\displaystyle j\omega \cdot {\text{ESL}}+{\text{ESR}}-{\frac {j}{\omega \cdot C}}.}" /></span></figcaption></figure> <figure class="mw-default-size skin-invert-image" typeof="mw:File/Thumb"><a href="/wiki/File:RLC_Series_Circuit_Bode_Magnitude_Plot,_relative_to_natural_frequency.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/RLC_Series_Circuit_Bode_Magnitude_Plot%2C_relative_to_natural_frequency.svg/260px-RLC_Series_Circuit_Bode_Magnitude_Plot%2C_relative_to_natural_frequency.svg.png" decoding="async" width="260" height="191" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/RLC_Series_Circuit_Bode_Magnitude_Plot%2C_relative_to_natural_frequency.svg/390px-RLC_Series_Circuit_Bode_Magnitude_Plot%2C_relative_to_natural_frequency.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/RLC_Series_Circuit_Bode_Magnitude_Plot%2C_relative_to_natural_frequency.svg/520px-RLC_Series_Circuit_Bode_Magnitude_Plot%2C_relative_to_natural_frequency.svg.png 2x" data-file-width="1445" data-file-height="1063" /></a><figcaption><a href="/wiki/Bode_magnitude_plot" class="mw-redirect" title="Bode magnitude plot">Bode magnitude plot</a> of voltages in an RLC circuit. Frequency is relative to the natural frequency <i>ω</i><sub>0</sub>. (Its <a href="/wiki/Damping#Damping_ratio_definition" title="Damping">damping ratio</a> <i>ζ</i> and <i>ω</i><sub>0</sub> would depend on the particular capacitor.) Lower frequencies are more capacitive. Around <i>ω</i><sub>0</sub>, the total impedance and voltage drop is primarily resistive. Higher frequencies are more inductive.</figcaption></figure> <p>As frequency increases, the capacitive impedance (a negative reactance) reduces, so the dielectric's conductance becomes less important and the series components become more significant. Thus, a simplified <a href="/wiki/RLC_circuit#Series_circuit" title="RLC circuit">RLC series</a> model valid for a large frequency range simply treats the capacitor as being in series with an equivalent series inductance <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{ESL}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>ESL</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{ESL}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1ca47fd3b03cf6612a1281b873c6f50597eaf6cf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.328ex; height:2.176ex;" alt="{\displaystyle {\text{ESL}}}" /></span> and a frequency-dependent <i><a href="/wiki/Equivalent_series_resistance" title="Equivalent series resistance">equivalent series resistance</a></i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{ESR}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>ESR</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{ESR}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/15c9e41bf1e753f4cbc096edd857ae295795498a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.586ex; height:2.176ex;" alt="{\displaystyle {\text{ESR}}}" /></span>, which varies little with frequency. Unlike the previous model, this model is not valid at <a href="/wiki/DC_component" class="mw-redirect" title="DC component">DC</a> and very low frequencies where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G_{\text{dielectric}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>dielectric</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G_{\text{dielectric}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fbf403a637d56b7802b6047d4f1cc8d4e67b1da8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.549ex; height:2.509ex;" alt="{\displaystyle G_{\text{dielectric}}}" /></span> is relevant. </p><p>Inductive reactance increases with frequency. Because its sign is positive, it counteracts the capacitance. </p><p>At the RLC circuit's <a href="/wiki/Natural_frequency" title="Natural frequency">natural frequency</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega _{0}{=}{\tfrac {1}{\sqrt {{\text{ESL}}\cdot {\text{C}}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>=</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <msqrt> <mrow class="MJX-TeXAtom-ORD"> <mtext>ESL</mtext> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>C</mtext> </mrow> </msqrt> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega _{0}{=}{\tfrac {1}{\sqrt {{\text{ESL}}\cdot {\text{C}}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2799cfc2773c0bbc3e177ff141d718b1696d292f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:11.218ex; height:4.176ex;" alt="{\displaystyle \omega _{0}{=}{\tfrac {1}{\sqrt {{\text{ESL}}\cdot {\text{C}}}}}}" /></span>, the inductance perfectly cancels the capacitance, so total reactance is zero. Since the total impedance at <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega _{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega _{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9a713d16c489051d4f515e12b1f86061c6be799b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.5ex; height:2.009ex;" alt="{\displaystyle \omega _{0}}" /></span> is just the real-value of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{ESR}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>ESR</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{ESR}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/15c9e41bf1e753f4cbc096edd857ae295795498a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.586ex; height:2.176ex;" alt="{\displaystyle {\text{ESR}}}" /></span>, <a href="/wiki/Root_mean_square#Average_power" title="Root mean square">average power</a> dissipation reaches its maximum of <style data-mw-deduplicate="TemplateStyles:r1214402035">.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="sfrac">⁠<span class="tion"><span class="num">V<sub>RMS</sub><sup>2</sup></span><span class="sr-only">/</span><span class="den">ESR</span></span>⁠</span>, where V<sub>RMS</sub> is the <a href="/wiki/Root_mean_square_voltage" class="mw-redirect" title="Root mean square voltage">root mean square (RMS) voltage</a> across the capacitor. </p><p>At even higher frequencies, the inductive impedance dominates, so the capacitor undesirably behaves instead like an inductor. High-frequency engineering involves accounting for the inductance of all connections and components. </p> <div class="mw-heading mw-heading5"><h5 id="Q_factor">Q factor</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=18" title="Edit section: Q factor"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Dielectric_loss#Discrete_circuit_perspective" title="Dielectric loss">Dielectric loss § Discrete circuit perspective</a></div> <p>For a simplified model of a capacitor as an ideal capacitor in series with an <a href="/wiki/Equivalent_series_resistance" title="Equivalent series resistance">equivalent series resistance</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{ESR}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>ESR</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{ESR}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/15c9e41bf1e753f4cbc096edd857ae295795498a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.586ex; height:2.176ex;" alt="{\displaystyle {\text{ESR}}}" /></span>, the capacitor's <a href="/wiki/Q_factor" title="Q factor">quality factor</a> (or <i>Q</i>) is the ratio of the magnitude of its <a href="/wiki/Electrical_reactance#Capacitive_reactance" title="Electrical reactance">capacitive reactance</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X_{C}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X_{C}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bbe98111b842bc759e8ca808cfc6a23d3b2b0317" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.406ex; height:2.509ex;" alt="{\displaystyle X_{C}}" /></span> to its resistance at a given <a href="/wiki/Angular_frequency" title="Angular frequency">frequency</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48eff443f9de7a985bb94ca3bde20813ea737be8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.446ex; height:1.676ex;" alt="{\displaystyle \omega }" /></span>: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q(\omega )={\frac {|X_{C}(\omega )|}{\text{ESR}}}={\frac {1}{\omega C\cdot {\text{ESR}}}}\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> <mo stretchy="false">(</mo> <mi>ω</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>ω</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mrow> <mtext>ESR</mtext> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>ω</mi> <mi>C</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>ESR</mtext> </mrow> </mrow> </mfrac> </mrow> <mspace width="thinmathspace"></mspace> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q(\omega )={\frac {|X_{C}(\omega )|}{\text{ESR}}}={\frac {1}{\omega C\cdot {\text{ESR}}}}\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0a188bcdc7dc74bb767a25e6944752ebf94ee6" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:31.428ex; height:5.843ex;" alt="{\displaystyle Q(\omega )={\frac {|X_{C}(\omega )|}{\text{ESR}}}={\frac {1}{\omega C\cdot {\text{ESR}}}}\,.}" /></span> </p><p>The Q factor is a measure of its efficiency: the higher the Q factor of the capacitor, the closer it approaches the behavior of an ideal capacitor. <a href="/wiki/Dissipation_factor" title="Dissipation factor">Dissipation factor</a> is its reciprocal. </p> <div class="mw-heading mw-heading3"><h3 id="Ripple_current">Ripple current</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=19" title="Edit section: Ripple current"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Ripple_(electrical)" title="Ripple (electrical)">Ripple</a> current is the AC component of an applied source (often a <a href="/wiki/Switched-mode_power_supply" title="Switched-mode power supply">switched-mode power supply</a>) whose frequency may be constant or varying. Ripple current causes heat to be generated within the capacitor due to the dielectric losses caused by the changing field strength together with the current flow across the slightly resistive supply lines or the electrolyte in the capacitor. The equivalent series resistance (ESR) is the amount of internal series resistance one would add to a perfect capacitor to model this. </p><p>Some <a href="/wiki/Types_of_capacitor" class="mw-redirect" title="Types of capacitor">types of capacitors</a>, primarily <a href="/wiki/Tantalum" title="Tantalum">tantalum</a> and <a href="/wiki/Aluminum" class="mw-redirect" title="Aluminum">aluminum</a> <a href="/wiki/Electrolytic_capacitor" title="Electrolytic capacitor">electrolytic capacitors</a>, as well as some <a href="/wiki/Film_capacitor" title="Film capacitor">film capacitors</a> have a specified rating value for maximum ripple current. </p> <ul><li>Tantalum electrolytic capacitors with solid manganese dioxide electrolyte are limited by ripple current and generally have the highest ESR ratings in the capacitor family. Exceeding their ripple limits can lead to shorts and burning parts.</li> <li>Aluminum electrolytic capacitors, the most common type of electrolytic, suffer a shortening of life expectancy at higher ripple currents. If ripple current exceeds the rated value of the capacitor, it tends to result in explosive failure.</li> <li><a href="/wiki/Ceramic_capacitor" title="Ceramic capacitor">Ceramic capacitors</a> generally have no ripple current limitation<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="everything has a current limitation, even if it is not specified. (October 2020)">citation needed</span></a></i>]</sup> and have some of the lowest ESR ratings.</li> <li><a href="/wiki/Film_capacitor" title="Film capacitor">Film capacitors</a> have very low ESR ratings but exceeding rated ripple current may cause degradation failures.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Capacitance_instability">Capacitance instability</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=20" title="Edit section: Capacitance instability"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The capacitance of certain capacitors decreases as the component ages. In <a href="/wiki/Ceramic_capacitor" title="Ceramic capacitor">ceramic capacitors</a>, this is caused by degradation of the dielectric. The type of dielectric, ambient operating and storage temperatures are the most significant aging factors, while the operating voltage usually has a smaller effect, i.e., usual capacitor design is to minimize voltage coefficient. The aging process may be reversed by heating the component above the <a href="/wiki/Curie_point" class="mw-redirect" title="Curie point">Curie point</a>. Aging is fastest near the beginning of life of the component, and the device stabilizes over time.<sup id="cite_ref-47" class="reference"><a href="#cite_note-47"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup> Electrolytic capacitors age as the <a href="/wiki/Electrolytic_capacitor#Electrical_behavior_of_electrolytics" title="Electrolytic capacitor">electrolyte evaporates</a>. In contrast with ceramic capacitors, this occurs towards the end of life of the component. </p><p>Temperature dependence of capacitance is usually expressed in parts per million (ppm) per °C. It can usually be taken as a broadly linear function but can be noticeably non-linear at the temperature extremes. The temperature coefficient may be positive or negative, depending mostly on the dielectric material. Some, designated C0G/NP0, but called <b>NPO</b>, have a somewhat negative coefficient at one temperature, positive at another, and zero in between. Such components may be specified for temperature-critical circuits.<sup id="cite_ref-48" class="reference"><a href="#cite_note-48"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> </p><p>Capacitors, especially ceramic capacitors, and older designs such as paper capacitors, can absorb sound waves resulting in a <a href="/wiki/Microphonic" class="mw-redirect" title="Microphonic">microphonic</a> effect. Vibration moves the plates, causing the capacitance to vary, in turn inducing AC current. Some dielectrics also generate <a href="/wiki/Piezoelectricity" title="Piezoelectricity">piezoelectricity</a>. The resulting interference is especially problematic in audio applications, potentially causing feedback or unintended recording. In the reverse microphonic effect, the varying electric field between the capacitor plates exerts a physical force, moving them as a speaker. This can generate audible sound, but drains energy and stresses the dielectric and the electrolyte, if any. </p> <div class="mw-heading mw-heading3"><h3 id="Current_and_voltage_reversal">Current and voltage reversal</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=21" title="Edit section: Current and voltage reversal"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Current reversal occurs when the current changes direction. Voltage reversal is the change of polarity in a circuit. Reversal is generally described as the percentage of the maximum rated voltage that reverses polarity. In DC circuits, this is usually less than 100%, often in the range of 0 to 90%, whereas AC circuits experience 100% reversal. </p><p>In DC circuits and pulsed circuits, current and voltage reversal are affected by the <a href="/wiki/Damping_ratio" class="mw-redirect" title="Damping ratio">damping</a> of the system. Voltage reversal is encountered in <a href="/wiki/RLC_circuits" class="mw-redirect" title="RLC circuits">RLC circuits</a> that are <a href="/wiki/Underdamped" class="mw-redirect" title="Underdamped">underdamped</a>. The current and voltage reverse direction, forming a <a href="/wiki/Harmonic_oscillator" title="Harmonic oscillator">harmonic oscillator</a> between the <a href="/wiki/Inductance" title="Inductance">inductance</a> and capacitance. The current and voltage tends to oscillate and may reverse direction several times, with each peak being lower than the previous, until the system reaches an equilibrium. This is often referred to as <a href="/wiki/Ringing_(signal)" title="Ringing (signal)">ringing</a>. In comparison, <a href="/wiki/Critically_damped" class="mw-redirect" title="Critically damped">critically damped</a> or <a href="/wiki/Overdamped" class="mw-redirect" title="Overdamped">overdamped</a> systems usually do not experience a voltage reversal. Reversal is also encountered in AC circuits, where the peak current is equal in each direction. </p><p>For maximum life, capacitors usually need to be able to handle the maximum amount of reversal that a system may experience. An AC circuit experiences 100% voltage reversal, while underdamped DC circuits experience less than 100%. Reversal creates excess electric fields in the dielectric, causes excess heating of both the dielectric and the conductors, and can dramatically shorten the life expectancy of the capacitor. Reversal ratings often affect the design considerations for the capacitor, from the choice of dielectric materials and voltage ratings to the types of internal connections used.<sup id="cite_ref-49" class="reference"><a href="#cite_note-49"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Dielectric_absorption">Dielectric absorption</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=22" title="Edit section: Dielectric absorption"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Capacitors made with any type of dielectric material show some level of "<a href="/wiki/Dielectric_absorption" title="Dielectric absorption">dielectric absorption</a>" or "soakage". On discharging a capacitor and disconnecting it, after a short time it may develop a voltage due to hysteresis in the dielectric. This effect is objectionable in applications such as precision <a href="/wiki/Sample_and_hold" title="Sample and hold">sample and hold</a> circuits or timing circuits. The level of absorption depends on many factors, from design considerations to charging time, since the absorption is a time-dependent process. However, the primary factor is the type of dielectric material. Capacitors such as tantalum electrolytic or <a href="/wiki/Polysulfone" title="Polysulfone">polysulfone</a> film exhibit relatively high absorption, while <a href="/wiki/Polystyrene" title="Polystyrene">polystyrene</a> or <a href="/wiki/Teflon" class="mw-redirect" title="Teflon">Teflon</a> allow very small levels of absorption.<sup id="cite_ref-Kaiser2012_50-0" class="reference"><a href="#cite_note-Kaiser2012-50"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup> In some capacitors where dangerous voltages and energies exist, such as in <a href="/wiki/Flashtube" title="Flashtube">flashtubes</a>, <a href="/wiki/Television_set" title="Television set">television sets</a>, <a href="/wiki/Microwave_oven" title="Microwave oven">microwave ovens</a> and <a href="/wiki/Defibrillator" class="mw-redirect" title="Defibrillator">defibrillators</a>, the dielectric absorption can recharge the capacitor to hazardous voltages after it has been shorted or discharged. Any capacitor containing over 10 joules of energy is generally considered hazardous, while 50 joules or higher is potentially lethal. A capacitor may regain anywhere from 0.01 to 20% of its original charge over a period of several minutes, allowing a seemingly safe capacitor to become surprisingly dangerous.<sup id="cite_ref-51" class="reference"><a href="#cite_note-51"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-52" class="reference"><a href="#cite_note-52"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Prutchi2012_53-0" class="reference"><a href="#cite_note-Prutchi2012-53"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-DixitYadav2010_54-0" class="reference"><a href="#cite_note-DixitYadav2010-54"><span class="cite-bracket">[</span>53<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-ReferenceA_55-0" class="reference"><a href="#cite_note-ReferenceA-55"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Leakage">Leakage</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=23" title="Edit section: Leakage"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>No material is a perfect insulator, thus all dielectrics allow some small level of current to leak through, which can be measured with a <a href="/wiki/Megohmmeter" title="Megohmmeter">megohmmeter</a>.<sup id="cite_ref-56" class="reference"><a href="#cite_note-56"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup> Leakage is equivalent to a resistor in parallel with the capacitor. Constant exposure to factors such as heat, mechanical stress, or humidity can cause the dielectric to deteriorate resulting in excessive leakage, a problem often seen in older vacuum tube circuits, particularly where oiled paper and foil capacitors were used. In many vacuum tube circuits, interstage coupling capacitors are used to conduct a varying signal from the plate of one tube to the grid circuit of the next stage. A leaky capacitor can cause the grid circuit voltage to be raised from its normal bias setting, causing excessive current or signal distortion in the downstream tube. In power amplifiers this can cause the plates to glow red, or current limiting resistors to overheat, even fail. Similar considerations apply to component fabricated solid-state (transistor) amplifiers, but, owing to lower heat production and the use of modern polyester dielectric-barriers, this once-common problem has become relatively rare. </p> <div class="mw-heading mw-heading3"><h3 id="Electrolytic_failure_from_disuse">Electrolytic failure from disuse</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=24" title="Edit section: Electrolytic failure from disuse"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Aluminum_electrolytic_capacitor" title="Aluminum electrolytic capacitor">Aluminum electrolytic capacitors</a> are <i>conditioned</i> when manufactured by applying a voltage sufficient to initiate the proper internal chemical state. This state is maintained by regular use of the equipment. If a system using electrolytic capacitors is unused for a long period of time it can <a href="/wiki/Aluminum_electrolytic_capacitor#Capacitor_behavior_after_storage_or_disuse" title="Aluminum electrolytic capacitor">lose its conditioning</a>. Sometimes they fail with a short circuit when next operated. </p> <div class="mw-heading mw-heading3"><h3 id="Lifespan">Lifespan</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=25" title="Edit section: Lifespan"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>All capacitors have varying lifespans, depending upon their construction, operational conditions, and environmental conditions. Solid-state ceramic capacitors generally have very long lives under normal use, which has little dependency on factors such as vibration or ambient temperature, but factors like humidity, mechanical stress, and <a href="/wiki/Fatigue_(material)" title="Fatigue (material)">fatigue</a> play a primary role in their failure. Failure modes may differ. Some capacitors may experience a gradual loss of capacitance, increased leakage or an increase in <a href="/wiki/Equivalent_series_resistance" title="Equivalent series resistance">equivalent series resistance</a> (ESR), while others may fail suddenly or even <a href="/wiki/Catastrophic_failure" title="Catastrophic failure">catastrophically</a>. For example, metal-film capacitors are more prone to damage from stress and humidity, but will self-heal when a breakdown in the dielectric occurs. The formation of a <a href="/wiki/Glow_discharge" title="Glow discharge">glow discharge</a> at the point of failure prevents arcing by vaporizing the metallic film in that spot, neutralizing any short circuit with minimal loss in capacitance. When enough pinholes accumulate in the film, a total failure occurs in a metal-film capacitor, generally happening suddenly without warning. </p><p>Electrolytic capacitors generally have the shortest lifespans. Electrolytic capacitors are affected very little by vibration or humidity, but factors such as ambient and operational temperatures play a large role in their failure, which gradually occur as an increase in ESR (up to 300%) and as much as a 20% decrease in capacitance. The capacitors contain electrolytes which will eventually diffuse through the seals and evaporate. An increase in temperature also increases internal pressure, and increases the reaction rate of the chemicals. Thus, the life of an electrolytic capacitor is generally defined by a modification of the <a href="/wiki/Arrhenius_equation" title="Arrhenius equation">Arrhenius equation</a>, which is used to determine chemical-reaction rates: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L=Be^{\frac {e_{A}}{kT_{o}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mo>=</mo> <mi>B</mi> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mrow> <mi>k</mi> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>o</mi> </mrow> </msub> </mrow> </mfrac> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L=Be^{\frac {e_{A}}{kT_{o}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/79be102d0711f7a6eb87bdbae149dcb3879d908f" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:10.853ex; height:4.009ex;" alt="{\displaystyle L=Be^{\frac {e_{A}}{kT_{o}}}}" /></span> </p><p>Manufacturers often use this equation to supply an expected lifespan, in hours, for electrolytic capacitors when used at their designed operating temperature, which is affected by both ambient temperature, ESR, and ripple current. However, these ideal conditions may not exist in every use. The rule of thumb for predicting lifespan under different conditions of use is determined by: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L_{a}=L_{0}2^{\frac {T_{0}-T_{a}}{10}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> </mrow> <mn>10</mn> </mfrac> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{a}=L_{0}2^{\frac {T_{0}-T_{a}}{10}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf33b8bf240852226f0ba4a046a02555d935f20d" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.888ex; height:4.343ex;" alt="{\displaystyle L_{a}=L_{0}2^{\frac {T_{0}-T_{a}}{10}}}" /></span> </p><p>This says that the capacitor's life decreases by half for every 10 degrees Celsius that the temperature is increased,<sup id="cite_ref-57" class="reference"><a href="#cite_note-57"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup> where: </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/db742b8c210fc611329a4c2dcc3af4b4e1a110cb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.637ex; height:2.509ex;" alt="{\displaystyle L_{0}}" /></span> is the rated life under rated conditions, e.g. 2000 hours</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/55b9e7d7b96196b5a6a26f4349caa3ac82fd67e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.412ex; height:2.509ex;" alt="{\displaystyle T_{0}}" /></span> is the rated max/min operational temperature</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{a}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{a}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d54b73a473771885bb5d025ecd2fb10469ab859d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.459ex; height:2.509ex;" alt="{\displaystyle T_{a}}" /></span> is the average operational temperature</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L_{a}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{a}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87a7bf511194a88867e63c66594f8c06f106bbbb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.685ex; height:2.509ex;" alt="{\displaystyle L_{a}}" /></span> is the expected lifespan under given conditions</li></ul> <div class="mw-heading mw-heading2"><h2 id="Capacitor_types">Capacitor types</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=26" title="Edit section: Capacitor types"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Capacitor_types" title="Capacitor types">Capacitor types</a></div> <p>Practical capacitors are available commercially in many different forms. The type of internal dielectric, the structure of the plates and the device packaging all strongly affect the characteristics of the capacitor, and its applications. </p><p>Values available range from very low (picofarad range; while arbitrarily low values are in principle possible, stray (parasitic) capacitance in any circuit is the limiting factor) to about 5 kF <a href="/wiki/Electric_double-layer_capacitor" class="mw-redirect" title="Electric double-layer capacitor">supercapacitors</a>. </p><p>Above approximately 1 microfarad electrolytic capacitors are usually used because of their small size and low cost compared with other types, unless their relatively poor stability, life and polarised nature make them unsuitable. Very high capacity supercapacitors use a porous carbon-based electrode material. </p> <div class="mw-heading mw-heading3"><h3 id="Dielectric_materials">Dielectric materials</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=27" title="Edit section: Dielectric materials"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Condensators.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/Condensators.JPG/260px-Condensators.JPG" decoding="async" width="260" height="96" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/Condensators.JPG/390px-Condensators.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/de/Condensators.JPG/520px-Condensators.JPG 2x" data-file-width="717" data-file-height="265" /></a><figcaption>An assortment of capacitor types. From left: multilayer ceramic, ceramic disc, multilayer polyester film, tubular ceramic, polystyrene, metalized polyester film, aluminum electrolytic. Major scale divisions are in centimetres.</figcaption></figure> <p>Most capacitors have a dielectric spacer, which increases their capacitance compared to air or a vacuum. In order to maximise the charge that a capacitor can hold, the dielectric material needs to have as high a <a href="/wiki/Permittivity" title="Permittivity">permittivity</a> as possible, while also having as high a <a href="/wiki/Breakdown_voltage" title="Breakdown voltage">breakdown voltage</a> as possible. The dielectric also needs to have as low a loss with frequency as possible. </p><p>However, low value capacitors are available with a high vacuum between their plates to allow extremely high voltage operation and low losses. <a href="/wiki/Variable_capacitor" title="Variable capacitor">Variable capacitors</a> with their plates open to the atmosphere were commonly used in radio tuning circuits. Later designs use polymer foil dielectric between the moving and stationary plates, with no significant air space between the plates. </p><p>Several solid dielectrics are available, including <a href="/wiki/Paper" title="Paper">paper</a>, <a href="/wiki/Plastic" title="Plastic">plastic</a>, <a href="/wiki/Glass" title="Glass">glass</a>, <a href="/wiki/Mica" title="Mica">mica</a> and <a href="/wiki/Ceramic" title="Ceramic">ceramic</a>.<sup id="cite_ref-Boggs_17-4" class="reference"><a href="#cite_note-Boggs-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p><p>Paper was used extensively in older capacitors and offers relatively high voltage performance. However, paper absorbs moisture, and has been largely replaced by plastic <a href="/wiki/Film_capacitor" title="Film capacitor">film capacitors</a>. </p><p>Most of the plastic films now used offer better stability and ageing performance than such older dielectrics such as oiled paper, which makes them useful in timer circuits, although they may be limited to relatively low <a href="/wiki/Operating_temperature" title="Operating temperature">operating temperatures</a> and frequencies, because of the limitations of the plastic film being used. Large plastic film capacitors are used extensively in suppression circuits, motor start circuits, and <a href="/wiki/Power-factor_correction" class="mw-redirect" title="Power-factor correction">power-factor correction</a> circuits. </p><p>Ceramic capacitors are generally small, cheap and useful for high frequency applications, although their capacitance varies strongly with voltage and temperature and they age poorly. They can also suffer from the piezoelectric effect. Ceramic capacitors are broadly categorized as <a href="/wiki/EIA_Class_1_dielectric" class="mw-redirect" title="EIA Class 1 dielectric">class 1 dielectrics</a>, which have predictable variation of capacitance with temperature or <a href="/wiki/EIA_Class_2_dielectric" class="mw-redirect" title="EIA Class 2 dielectric">class 2 dielectrics</a>, which can operate at higher voltage. Modern multilayer ceramics are usually quite small, but some types have inherently wide value tolerances, microphonic issues, and are usually physically brittle. </p><p>Glass and mica capacitors are extremely reliable, stable and tolerant to high temperatures and voltages, but are too expensive for most mainstream applications. </p><p>Electrolytic capacitors and <a href="/wiki/Supercapacitor" title="Supercapacitor">supercapacitors</a> are used to store small and larger amounts of energy, respectively, ceramic capacitors are often used in <a href="/wiki/LC_circuit" title="LC circuit">resonators</a>, and <a href="/wiki/Parasitic_capacitance" title="Parasitic capacitance">parasitic capacitance</a> occurs in circuits wherever the simple conductor-insulator-conductor structure is formed unintentionally by the configuration of the circuit layout. </p> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Electronic-Component-Elec-Capacitors.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/28/Electronic-Component-Elec-Capacitors.jpg/220px-Electronic-Component-Elec-Capacitors.jpg" decoding="async" width="220" height="192" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/28/Electronic-Component-Elec-Capacitors.jpg/330px-Electronic-Component-Elec-Capacitors.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/28/Electronic-Component-Elec-Capacitors.jpg/440px-Electronic-Component-Elec-Capacitors.jpg 2x" data-file-width="3000" data-file-height="2620" /></a><figcaption>Three aluminum electrolytic capacitors of varying capacity</figcaption></figure> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Capacitor3Dmodel.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/Capacitor3Dmodel.png/220px-Capacitor3Dmodel.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/Capacitor3Dmodel.png/330px-Capacitor3Dmodel.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/60/Capacitor3Dmodel.png/440px-Capacitor3Dmodel.png 2x" data-file-width="1080" data-file-height="1080" /></a><figcaption>3D model of a capacitor</figcaption></figure> <p><a href="/wiki/Electrolytic_capacitor" title="Electrolytic capacitor">Electrolytic capacitors</a> use an <a href="/wiki/Aluminum" class="mw-redirect" title="Aluminum">aluminum</a> or <a href="/wiki/Tantalum" title="Tantalum">tantalum</a> plate with an oxide dielectric layer. The second electrode is a liquid <a href="/wiki/Electrolyte" title="Electrolyte">electrolyte</a>, connected to the circuit by another foil plate. Electrolytic capacitors offer very high capacitance but suffer from poor tolerances, high instability, gradual loss of capacitance especially when subjected to heat, and high leakage current. <a href="/wiki/Capacitor_plague" title="Capacitor plague">Poor quality capacitors</a> may leak electrolyte, which is harmful to printed circuit boards. The conductivity of the electrolyte drops at low temperatures, which increases equivalent series resistance. While widely used for power-supply conditioning, poor high-frequency characteristics make them unsuitable for many applications. Electrolytic capacitors suffer from self-degradation if unused for a period (around a year), and when full power is applied may short circuit, permanently damaging the capacitor and usually blowing a fuse or causing failure of rectifier diodes. For example, in older equipment, this may cause arcing in rectifier tubes. They can be restored before use by gradually applying the operating voltage, often performed on antique <a href="/wiki/Vacuum_tube" title="Vacuum tube">vacuum tube</a> equipment over a period of thirty minutes by using a variable transformer to supply AC power. The use of this technique may be less satisfactory for some solid state equipment, which may be damaged by operation below its normal power range, requiring that the power supply first be isolated from the consuming circuits. Such remedies may not be applicable to modern high-frequency power supplies as these produce full output voltage even with reduced input.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="how-to (November 2016)">citation needed</span></a></i>]</sup> </p><p>Tantalum capacitors offer better frequency and temperature characteristics than aluminum, but higher <a href="/wiki/Dielectric_absorption" title="Dielectric absorption">dielectric absorption</a> and leakage.<sup id="cite_ref-58" class="reference"><a href="#cite_note-58"><span class="cite-bracket">[</span>57<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Polymer_capacitor" title="Polymer capacitor">Polymer capacitors</a> (OS-CON, OC-CON, KO, AO) use solid conductive polymer (or polymerized organic semiconductor) as electrolyte and offer longer life and lower <a href="/wiki/Equivalent_series_resistance" title="Equivalent series resistance">ESR</a> at higher cost than standard electrolytic capacitors. </p><p>A <a href="/wiki/Feedthrough" title="Feedthrough">feedthrough capacitor</a> is a component that, while not serving as its main use, has capacitance and is used to conduct signals through a conductive sheet. </p><p>Several other types of capacitor are available for specialist applications. <a href="/wiki/Supercapacitor" title="Supercapacitor">Supercapacitors</a> store large amounts of energy. Supercapacitors made from carbon <a href="/wiki/Aerogel" title="Aerogel">aerogel</a>, carbon nanotubes, or highly porous electrode materials, offer extremely high capacitance (up to 5 kF as of 2010<sup class="plainlinks noexcerpt noprint asof-tag update" style="display:none;"><a class="external text" href="https://en.wikipedia.org/w/index.php?title=Capacitor&action=edit">[update]</a></sup>) and can be used in some applications instead of <a href="/wiki/Rechargeable_battery" title="Rechargeable battery">rechargeable batteries</a>. <a href="/wiki/Alternating_current" title="Alternating current">Alternating current</a> capacitors are specifically designed to work on line (mains) voltage AC power circuits. They are commonly used in <a href="/wiki/Electric_motor" title="Electric motor">electric motor</a> circuits and are often designed to handle large currents, so they tend to be physically large. They are usually ruggedly packaged, often in metal cases that can be easily grounded/earthed. They also are designed with <a href="/wiki/Direct_current" title="Direct current">direct current</a> breakdown voltages of at least five times the maximum AC voltage. </p> <div class="mw-heading mw-heading3"><h3 id="Voltage-dependent_capacitors">Voltage-dependent capacitors</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=28" title="Edit section: Voltage-dependent capacitors"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The dielectric constant for a number of very useful dielectrics changes as a function of the applied electrical field, for example <a href="/wiki/Ferroelectric" class="mw-redirect" title="Ferroelectric">ferroelectric</a> materials, so the capacitance for these devices is more complex. For example, in charging such a capacitor the differential increase in voltage with charge is governed by: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle dQ=C(V)\,dV}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>Q</mi> <mo>=</mo> <mi>C</mi> <mo stretchy="false">(</mo> <mi>V</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace"></mspace> <mi>d</mi> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dQ=C(V)\,dV}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4cd1788d54dcb309c928e0187866f5c2814f8394" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.906ex; height:2.843ex;" alt="{\displaystyle dQ=C(V)\,dV}" /></span> where the voltage dependence of capacitance, <span class="texhtml"><i>C</i>(<i>V</i>)</span>, suggests that the capacitance is a function of the electric field strength, which in a large area parallel plate device is given by <span class="texhtml"><i><big>ε</big></i> = <i>V</i>/<i>d</i></span>. This field polarizes the dielectric, which polarization, in the case of a ferroelectric, is a nonlinear <i>S</i>-shaped function of the electric field, which, in the case of a large area parallel plate device, translates into a capacitance that is a nonlinear function of the voltage.<sup id="cite_ref-Araujo_59-0" class="reference"><a href="#cite_note-Araujo-59"><span class="cite-bracket">[</span>58<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Musikant_60-0" class="reference"><a href="#cite_note-Musikant-60"><span class="cite-bracket">[</span>59<span class="cite-bracket">]</span></a></sup> </p><p>Corresponding to the voltage-dependent capacitance, to charge the capacitor to voltage <span class="texhtml mvar" style="font-style:italic;">V</span> an integral relation is found: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q=\int _{0}^{V}C(V)\,dV}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msubsup> <mi>C</mi> <mo stretchy="false">(</mo> <mi>V</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace"></mspace> <mi>d</mi> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q=\int _{0}^{V}C(V)\,dV}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/daa024c091c84ec045264018b82f4380a451d2d1" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:18.037ex; height:6.176ex;" alt="{\displaystyle Q=\int _{0}^{V}C(V)\,dV}" /></span> which agrees with <span class="texhtml"><i>Q</i> = <i>CV</i></span> only when <span class="texhtml mvar" style="font-style:italic;">C</span> does not depend on voltage <span class="texhtml mvar" style="font-style:italic;">V</span>. </p><p>By the same token, the energy stored in the capacitor now is given by <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle dW=Q\,dV=\left[\int _{0}^{V}dV'\,C(V')\right]dV\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>W</mi> <mo>=</mo> <mi>Q</mi> <mspace width="thinmathspace"></mspace> <mi>d</mi> <mi>V</mi> <mo>=</mo> <mrow> <mo>[</mo> <mrow> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msubsup> <mi>d</mi> <msup> <mi>V</mi> <mo>′</mo> </msup> <mspace width="thinmathspace"></mspace> <mi>C</mi> <mo stretchy="false">(</mo> <msup> <mi>V</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> </mrow> <mo>]</mo> </mrow> <mi>d</mi> <mi>V</mi> <mspace width="thinmathspace"></mspace> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dW=Q\,dV=\left[\int _{0}^{V}dV'\,C(V')\right]dV\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6cbac71e27b7dd2c7c9156f89df76670526292c" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:36.685ex; height:6.343ex;" alt="{\displaystyle dW=Q\,dV=\left[\int _{0}^{V}dV'\,C(V')\right]dV\,.}" /></span> </p><p>Integrating: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle W=\int _{0}^{V}dV\int _{0}^{V}dV'\,C(V')=\int _{0}^{V}dV'\int _{V'}^{V}dV\,C(V')=\int _{0}^{V}dV'\left(V-V'\right)C(V')\,,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>W</mi> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msubsup> <mi>d</mi> <mi>V</mi> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msubsup> <mi>d</mi> <msup> <mi>V</mi> <mo>′</mo> </msup> <mspace width="thinmathspace"></mspace> <mi>C</mi> <mo stretchy="false">(</mo> <msup> <mi>V</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msubsup> <mi>d</mi> <msup> <mi>V</mi> <mo>′</mo> </msup> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>V</mi> <mo>′</mo> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msubsup> <mi>d</mi> <mi>V</mi> <mspace width="thinmathspace"></mspace> <mi>C</mi> <mo stretchy="false">(</mo> <msup> <mi>V</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> </mrow> </msubsup> <mi>d</mi> <msup> <mi>V</mi> <mo>′</mo> </msup> <mrow> <mo>(</mo> <mrow> <mi>V</mi> <mo>−</mo> <msup> <mi>V</mi> <mo>′</mo> </msup> </mrow> <mo>)</mo> </mrow> <mi>C</mi> <mo stretchy="false">(</mo> <msup> <mi>V</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> <mspace width="thinmathspace"></mspace> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W=\int _{0}^{V}dV\int _{0}^{V}dV'\,C(V')=\int _{0}^{V}dV'\int _{V'}^{V}dV\,C(V')=\int _{0}^{V}dV'\left(V-V'\right)C(V')\,,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/84cbf7e1b9916ef77cea67450ceca9299925818e" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:81.853ex; height:6.176ex;" alt="{\displaystyle W=\int _{0}^{V}dV\int _{0}^{V}dV'\,C(V')=\int _{0}^{V}dV'\int _{V'}^{V}dV\,C(V')=\int _{0}^{V}dV'\left(V-V'\right)C(V')\,,}" /></span> where interchange of the <a href="/wiki/Order_of_integration_(calculus)" title="Order of integration (calculus)">order of integration</a> is used. </p><p>The nonlinear capacitance of a microscope probe scanned along a ferroelectric surface is used to study the domain structure of ferroelectric materials.<sup id="cite_ref-Cho_61-0" class="reference"><a href="#cite_note-Cho-61"><span class="cite-bracket">[</span>60<span class="cite-bracket">]</span></a></sup> </p><p>Another example of voltage dependent capacitance occurs in <a href="/wiki/Semiconductor_devices" class="mw-redirect" title="Semiconductor devices">semiconductor devices</a> such as semiconductor <a href="/wiki/Diode" title="Diode">diodes</a>, where the voltage dependence stems not from a change in dielectric constant but in a voltage dependence of the spacing between the charges on the two sides of the capacitor.<sup id="cite_ref-FOOTNOTESzeNg2006217_62-0" class="reference"><a href="#cite_note-FOOTNOTESzeNg2006217-62"><span class="cite-bracket">[</span>61<span class="cite-bracket">]</span></a></sup> This effect is intentionally exploited in diode-like devices known as <a href="/wiki/Varicap" title="Varicap">varicaps</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Frequency-dependent_capacitors">Frequency-dependent capacitors</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=29" title="Edit section: Frequency-dependent capacitors"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>If a capacitor is driven with a time-varying voltage that changes rapidly enough, at some frequency the polarization of the dielectric cannot follow the voltage. As an example of the origin of this mechanism, the internal microscopic dipoles contributing to the dielectric constant cannot move instantly, and so as frequency of an applied alternating voltage increases, the dipole response is limited and the dielectric constant diminishes. A changing dielectric constant with frequency is referred to as <a href="/wiki/Dielectric_dispersion" class="mw-redirect" title="Dielectric dispersion">dielectric dispersion</a>, and is governed by <a href="/wiki/Dielectric_relaxation" class="mw-redirect" title="Dielectric relaxation">dielectric relaxation</a> processes, such as <a href="/wiki/Debye_relaxation" class="mw-redirect" title="Debye relaxation">Debye relaxation</a>. Under transient conditions, the displacement field can be expressed as (see <a href="/wiki/Electric_susceptibility" title="Electric susceptibility">electric susceptibility</a>): <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {D(t)}}=\varepsilon _{0}\int _{-\infty }^{t}\varepsilon _{r}(t-t'){\boldsymbol {E}}(t')\,dt',}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">D</mi> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">t</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> <mo>=</mo> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msubsup> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>t</mi> <mo>−</mo> <msup> <mi>t</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">E</mi> </mrow> <mo stretchy="false">(</mo> <msup> <mi>t</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> <mspace width="thinmathspace"></mspace> <mi>d</mi> <msup> <mi>t</mi> <mo>′</mo> </msup> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {D(t)}}=\varepsilon _{0}\int _{-\infty }^{t}\varepsilon _{r}(t-t'){\boldsymbol {E}}(t')\,dt',}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1b1351b4b085957c311fbee4aaf12c4a1319f57b" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:33.776ex; height:6.343ex;" alt="{\displaystyle {\boldsymbol {D(t)}}=\varepsilon _{0}\int _{-\infty }^{t}\varepsilon _{r}(t-t'){\boldsymbol {E}}(t')\,dt',}" /></span> </p><p>indicating the lag in response by the time dependence of <span class="texhtml"><i>ε<sub>r</sub></i></span>, calculated in principle from an underlying microscopic analysis, for example, of the dipole behavior in the dielectric. See, for example, <a href="/wiki/Linear_response_function" title="Linear response function">linear response function</a>.<sup id="cite_ref-Giuliani_63-0" class="reference"><a href="#cite_note-Giuliani-63"><span class="cite-bracket">[</span>62<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Rammer_64-0" class="reference"><a href="#cite_note-Rammer-64"><span class="cite-bracket">[</span>63<span class="cite-bracket">]</span></a></sup> The integral extends over the entire past history up to the present time. A <a href="/wiki/Fourier_analysis#(Continuous)_Fourier_transform" title="Fourier analysis">Fourier transform</a> in time then results in: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {D}}(\omega )=\varepsilon _{0}\varepsilon _{r}(\omega ){\boldsymbol {E}}(\omega )\,,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">D</mi> </mrow> <mo stretchy="false">(</mo> <mi>ω</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>ω</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">E</mi> </mrow> <mo stretchy="false">(</mo> <mi>ω</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace"></mspace> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {D}}(\omega )=\varepsilon _{0}\varepsilon _{r}(\omega ){\boldsymbol {E}}(\omega )\,,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/15885dfdfe16e4b52efbd9bce48addd725730e44" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:22.19ex; height:2.843ex;" alt="{\displaystyle {\boldsymbol {D}}(\omega )=\varepsilon _{0}\varepsilon _{r}(\omega ){\boldsymbol {E}}(\omega )\,,}" /></span> </p><p>where <i>ε</i><sub>r</sub>(<i>ω</i>) is now a <a href="/wiki/Complex_function#Complex_functions" class="mw-redirect" title="Complex function">complex function</a>, with an imaginary part related to absorption of energy from the field by the medium. See <a href="/wiki/Permittivity#Complex_permittivity" title="Permittivity">permittivity</a>. The capacitance, being proportional to the dielectric constant, also exhibits this frequency behavior. Fourier transforming Gauss's law with this form for displacement field: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}I(\omega )&=j\omega Q(\omega )=j\omega \oint _{\Sigma }{\boldsymbol {D}}({\boldsymbol {r}},\omega )\cdot d{\boldsymbol {\Sigma }}\\&=\left[G(\omega )+j\omega C(\omega )\right]V(\omega )={\frac {V(\omega )}{Z(\omega )}}\,,\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>I</mi> <mo stretchy="false">(</mo> <mi>ω</mi> <mo stretchy="false">)</mo> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>j</mi> <mi>ω</mi> <mi>Q</mi> <mo stretchy="false">(</mo> <mi>ω</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>j</mi> <mi>ω</mi> <msub> <mo>∮</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Σ</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">D</mi> </mrow> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> <mo>,</mo> <mi>ω</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">Σ</mi> </mrow> </mtd> </mtr> <mtr> <mtd></mtd> <mtd> <mi></mi> <mo>=</mo> <mrow> <mo>[</mo> <mrow> <mi>G</mi> <mo stretchy="false">(</mo> <mi>ω</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>j</mi> <mi>ω</mi> <mi>C</mi> <mo stretchy="false">(</mo> <mi>ω</mi> <mo stretchy="false">)</mo> </mrow> <mo>]</mo> </mrow> <mi>V</mi> <mo stretchy="false">(</mo> <mi>ω</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>V</mi> <mo stretchy="false">(</mo> <mi>ω</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>Z</mi> <mo stretchy="false">(</mo> <mi>ω</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mspace width="thinmathspace"></mspace> <mo>,</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}I(\omega )&=j\omega Q(\omega )=j\omega \oint _{\Sigma }{\boldsymbol {D}}({\boldsymbol {r}},\omega )\cdot d{\boldsymbol {\Sigma }}\\&=\left[G(\omega )+j\omega C(\omega )\right]V(\omega )={\frac {V(\omega )}{Z(\omega )}}\,,\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/654a10c670f2fa6bc1763d52f2159161362b5fcb" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.671ex; width:40.358ex; height:12.509ex;" alt="{\displaystyle {\begin{aligned}I(\omega )&=j\omega Q(\omega )=j\omega \oint _{\Sigma }{\boldsymbol {D}}({\boldsymbol {r}},\omega )\cdot d{\boldsymbol {\Sigma }}\\&=\left[G(\omega )+j\omega C(\omega )\right]V(\omega )={\frac {V(\omega )}{Z(\omega )}}\,,\end{aligned}}}" /></span> where <span class="texhtml"><i>j</i></span> is the <a href="/wiki/Imaginary_unit" title="Imaginary unit">imaginary unit</a>, <span class="texhtml"><i>V</i>(<i>ω</i>)</span> is the voltage component at angular frequency <span class="texhtml mvar" style="font-style:italic;">ω</span>, <span class="texhtml"><i>G</i>(<i>ω</i>)</span> is the <i>real</i> part of the current, called the <i>conductance</i>, and <span class="texhtml"><i>C</i>(<i>ω</i>)</span> determines the <i>imaginary</i> part of the current and is the <i>capacitance</i>. <span class="texhtml"><i>Z</i>(<i>ω</i>)</span> is the complex impedance. </p><p>When a parallel-plate capacitor is filled with a dielectric, the measurement of dielectric properties of the medium is based upon the relation: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varepsilon _{r}(\omega )=\varepsilon '_{r}(\omega )-j\varepsilon ''_{r}(\omega )={\frac {1}{j\omega Z(\omega )C_{0}}}={\frac {C_{\text{cmplx}}(\omega )}{C_{0}}}\,,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>ω</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msubsup> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> <mo>′</mo> </msubsup> <mo stretchy="false">(</mo> <mi>ω</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>j</mi> <msubsup> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> <mo>″</mo> </msubsup> <mo stretchy="false">(</mo> <mi>ω</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>j</mi> <mi>ω</mi> <mi>Z</mi> <mo stretchy="false">(</mo> <mi>ω</mi> <mo stretchy="false">)</mo> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>cmplx</mtext> </mrow> </msub> <mo stretchy="false">(</mo> <mi>ω</mi> <mo stretchy="false">)</mo> </mrow> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mspace width="thinmathspace"></mspace> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varepsilon _{r}(\omega )=\varepsilon '_{r}(\omega )-j\varepsilon ''_{r}(\omega )={\frac {1}{j\omega Z(\omega )C_{0}}}={\frac {C_{\text{cmplx}}(\omega )}{C_{0}}}\,,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1ddc370c7f09655dceff9ae3b43857ffb37f73c1" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:51.443ex; height:6.509ex;" alt="{\displaystyle \varepsilon _{r}(\omega )=\varepsilon '_{r}(\omega )-j\varepsilon ''_{r}(\omega )={\frac {1}{j\omega Z(\omega )C_{0}}}={\frac {C_{\text{cmplx}}(\omega )}{C_{0}}}\,,}" /></span> where a single <i>prime</i> denotes the real part and a double <i>prime</i> the imaginary part, <span class="texhtml"><i>Z</i>(<i>ω</i>)</span> is the complex impedance with the dielectric present, <span class="texhtml"><i>C</i><sub>cmplx</sub>(<i>ω</i>)</span> is the so-called <i>complex</i> capacitance with the dielectric present, and <span class="texhtml"><i>C</i><sub>0</sub></span> is the capacitance without the dielectric.<sup id="cite_ref-Handbook_65-0" class="reference"><a href="#cite_note-Handbook-65"><span class="cite-bracket">[</span>64<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Coffey_66-0" class="reference"><a href="#cite_note-Coffey-66"><span class="cite-bracket">[</span>65<span class="cite-bracket">]</span></a></sup> (Measurement "without the dielectric" in principle means measurement in <a href="/wiki/Free_space" class="mw-redirect" title="Free space">free space</a>, an unattainable goal inasmuch as even the <a href="/wiki/Vacuum_state" class="mw-redirect" title="Vacuum state">quantum vacuum</a> is predicted to exhibit nonideal behavior, such as <a href="/wiki/Dichroism" title="Dichroism">dichroism</a>. For practical purposes, when measurement errors are taken into account, often a measurement in terrestrial vacuum, or simply a calculation of <i>C</i><sub>0</sub>, is sufficiently accurate.<sup id="cite_ref-67" class="reference"><a href="#cite_note-67"><span class="cite-bracket">[</span>66<span class="cite-bracket">]</span></a></sup>) </p><p>Using this measurement method, the dielectric constant may exhibit a <a href="/wiki/Resonance" title="Resonance">resonance</a> at certain frequencies corresponding to characteristic response frequencies (excitation energies) of contributors to the dielectric constant. These resonances are the basis for a number of experimental techniques for detecting defects. The <i>conductance method</i> measures absorption as a function of frequency.<sup id="cite_ref-FOOTNOTESchroder2006347_68-0" class="reference"><a href="#cite_note-FOOTNOTESchroder2006347-68"><span class="cite-bracket">[</span>67<span class="cite-bracket">]</span></a></sup> Alternatively, the time response of the capacitance can be used directly, as in <i><a href="/wiki/Deep-level_transient_spectroscopy" title="Deep-level transient spectroscopy">deep-level transient spectroscopy</a></i>.<sup id="cite_ref-FOOTNOTESchroder2006305_69-0" class="reference"><a href="#cite_note-FOOTNOTESchroder2006305-69"><span class="cite-bracket">[</span>68<span class="cite-bracket">]</span></a></sup> </p><p>Another example of frequency dependent capacitance occurs with <a href="/wiki/MOSFET#Metal–oxide–semiconductor_structure" title="MOSFET">MOS capacitors</a>, where the slow generation of minority carriers means that at high frequencies the capacitance measures only the majority carrier response, while at low frequencies both types of carrier respond.<sup id="cite_ref-FOOTNOTESzeNg2006217_62-1" class="reference"><a href="#cite_note-FOOTNOTESzeNg2006217-62"><span class="cite-bracket">[</span>61<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Kasap_70-0" class="reference"><a href="#cite_note-Kasap-70"><span class="cite-bracket">[</span>69<span class="cite-bracket">]</span></a></sup> </p><p>At optical frequencies, in semiconductors the dielectric constant exhibits structure related to the band structure of the solid. Sophisticated modulation spectroscopy measurement methods based upon modulating the crystal structure by pressure or by other stresses and observing the related changes in absorption or reflection of light have advanced our knowledge of these materials.<sup id="cite_ref-Cardona_71-0" class="reference"><a href="#cite_note-Cardona-71"><span class="cite-bracket">[</span>70<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Styles">Styles</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=30" title="Edit section: Styles"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Photo-SMDcapacitors.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/86/Photo-SMDcapacitors.jpg/220px-Photo-SMDcapacitors.jpg" decoding="async" width="220" height="155" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/86/Photo-SMDcapacitors.jpg/330px-Photo-SMDcapacitors.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/86/Photo-SMDcapacitors.jpg/440px-Photo-SMDcapacitors.jpg 2x" data-file-width="603" data-file-height="426" /></a><figcaption>Capacitor packages: <a href="/wiki/Surface-mount_technology" title="Surface-mount technology">SMD</a> ceramic at top left; SMD tantalum electrolytic at bottom left; <a href="/wiki/Through-hole" class="mw-redirect" title="Through-hole">through-hole</a> ceramic at top right; through-hole aluminium electrolytic at bottom right. Major scale divisions are cm.</figcaption></figure> <p>The arrangement of plates and dielectric has many variations in different styles depending on the desired ratings of the capacitor. For small values of capacitance (microfarads and less), ceramic disks use metallic coatings, with wire leads bonded to the coating. Larger values can be made by multiple stacks of plates and disks. Larger value capacitors usually use a metal foil or metal film layer deposited on the surface of a dielectric film to make the plates, and a dielectric film of impregnated <a href="/wiki/Electrical_insulation_paper" title="Electrical insulation paper">paper</a> or plastic – these are rolled up to save space. To reduce the series resistance and inductance for long plates, the plates and dielectric are staggered so that connection is made at the common edge of the rolled-up plates, not at the ends of the foil or metalized film strips that comprise the plates. </p><p>The assembly is encased to prevent moisture entering the dielectric – early radio equipment used a cardboard tube sealed with wax. Modern paper or film dielectric capacitors are dipped in a hard thermoplastic. Large capacitors for high-voltage use may have the roll form compressed to fit into a rectangular metal case, with bolted terminals and bushings for connections. The dielectric in larger capacitors is often impregnated with a liquid to improve its properties. </p> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Axial_electrolytic_capacitors.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Axial_electrolytic_capacitors.jpg/220px-Axial_electrolytic_capacitors.jpg" decoding="async" width="220" height="152" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Axial_electrolytic_capacitors.jpg/330px-Axial_electrolytic_capacitors.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Axial_electrolytic_capacitors.jpg/440px-Axial_electrolytic_capacitors.jpg 2x" data-file-width="2764" data-file-height="1912" /></a><figcaption>Several axial-lead <a href="/wiki/Electrolytic_capacitor" title="Electrolytic capacitor">electrolytic capacitors</a></figcaption></figure> <p>Capacitors may have their connecting leads arranged in many configurations, for example axially or radially. "Axial" means that the leads are on a common axis, typically the axis of the capacitor's cylindrical body – the leads extend from opposite ends. Radial leads are rarely aligned along radii of the body's circle, so the term is conventional. The leads (until bent) are usually in planes parallel to that of the flat body of the capacitor, and extend in the same direction; they are often parallel as manufactured. </p><p>Small, cheap discoidal <a href="/wiki/Ceramic_capacitor" title="Ceramic capacitor">ceramic capacitors</a> have existed from the 1930s onward, and remain in widespread use. After the 1980s, <a href="/wiki/Surface_mount" class="mw-redirect" title="Surface mount">surface mount</a> packages for capacitors have been widely used. These packages are extremely small and lack connecting leads, allowing them to be soldered directly onto the surface of <a href="/wiki/Printed_circuit_boards" class="mw-redirect" title="Printed circuit boards">printed circuit boards</a>. Surface mount components avoid undesirable high-frequency effects due to the leads and simplify automated assembly, although manual handling is made difficult due to their small size. </p><p>Mechanically controlled variable capacitors allow the plate spacing to be adjusted, for example by rotating or sliding a set of movable plates into alignment with a set of stationary plates. Low cost variable capacitors squeeze together alternating layers of aluminum and plastic with a <a href="/wiki/Trimmer_(electronics)" title="Trimmer (electronics)">screw</a>. Electrical control of capacitance is achievable with <a href="/wiki/Varactor" class="mw-redirect" title="Varactor">varactors</a> (or varicaps), which are <a href="/wiki/Reverse-biased" class="mw-redirect" title="Reverse-biased">reverse-biased</a> <a href="/wiki/Semiconductor_diode" class="mw-redirect" title="Semiconductor diode">semiconductor diodes</a> whose depletion region width varies with applied voltage. They are used in <a href="/wiki/Phase_locked_loop" class="mw-redirect" title="Phase locked loop">phase-locked loops</a>, amongst other applications. </p> <div class="mw-heading mw-heading2"><h2 id="Capacitor_markings">Capacitor markings</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=31" title="Edit section: Capacitor markings"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Marking_codes_for_larger_parts">Marking codes for larger parts</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=32" title="Edit section: Marking codes for larger parts"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Most capacitors have designations printed on their bodies to indicate their electrical characteristics. Larger capacitors, such as electrolytic types usually display the capacitance as value with explicit unit, for example, <i>220 μF</i>. </p><p>For typographical reasons, some manufacturers print <i>MF</i> on capacitors to indicate microfarads (μF).<sup id="cite_ref-KaplanWhite2003_72-0" class="reference"><a href="#cite_note-KaplanWhite2003-72"><span class="cite-bracket">[</span>71<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Three-/four-character_marking_code_for_small_capacitors"><span id="Three-.2Ffour-character_marking_code_for_small_capacitors"></span>Three-/four-character marking code for small capacitors</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=33" title="Edit section: Three-/four-character marking code for small capacitors"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Smaller capacitors, such as ceramic types, often use a shorthand-notation consisting of three digits and an optional letter, where the digits (<i>XYZ</i>) denote the capacitance in <a href="/wiki/Picofarad" class="mw-redirect" title="Picofarad">picofarad</a> (pF), calculated as <i>XY</i> × 10<sup><i>Z</i></sup>, and the letter indicating the tolerance. Common tolerances are ±5%, ±10%, and ±20%, denotes as J, K, and M, respectively. </p><p>A capacitor may also be labeled with its working voltage, temperature, and other relevant characteristics. </p><p>Example: A capacitor labeled or designated as <i>473K 330V</i> has a capacitance of <span class="nowrap"><span data-sort-value="6992470000000000000♠"></span>47<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>3</sup> pF</span> = 47 nF (±10%) with a maximum working voltage of 330 V. The working voltage of a capacitor is nominally the highest voltage that may be applied across it without undue risk of breaking down the dielectric layer. </p> <div class="mw-heading mw-heading3"><h3 id="Two-character_marking_code_for_small_capacitors"><span class="anchor" id="2-char-capacitor-marking-code"></span>Two-character marking code for small capacitors</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=34" title="Edit section: Two-character marking code for small capacitors"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>For capacitances following the <a href="/wiki/E3_series_(preferred_numbers)" class="mw-redirect" title="E3 series (preferred numbers)">E3</a>, <a href="/wiki/E6_series_(preferred_numbers)" class="mw-redirect" title="E6 series (preferred numbers)">E6</a>, <a href="/wiki/E12_series_(preferred_numbers)" class="mw-redirect" title="E12 series (preferred numbers)">E12</a> or <a href="/wiki/E24_series_(preferred_numbers)" class="mw-redirect" title="E24 series (preferred numbers)">E24 series</a> of preferred values, the former ANSI/EIA-198-D:1991, ANSI/EIA-198-1-E:1998 and ANSI/EIA-198-1-F:2002 as well as the amendment IEC 60062:2016/AMD1:2019 to <a href="/wiki/IEC_60062" class="mw-redirect" title="IEC 60062">IEC 60062</a> define a <i>special two-character marking code for capacitors</i> for very small parts which leave no room to print the above-mentioned three-/four-character code onto them. The code consists of an uppercase letter denoting the two significant digits of the value followed by a digit indicating the multiplier. The EIA standard also defines a number of lowercase letters to specify a number of values not found in E24.<sup id="cite_ref-SIST-EN60062-A1_2019_73-0" class="reference"><a href="#cite_note-SIST-EN60062-A1_2019-73"><span class="cite-bracket">[</span>72<span class="cite-bracket">]</span></a></sup> </p> <table class="wikitable" style="float:left; margin-right:2em;"> <tbody><tr> <th>Code </th> <th>Series </th> <th colspan="10">Digit </th></tr> <tr> <th>Letter<sup id="cite_ref-NB_AmbiguousLetters_74-0" class="reference"><a href="#cite_note-NB_AmbiguousLetters-74"><span class="cite-bracket">[</span>nb 1<span class="cite-bracket">]</span></a></sup> </th> <th>E24 </th> <th>9 </th> <th>0 </th> <th>1 </th> <th>2 </th> <th>3 </th> <th>4 </th> <th>5 </th> <th>6 </th> <th>7 </th> <th>8 </th></tr> <tr> <th>A </th> <th>1.0 </th> <td>0.10 pF</td> <td>1.0 pF</td> <td>10 pF</td> <td>100 pF</td> <td>1.0 nF</td> <td>10 nF</td> <td>100 nF</td> <td>1.0 μF</td> <td>10 μF</td> <td>100 μF </td></tr> <tr> <th>B </th> <th>1.1 </th> <td>0.11 pF</td> <td>1.1 pF</td> <td>11 pF</td> <td>110 pF</td> <td>1.1 nF</td> <td>11 nF</td> <td>110 nF</td> <td>1.1 μF</td> <td>11 μF</td> <td>110 μF </td></tr> <tr> <th>C </th> <th>1.2 </th> <td>0.12 pF</td> <td>1.2 pF</td> <td>12 pF</td> <td>120 pF</td> <td>1.2 nF</td> <td>12 nF</td> <td>120 nF</td> <td>1.2 μF</td> <td>12 μF</td> <td>120 μF </td></tr> <tr> <th>D </th> <th>1.3 </th> <td>0.13 pF</td> <td>1.3 pF</td> <td>13 pF</td> <td>130 pF</td> <td>1.3 nF</td> <td>13 nF</td> <td>130 nF</td> <td>1.3 μF</td> <td>13 μF</td> <td>130 μF </td></tr> <tr> <th>E </th> <th>1.5 </th> <td>0.15 pF</td> <td>1.5 pF</td> <td>15 pF</td> <td>150 pF</td> <td>1.5 nF</td> <td>15 nF</td> <td>150 nF</td> <td>1.5 μF</td> <td>15 μF</td> <td>150 μF </td></tr> <tr> <th>F </th> <th>1.6 </th> <td>0.16 pF</td> <td>1.6 pF</td> <td>16 pF</td> <td>160 pF</td> <td>1.6 nF</td> <td>16 nF</td> <td>160 nF</td> <td>1.6 μF</td> <td>16 μF</td> <td>160 μF </td></tr> <tr> <th>G </th> <th>1.8 </th> <td>0.18 pF</td> <td>1.8 pF</td> <td>18 pF</td> <td>180 pF</td> <td>1.8 nF</td> <td>18 nF</td> <td>180 nF</td> <td>1.8 μF</td> <td>18 μF</td> <td>180 μF </td></tr> <tr> <th>H </th> <th>2.0 </th> <td>0.20 pF</td> <td>2.0 pF</td> <td>20 pF</td> <td>200 pF</td> <td>2.0 nF</td> <td>20 nF</td> <td>200 nF</td> <td>2.0 μF</td> <td>20 μF</td> <td>200 μF </td></tr> <tr> <th>J </th> <th>2.2 </th> <td>0.22 pF</td> <td>2.2 pF</td> <td>22 pF</td> <td>220 pF</td> <td>2.2 nF</td> <td>22 nF</td> <td>220 nF</td> <td>2.2 μF</td> <td>22 μF</td> <td>220 μF </td></tr> <tr> <th>K </th> <th>2.4 </th> <td>0.24 pF</td> <td>2.4 pF</td> <td>24 pF</td> <td>240 pF</td> <td>2.4 nF</td> <td>24 nF</td> <td>240 nF</td> <td>2.4 μF</td> <td>24 μF</td> <td>240 μF </td></tr> <tr> <th>L </th> <th>2.7 </th> <td>0.27 pF</td> <td>2.7 pF</td> <td>27 pF</td> <td>270 pF</td> <td>2.7 nF</td> <td>27 nF</td> <td>270 nF</td> <td>2.7 μF</td> <td>27 μF</td> <td>270 μF </td></tr> <tr> <th>M </th> <th>3.0 </th> <td>0.30 pF</td> <td>3.0 pF</td> <td>30 pF</td> <td>300 pF</td> <td>3.0 nF</td> <td>30 nF</td> <td>300 nF</td> <td>3.0 μF</td> <td>30 μF</td> <td>300 μF </td></tr> <tr> <th>N </th> <th>3.3 </th> <td>0.33 pF</td> <td>3.3 pF</td> <td>33 pF</td> <td>330 pF</td> <td>3.3 nF</td> <td>33 nF</td> <td>330 nF</td> <td>3.3 μF</td> <td>33 μF</td> <td>330 μF </td></tr> <tr> <th>P </th> <th>3.6 </th> <td>0.36 pF</td> <td>3.6 pF</td> <td>36 pF</td> <td>360 pF</td> <td>3.6 nF</td> <td>36 nF</td> <td>360 nF</td> <td>3.6 μF</td> <td>36 μF</td> <td>360 μF </td></tr> <tr> <th>Q </th> <th>3.9 </th> <td>0.39 pF</td> <td>3.9 pF</td> <td>39 pF</td> <td>390 pF</td> <td>3.9 nF</td> <td>39 nF</td> <td>390 nF</td> <td>3.9 μF</td> <td>39 μF</td> <td>390 μF </td></tr> <tr> <th>R </th> <th>4.3 </th> <td>0.43 pF</td> <td>4.3 pF</td> <td>43 pF</td> <td>430 pF</td> <td>4.3 nF</td> <td>43 nF</td> <td>430 nF</td> <td>4.3 μF</td> <td>43 μF</td> <td>430 μF </td></tr> <tr> <th>S </th> <th>4.7 </th> <td>0.47 pF</td> <td>4.7 pF</td> <td>47 pF</td> <td>470 pF</td> <td>4.7 nF</td> <td>47 nF</td> <td>470 nF</td> <td>4.7 μF</td> <td>47 μF</td> <td>470 μF </td></tr> <tr> <th>T </th> <th>5.1 </th> <td>0.51 pF</td> <td>5.1 pF</td> <td>51 pF</td> <td>510 pF</td> <td>5.1 nF</td> <td>51 nF</td> <td>510 nF</td> <td>5.1 μF</td> <td>51 μF</td> <td>510 μF </td></tr> <tr> <th>U </th> <th>5.6 </th> <td>0.56 pF</td> <td>5.6 pF</td> <td>56 pF</td> <td>560 pF</td> <td>5.6 nF</td> <td>56 nF</td> <td>560 nF</td> <td>5.6 μF</td> <td>56 μF</td> <td>560 μF </td></tr> <tr> <th>V </th> <th>6.2 </th> <td>0.62 pF</td> <td>6.2 pF</td> <td>62 pF</td> <td>620 pF</td> <td>6.2 nF</td> <td>62 nF</td> <td>620 nF</td> <td>6.2 μF</td> <td>62 μF</td> <td>620 μF </td></tr> <tr> <th>W </th> <th>6.8 </th> <td>0.68 pF</td> <td>6.8 pF</td> <td>68 pF</td> <td>680 pF</td> <td>6.8 nF</td> <td>68 nF</td> <td>680 nF</td> <td>6.8 μF</td> <td>68 μF</td> <td>680 μF </td></tr> <tr> <th>X </th> <th>7.5 </th> <td>0.75 pF</td> <td>7.5 pF</td> <td>75 pF</td> <td>750 pF</td> <td>7.5 nF</td> <td>75 nF</td> <td>750 nF</td> <td>7.5 μF</td> <td>75 μF</td> <td>750 μF </td></tr> <tr> <th>Y </th> <th>8.2 </th> <td>0.82 pF</td> <td>8.2 pF</td> <td>82 pF</td> <td>820 pF</td> <td>8.2 nF</td> <td>82 nF</td> <td>820 nF</td> <td>8.2 μF</td> <td>82 μF</td> <td>820 μF </td></tr> <tr> <th>Z </th> <th>9.1 </th> <td>0.91 pF</td> <td>9.1 pF</td> <td>91 pF</td> <td>910 pF</td> <td>9.1 nF</td> <td>91 nF</td> <td>910 nF</td> <td>9.1 μF</td> <td>91 μF</td> <td>910 μF </td></tr></tbody></table> <table class="wikitable" style="float:left; margin-right:2em;"> <tbody><tr> <th>Code </th> <th>Series </th> <th colspan="10">Digit </th></tr> <tr> <th>Letter </th> <th>EIA </th> <th>9 </th> <th>0 </th> <th>1 </th> <th>2 </th> <th>3 </th> <th>4 </th> <th>5 </th> <th>6 </th> <th>7 </th> <th>8 </th></tr> <tr> <th>a </th> <th>2.5 </th> <td>0.25 pF</td> <td>2.5 pF</td> <td>25 pF</td> <td>250 pF</td> <td>2.5 nF</td> <td>25 nF</td> <td>250 nF</td> <td>2.5 μF</td> <td>25 μF</td> <td>250 μF </td></tr> <tr> <th>b?<sup id="cite_ref-Zabkar_2011_75-0" class="reference"><a href="#cite_note-Zabkar_2011-75"><span class="cite-bracket">[</span>73<span class="cite-bracket">]</span></a></sup> </th> <th>3.0?<sup id="cite_ref-Zabkar_2011_75-1" class="reference"><a href="#cite_note-Zabkar_2011-75"><span class="cite-bracket">[</span>73<span class="cite-bracket">]</span></a></sup> </th> <td>0.30 pF</td> <td>3.0 pF</td> <td>30 pF</td> <td>300 pF</td> <td>3.0 nF</td> <td>30 nF</td> <td>300 nF</td> <td>3.0 μF</td> <td>30 μF</td> <td>300 μF </td></tr> <tr> <th>b?<sup id="cite_ref-SIST-EN60062-A1_2019_73-1" class="reference"><a href="#cite_note-SIST-EN60062-A1_2019-73"><span class="cite-bracket">[</span>72<span class="cite-bracket">]</span></a></sup>/c?<sup id="cite_ref-Zabkar_2011_75-2" class="reference"><a href="#cite_note-Zabkar_2011-75"><span class="cite-bracket">[</span>73<span class="cite-bracket">]</span></a></sup> </th> <th>3.5 </th> <td>0.35 pF</td> <td>3.5 pF</td> <td>35 pF</td> <td>350 pF</td> <td>3.5 nF</td> <td>35 nF</td> <td>350 nF</td> <td>3.5 μF</td> <td>35 μF</td> <td>350 μF </td></tr> <tr> <th>d </th> <th>4.0 </th> <td>0.40 pF</td> <td>4.0 pF</td> <td>40 pF</td> <td>400 pF</td> <td>4.0 nF</td> <td>40 nF</td> <td>400 nF</td> <td>4.0 μF</td> <td>40 μF</td> <td>400 μF </td></tr> <tr> <th>e </th> <th>4.5 </th> <td>0.45 pF</td> <td>4.5 pF</td> <td>45 pF</td> <td>450 pF</td> <td>4.5 nF</td> <td>45 nF</td> <td>450 nF</td> <td>4.5 μF</td> <td>45 μF</td> <td>450 μF </td></tr> <tr> <th>f </th> <th>5.0 </th> <td>0.50 pF</td> <td>5.0 pF</td> <td>50 pF</td> <td>500 pF</td> <td>5.0 nF</td> <td>50 nF</td> <td>500 nF</td> <td>5.0 μF</td> <td>50 μF</td> <td>500 μF </td></tr> <tr> <th>m </th> <th>6.0 </th> <td>0.60 pF</td> <td>6.0 pF</td> <td>60 pF</td> <td>600 pF</td> <td>6.0 nF</td> <td>60 nF</td> <td>600 nF</td> <td>6.0 μF</td> <td>60 μF</td> <td>600 μF </td></tr> <tr> <th>n </th> <th>7.0 </th> <td>0.70 pF</td> <td>7.0 pF</td> <td>70 pF</td> <td>700 pF</td> <td>7.0 nF</td> <td>70 nF</td> <td>700 nF</td> <td>7.0 μF</td> <td>70 μF</td> <td>700 μF </td></tr> <tr> <th>t </th> <th>8.0 </th> <td>0.80 pF</td> <td>8.0 pF</td> <td>80 pF</td> <td>800 pF</td> <td>8.0 nF</td> <td>80 nF</td> <td>800 nF</td> <td>8.0 μF</td> <td>80 μF</td> <td>800 μF </td></tr> <tr> <th>g </th> <th>9.0 </th> <td>0.90 pF</td> <td>9.0 pF</td> <td>90 pF</td> <td>900 pF</td> <td>9.0 nF</td> <td>90 nF</td> <td>900 nF</td> <td>9.0 μF</td> <td>90 μF</td> <td>900 μF </td></tr></tbody></table> <div style="clear:both;" class=""></div> <div class="mw-heading mw-heading3"><h3 id="RKM_code">RKM code</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=35" title="Edit section: RKM code"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/RKM_code" title="RKM code">RKM code</a> following <a href="/wiki/IEC_60062" class="mw-redirect" title="IEC 60062">IEC 60062</a> and <a href="/wiki/BS_1852" class="mw-redirect" title="BS 1852">BS 1852</a> is a notation to state a capacitor's value in a circuit diagram. It avoids using a <a href="/wiki/Decimal_separator" title="Decimal separator">decimal separator</a> and replaces the decimal separator with the SI prefix symbol for the particular value (and the letter <style data-mw-deduplicate="TemplateStyles:r886049734">.mw-parser-output .monospaced{font-family:monospace,monospace}</style><span class="monospaced">F</span> for weight 1). The code is also used for part markings. Example: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886049734" /><span class="monospaced">4n7</span> for 4.7 nF or <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886049734" /><span class="monospaced">2F2</span> for 2.2 F. </p> <div class="mw-heading mw-heading3"><h3 id="Historical">Historical</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=36" title="Edit section: Historical"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Farad#Informal_and_deprecated_terminology" title="Farad">Farad § Informal and deprecated terminology</a></div> <p>In texts prior to the 1960s and on some capacitor packages until more recently,<sup id="cite_ref-Boggs_17-5" class="reference"><a href="#cite_note-Boggs-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> obsolete capacitance units were utilized in electronic books,<sup id="cite_ref-FoE-1965_76-0" class="reference"><a href="#cite_note-FoE-1965-76"><span class="cite-bracket">[</span>74<span class="cite-bracket">]</span></a></sup> magazines, and electronics catalogs.<sup id="cite_ref-77" class="reference"><a href="#cite_note-77"><span class="cite-bracket">[</span>75<span class="cite-bracket">]</span></a></sup> The old units "mfd" and "mf" meant <i>microfarad</i> (μF); and the old units "mmfd", "mmf", "uuf", "μμf", "pfd" meant <i>picofarad</i> (pF); but they are rarely used any more.<sup id="cite_ref-78" class="reference"><a href="#cite_note-78"><span class="cite-bracket">[</span>76<span class="cite-bracket">]</span></a></sup> Also, "Micromicrofarad" or "micro-microfarad" are obsolete units that are found in some older texts that is equivalent to <i>picofarad</i> (pF).<sup id="cite_ref-FoE-1965_76-1" class="reference"><a href="#cite_note-FoE-1965-76"><span class="cite-bracket">[</span>74<span class="cite-bracket">]</span></a></sup> </p><p>Summary of obsolete capacitance units: (upper/lower case variations are not shown) </p> <ul><li>μF (microfarad) = mf, mfd</li> <li>pF (picofarad) = mmf, mmfd, pfd, μμF</li></ul> <div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=37" title="Edit section: Applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Applications_of_capacitors" title="Applications of capacitors">Applications of capacitors</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:24_Million_Watt_high_speed_flash_through_welding_lens.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/30/24_Million_Watt_high_speed_flash_through_welding_lens.jpg/250px-24_Million_Watt_high_speed_flash_through_welding_lens.jpg" decoding="async" width="220" height="161" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/30/24_Million_Watt_high_speed_flash_through_welding_lens.jpg/330px-24_Million_Watt_high_speed_flash_through_welding_lens.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/30/24_Million_Watt_high_speed_flash_through_welding_lens.jpg/500px-24_Million_Watt_high_speed_flash_through_welding_lens.jpg 2x" data-file-width="781" data-file-height="571" /></a><figcaption>A capacitor discharging its stored energy through a <a href="/wiki/Flashtube" title="Flashtube">flashtube</a>. The mylar-film capacitor has very low inductance and low resistance, producing a 3.5 microsecond pulse with 24 million watts of power, to operate a <a href="/wiki/Dye_laser" title="Dye laser">dye laser</a>.</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Energy_storage">Energy storage</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=38" title="Edit section: Energy storage"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A capacitor can store electric energy when disconnected from its charging circuit, so it can be used like a temporary <a href="/wiki/Battery_(electricity)" class="mw-redirect" title="Battery (electricity)">battery</a>, or like other types of <a href="/wiki/Rechargeable_energy_storage_system" class="mw-redirect" title="Rechargeable energy storage system">rechargeable energy storage system</a>.<sup id="cite_ref-79" class="reference"><a href="#cite_note-79"><span class="cite-bracket">[</span>77<span class="cite-bracket">]</span></a></sup> Capacitors are commonly used in electronic devices to maintain power supply while batteries are being changed. (This prevents loss of information in volatile memory.) </p><p>A capacitor can facilitate conversion of kinetic energy of charged particles into electric energy and store it.<sup id="cite_ref-80" class="reference"><a href="#cite_note-80"><span class="cite-bracket">[</span>78<span class="cite-bracket">]</span></a></sup> </p><p>There are tradeoffs between capacitors and batteries as storage devices. Without external resistors or inductors, capacitors can generally release their stored energy in a very short time compared to batteries. Conversely, batteries can hold a far greater charge per their size. Conventional capacitors provide less than 360 <a href="/wiki/Joule" title="Joule">joules</a> per kilogram of <a href="/wiki/Specific_energy" title="Specific energy">specific energy</a>, whereas a conventional <a href="/wiki/Alkaline_battery" title="Alkaline battery">alkaline battery</a> has a density of 590 kJ/kg. There is an intermediate solution: <a href="/wiki/Supercapacitor" title="Supercapacitor">supercapacitors</a>, which can accept and deliver charge much faster than batteries, and tolerate many more charge and discharge cycles than rechargeable batteries. They are, however, 10 times larger than conventional batteries for a given charge. On the other hand, it has been shown that the amount of charge stored in the dielectric layer of the thin film capacitor can be equal to, or can even exceed, the amount of charge stored on its plates.<sup id="cite_ref-81" class="reference"><a href="#cite_note-81"><span class="cite-bracket">[</span>79<span class="cite-bracket">]</span></a></sup> </p><p>In <a href="/wiki/Car_audio" class="mw-redirect" title="Car audio">car audio</a> systems, large capacitors store energy for the <a href="/wiki/Amplifier" title="Amplifier">amplifier</a> to use on demand. Also, for a <a href="/wiki/Flash_tube" class="mw-redirect" title="Flash tube">flash tube</a>, a capacitor is used to hold the <a href="/wiki/High_voltage" title="High voltage">high voltage</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Digital_memory">Digital memory</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=39" title="Edit section: Digital memory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the 1930s, <a href="/wiki/John_Vincent_Atanasoff" title="John Vincent Atanasoff">John Atanasoff</a> applied the principle of energy storage in capacitors to construct dynamic digital memories for the first binary computers that used electron tubes for logic.<sup id="cite_ref-Floyd2017_82-0" class="reference"><a href="#cite_note-Floyd2017-82"><span class="cite-bracket">[</span>80<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Pulsed_power_and_weapons">Pulsed power and weapons</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=40" title="Edit section: Pulsed power and weapons"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Pulsed_power" title="Pulsed power">Pulsed power</a> is used in many applications to increase the power intensity (watts) of a volume of energy (joules) by releasing that volume within a very short time. Pulses in the nanosecond range and powers in the gigawatts are achievable. Short pulses often require specially constructed, low-inductance, high-voltage capacitors that are often used in large groups (<i>capacitor banks</i>) to supply huge pulses of current for many pulsed power applications. These include <a href="/wiki/Electromagnetic_forming" title="Electromagnetic forming">electromagnetic forming</a>, <a href="/wiki/Marx_generator" title="Marx generator">Marx generators</a>, pulsed <a href="/wiki/Laser" title="Laser">lasers</a> (especially <a href="/wiki/TEA_laser" title="TEA laser">TEA lasers</a>), <a href="/wiki/Pulse_forming_network" class="mw-redirect" title="Pulse forming network">pulse forming networks</a>, <a href="/wiki/Radar" title="Radar">radar</a>, <a href="/wiki/Fusion_power" title="Fusion power">fusion</a> research, and <a href="/wiki/Particle_accelerator" title="Particle accelerator">particle accelerators</a>.<sup id="cite_ref-83" class="reference"><a href="#cite_note-83"><span class="cite-bracket">[</span>81<span class="cite-bracket">]</span></a></sup> </p><p>Large capacitor banks (reservoir) are used as energy sources for the <a href="/wiki/Exploding-bridgewire_detonator" title="Exploding-bridgewire detonator">exploding-bridgewire detonators</a> or <a href="/wiki/Slapper_detonator" title="Slapper detonator">slapper detonators</a> in <a href="/wiki/Nuclear_weapon" title="Nuclear weapon">nuclear weapons</a> and other specialty weapons. Experimental work is under way using banks of capacitors as power sources for <a href="/wiki/Electromagnetic_armour" class="mw-redirect" title="Electromagnetic armour">electromagnetic armour</a> and electromagnetic <a href="/wiki/Railgun" title="Railgun">railguns</a> and <a href="/wiki/Coilgun" title="Coilgun">coilguns</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Power_conditioning">Power conditioning</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=41" title="Edit section: Power conditioning"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Capacitor.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5a/Capacitor.jpg/180px-Capacitor.jpg" decoding="async" width="180" height="135" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5a/Capacitor.jpg/270px-Capacitor.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5a/Capacitor.jpg/360px-Capacitor.jpg 2x" data-file-width="1024" data-file-height="768" /></a><figcaption>A 10,000 <a href="/wiki/Microfarad" class="mw-redirect" title="Microfarad">microfarad</a> capacitor in an amplifier power supply</figcaption></figure> <p><a href="/wiki/Reservoir_capacitor" class="mw-redirect" title="Reservoir capacitor">Reservoir capacitors</a> are used in <a href="/wiki/Power_supply" title="Power supply">power supplies</a> where they smooth the output of a full or half wave <a href="/wiki/Rectifier" title="Rectifier">rectifier</a>. They can also be used in <a href="/wiki/Charge_pump" title="Charge pump">charge pump</a> circuits as the energy storage element in the generation of higher voltages than the input voltage. </p><p>Capacitors are connected in parallel with the power circuits of most electronic devices and larger systems (such as factories) to shunt away and conceal current fluctuations from the primary power source to provide a "clean" power supply for signal or control circuits. Audio equipment, for example, uses several capacitors in this way, to shunt away power line hum before it gets into the signal circuitry. The capacitors act as a local reserve for the DC power source, and <a href="/wiki/Bypass_capacitor" class="mw-redirect" title="Bypass capacitor">bypass</a> AC currents from the power supply. This is used in car audio applications, when a stiffening capacitor compensates for the inductance and resistance of the leads to the <a href="/wiki/Lead%E2%80%93acid_battery" title="Lead–acid battery">lead–acid</a> <a href="/wiki/Car_battery" class="mw-redirect" title="Car battery">car battery</a>. </p> <div class="mw-heading mw-heading4"><h4 id="Power-factor_correction">Power-factor correction</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=42" title="Edit section: Power-factor correction"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Condensor_bank_150kV_-_75MVAR.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Condensor_bank_150kV_-_75MVAR.jpg/180px-Condensor_bank_150kV_-_75MVAR.jpg" decoding="async" width="180" height="269" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Condensor_bank_150kV_-_75MVAR.jpg/270px-Condensor_bank_150kV_-_75MVAR.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Condensor_bank_150kV_-_75MVAR.jpg/360px-Condensor_bank_150kV_-_75MVAR.jpg 2x" data-file-width="926" data-file-height="1382" /></a><figcaption>A high-voltage capacitor bank used for <a href="/wiki/Power-factor_correction" class="mw-redirect" title="Power-factor correction">power-factor correction</a> on a power transmission system</figcaption></figure> <p>In electric power distribution, capacitors are used for <a href="/wiki/Power-factor_correction" class="mw-redirect" title="Power-factor correction">power-factor correction</a>. Such capacitors often come as three capacitors connected as a <a href="/wiki/Three-phase_electric_power" title="Three-phase electric power">three phase</a> <a href="/wiki/Electrical_load" title="Electrical load">load</a>. Usually, the values of these capacitors are not given in farads but rather as a <a href="/wiki/Reactive_power" class="mw-redirect" title="Reactive power">reactive power</a> in volt-amperes reactive (var). The purpose is to counteract inductive loading from devices like <a href="/wiki/Induction_motor" title="Induction motor">electric motors</a> and <a href="/wiki/Transmission_line" title="Transmission line">transmission lines</a> to make the load appear to be mostly resistive. Individual motor or lamp loads may have capacitors for power-factor correction, or larger sets of capacitors (usually with automatic switching devices) may be installed at a load center within a building or in a large utility <a href="/wiki/Electrical_substation" class="mw-redirect" title="Electrical substation">substation</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Suppression_and_coupling">Suppression and coupling</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=43" title="Edit section: Suppression and coupling"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Signal_coupling">Signal coupling</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=44" title="Edit section: Signal coupling"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Capacitive_coupling" title="Capacitive coupling">capacitive coupling</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Polyester_film_capacitor.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/13/Polyester_film_capacitor.jpg/180px-Polyester_film_capacitor.jpg" decoding="async" width="180" height="115" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/13/Polyester_film_capacitor.jpg/270px-Polyester_film_capacitor.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/13/Polyester_film_capacitor.jpg/360px-Polyester_film_capacitor.jpg 2x" data-file-width="2224" data-file-height="1416" /></a><figcaption>Polyester <a href="/wiki/Film_capacitor" title="Film capacitor">film capacitors</a> are frequently used as coupling capacitors.</figcaption></figure> <p>Because capacitors pass AC but block DC <a href="/wiki/Signal_(information_theory)" class="mw-redirect" title="Signal (information theory)">signals</a> (when charged up to the applied DC voltage), they are often used to separate the AC and DC components of a signal. This method is known as <i>AC coupling</i> or "capacitive coupling". Here, a large value of capacitance, whose value need not be accurately controlled, but whose <a href="/wiki/Reactance_(electronics)" class="mw-redirect" title="Reactance (electronics)">reactance</a> is small at the signal frequency, is employed. </p> <div class="mw-heading mw-heading4"><h4 id="Decoupling">Decoupling</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=45" title="Edit section: Decoupling"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Decoupling_capacitor" title="Decoupling capacitor">decoupling capacitor</a></div> <p>A <a href="/wiki/Decoupling_capacitor" title="Decoupling capacitor">decoupling capacitor</a> is a capacitor used to protect one part of a circuit from the effect of another, for instance to suppress noise or transients. Noise caused by other circuit elements is shunted through the capacitor, reducing the effect they have on the rest of the circuit. It is most commonly used between the power supply and ground. An alternative name is <i><a href="/wiki/Bypass_capacitor" class="mw-redirect" title="Bypass capacitor">bypass capacitor</a></i> as it is used to bypass the power supply or other high impedance component of a circuit. </p><p>Decoupling capacitors need not always be discrete components. Capacitors used in these applications may be built into a <a href="/wiki/Printed_circuit_board" title="Printed circuit board">printed circuit board</a>, between the various layers. These are often referred to as embedded capacitors.<sup id="cite_ref-84" class="reference"><a href="#cite_note-84"><span class="cite-bracket">[</span>82<span class="cite-bracket">]</span></a></sup> The layers in the board contributing to the capacitive properties also function as power and ground planes, and have a dielectric in between them, enabling them to operate as a parallel plate capacitor. </p> <div class="mw-heading mw-heading4"><h4 id="High-pass_and_low-pass_filters">High-pass and low-pass filters</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=46" title="Edit section: High-pass and low-pass filters"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/High-pass_filter" title="High-pass filter">High-pass filter</a> and <a href="/wiki/Low-pass_filter" title="Low-pass filter">Low-pass filter</a></div> <div class="mw-heading mw-heading4"><h4 id="Noise_suppression,_spikes,_and_snubbers"><span id="Noise_suppression.2C_spikes.2C_and_snubbers"></span>Noise suppression, spikes, and snubbers</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=47" title="Edit section: Noise suppression, spikes, and snubbers"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/High-pass_filter" title="High-pass filter">High-pass filter</a> and <a href="/wiki/Low-pass_filter" title="Low-pass filter">Low-pass filter</a></div> <p>When an inductive circuit is opened, the current through the inductance collapses quickly, creating a large voltage across the open circuit of the switch or relay. If the inductance is large enough, the energy may generate a spark, causing the contact points to oxidize, deteriorate, or sometimes weld together, or destroying a solid-state switch. A <a href="/wiki/Snubber" title="Snubber">snubber</a> capacitor across the newly opened circuit creates a path for this impulse to bypass the contact points, thereby preserving their life; these were commonly found in <a href="/wiki/Contact_breaker" title="Contact breaker">contact breaker</a> <a href="/wiki/Ignition_system" title="Ignition system">ignition systems</a>, for instance. Similarly, in smaller scale circuits, the spark may not be enough to damage the switch but may still <a href="/wiki/Spark-gap_transmitter" title="Spark-gap transmitter">radiate</a> undesirable <a href="/wiki/Radio_frequency_interference" class="mw-redirect" title="Radio frequency interference">radio frequency interference</a> (RFI), which a <a href="/wiki/Filter_capacitor" class="mw-redirect" title="Filter capacitor">filter capacitor</a> absorbs. Snubber capacitors are usually employed with a low-value resistor in series, to dissipate energy and minimize RFI. Such resistor-capacitor combinations are available in a single package. </p><p>Capacitors are also used in parallel with interrupting units of a high-voltage <a href="/wiki/Circuit_breaker" title="Circuit breaker">circuit breaker</a> to equally distribute the voltage between these units. These are called "grading capacitors". </p><p>In schematic diagrams, a capacitor used primarily for DC charge storage is often drawn vertically in circuit diagrams with the lower, more negative, plate drawn as an arc. The straight plate indicates the positive terminal of the device, if it is polarized (see <a href="/wiki/Electrolytic_capacitor" title="Electrolytic capacitor">electrolytic capacitor</a>). </p> <div class="mw-heading mw-heading3"><h3 id="Motor_starters">Motor starters</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=48" title="Edit section: Motor starters"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Motor_capacitor" title="Motor capacitor">Motor capacitor</a></div> <p>In single phase <a href="/wiki/Squirrel-cage_rotor" title="Squirrel-cage rotor">squirrel cage</a> motors, the primary winding within the motor housing is not capable of starting a rotational motion on the rotor, but is capable of sustaining one. To start the motor, a secondary "start" winding has a series non-polarized <i><a href="/wiki/Starting_capacitor" class="mw-redirect" title="Starting capacitor">starting capacitor</a></i> to introduce a lead in the sinusoidal current. When the secondary (start) winding is placed at an angle with respect to the primary (run) winding, a rotating electric field is created. The force of the rotational field is not constant, but is sufficient to start the rotor spinning. When the rotor comes close to operating speed, a centrifugal switch (or current-sensitive relay in series with the main winding) disconnects the capacitor. The start capacitor is typically mounted to the side of the motor housing. These are called capacitor-start motors, that have relatively high starting torque. Typically they can have up-to four times as much starting torque as a split-phase motor and are used on applications such as compressors, pressure washers and any small device requiring high starting torques. </p><p>Capacitor-run induction motors have a permanently connected phase-shifting capacitor in series with a second winding. The motor is much like a two-phase induction motor. </p><p>Motor-starting capacitors are typically non-polarized electrolytic types, while running capacitors are conventional paper or plastic film dielectric types. </p> <div class="mw-heading mw-heading3"><h3 id="Signal_processing">Signal processing</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=49" title="Edit section: Signal processing"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The energy stored in a capacitor can be used to represent <a href="/wiki/Information" title="Information">information</a>, either in binary form, as in <a href="/wiki/DRAM" class="mw-redirect" title="DRAM">DRAMs</a>, or in analogue form, as in <a href="/wiki/Analog_sampled_filter" title="Analog sampled filter">analog sampled filters</a> and <a href="/wiki/Charge-coupled_device" title="Charge-coupled device">CCDs</a>. Capacitors can be used in <a href="/wiki/Analog_circuit" class="mw-redirect" title="Analog circuit">analog circuits</a> as components of integrators or more complex filters and in <a href="/wiki/Negative_feedback" title="Negative feedback">negative feedback</a> loop stabilization. Signal processing circuits also use capacitors to <a href="/wiki/Integral" title="Integral">integrate</a> a current signal. </p> <div class="mw-heading mw-heading4"><h4 id="Tuned_circuits">Tuned circuits</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=50" title="Edit section: Tuned circuits"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Capacitors and inductors are applied together in <a href="/wiki/RLC_circuit" title="RLC circuit">tuned circuits</a> to select information in particular frequency bands. For example, <a href="/wiki/Radio_receiver" title="Radio receiver">radio receivers</a> rely on variable capacitors to tune the station frequency. Speakers use passive analog <a href="/wiki/Audio_crossover" title="Audio crossover">crossovers</a>, and analog equalizers use capacitors to select different audio bands. </p><p>The <a href="/wiki/Resonant_frequency" class="mw-redirect" title="Resonant frequency">resonant frequency</a> <i>f</i> of a tuned circuit is a function of the inductance (<i>L</i>) and capacitance (<i>C</i>) in series, and is given by: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f={\frac {1}{2\pi {\sqrt {LC}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>L</mi> <mi>C</mi> </msqrt> </mrow> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f={\frac {1}{2\pi {\sqrt {LC}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aecff5abc5353196145d127190122b169bd91161" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:12.993ex; height:6.176ex;" alt="{\displaystyle f={\frac {1}{2\pi {\sqrt {LC}}}}}" /></span> where <span class="texhtml mvar" style="font-style:italic;">L</span> is in <a href="/wiki/Henry_(unit)" title="Henry (unit)">henries</a> and <span class="texhtml mvar" style="font-style:italic;">C</span> is in farads. </p> <div class="mw-heading mw-heading3"><h3 id="Sensing">Sensing</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=51" title="Edit section: Sensing"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Capacitive_sensing" title="Capacitive sensing">capacitive sensing</a> and <a href="/wiki/Capacitive_displacement_sensor" title="Capacitive displacement sensor">Capacitive displacement sensor</a></div> <p>Most capacitors are designed to maintain a fixed physical structure. However, various factors can change the structure of the capacitor, and the resulting change in capacitance can be used to <a href="/wiki/Sensor" title="Sensor">sense</a> those factors. </p> <dl><dt>Changing the dielectric</dt> <dd></dd> <dd>The effects of varying the characteristics of the <b>dielectric</b> can be used for sensing purposes. Capacitors with an exposed and porous dielectric can be used to measure humidity in air. Capacitors are used to accurately measure the fuel level in <a href="/wiki/Airplane" title="Airplane">airplanes</a>; as the fuel covers more of a pair of plates, the circuit capacitance increases. Squeezing the dielectric can change a capacitor at a few tens of bar pressure sufficiently that it can be used as a pressure sensor.<sup id="cite_ref-85" class="reference"><a href="#cite_note-85"><span class="cite-bracket">[</span>83<span class="cite-bracket">]</span></a></sup> A selected, but otherwise standard, polymer dielectric capacitor, when immersed in a compatible gas or liquid, can work usefully as a very low cost pressure sensor up to many hundreds of bar.</dd> <dt>Changing the distance between the plates</dt> <dd></dd> <dd>Capacitors with a flexible plate can be used to measure strain or pressure. Industrial pressure transmitters used for <a href="/wiki/Process_control" class="mw-redirect" title="Process control">process control</a> use pressure-sensing diaphragms, which form a capacitor plate of an oscillator circuit. Capacitors are used as the <a href="/wiki/Sensor" title="Sensor">sensor</a> in <a href="/wiki/Condenser_microphone" class="mw-redirect" title="Condenser microphone">condenser microphones</a>, where one plate is moved by air pressure, relative to the fixed position of the other plate. Some <a href="/wiki/Accelerometer" title="Accelerometer">accelerometers</a> use <a href="/wiki/MEMS" title="MEMS">MEMS</a> capacitors etched on a chip to measure the magnitude and direction of the acceleration vector. They are used to detect changes in acceleration, in tilt sensors, or to detect free fall, as sensors triggering <a href="/wiki/Airbag" title="Airbag">airbag</a> deployment, and in many other applications. Some <a href="/wiki/Fingerprint_authentication#Fingerprint_sensors" class="mw-redirect" title="Fingerprint authentication">fingerprint sensors</a> use capacitors. Additionally, a user can adjust the pitch of a <a href="/wiki/Theremin" title="Theremin">theremin</a> musical instrument by moving their hand since this changes the effective capacitance between the user's hand and the antenna.</dd> <dt>Changing the effective area of the plates</dt> <dd></dd> <dd>Capacitive <a href="/wiki/Touch_switch" title="Touch switch">touch switches</a> are now<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Manual_of_Style/Dates_and_numbers#Chronological_items" title="Wikipedia:Manual of Style/Dates and numbers"><span title="The time period mentioned near this tag is ambiguous. (May 2018)">when?</span></a></i>]</sup> used on many consumer electronic products.</dd></dl> <div class="mw-heading mw-heading3"><h3 id="Oscillators">Oscillators</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=52" title="Edit section: Oscillators"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Hartley_oscillator" title="Hartley oscillator">Hartley oscillator</a></div> <figure class="mw-default-size skin-invert-image" typeof="mw:File/Thumb"><a href="/wiki/File:Garner_oscillator.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b6/Garner_oscillator.svg/220px-Garner_oscillator.svg.png" decoding="async" width="220" height="293" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b6/Garner_oscillator.svg/330px-Garner_oscillator.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b6/Garner_oscillator.svg/440px-Garner_oscillator.svg.png 2x" data-file-width="190" data-file-height="253" /></a><figcaption>Example of a simple oscillator incorporating a capacitor</figcaption></figure> <p>A capacitor can possess spring-like qualities in an oscillator circuit. In the image example, a capacitor acts to influence the biasing voltage at the npn transistor's base. The resistance values of the voltage-divider resistors and the capacitance value of the capacitor together control the oscillatory frequency. </p> <div class="mw-heading mw-heading3"><h3 id="Producing_light">Producing light</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=53" title="Edit section: Producing light"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Light_emitting_capacitor" class="mw-redirect" title="Light emitting capacitor">light emitting capacitor</a></div> <p>A light-emitting capacitor is made from a dielectric that uses <a href="/wiki/Phosphorescence" title="Phosphorescence">phosphorescence</a> to produce light. If one of the conductive plates is made with a transparent material, the light is visible. Light-emitting capacitors are used in the construction of electroluminescent panels, for applications such as backlighting for laptop computers. In this case, the entire panel is a capacitor used for the purpose of generating light. </p> <div class="mw-heading mw-heading2"><h2 id="Hazards_and_safety">Hazards and safety</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=54" title="Edit section: Hazards and safety"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The hazards posed by a capacitor are usually determined, foremost, by the amount of energy stored, which is the cause of things like electrical burns or heart <a href="/wiki/Fibrillation" title="Fibrillation">fibrillation</a>. Factors such as voltage and chassis material are of secondary consideration, which are more related to how easily a shock can be initiated rather than how much damage can occur.<sup id="cite_ref-ReferenceA_55-1" class="reference"><a href="#cite_note-ReferenceA-55"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup> Under certain conditions, including conductivity of the surfaces, preexisting medical conditions, the humidity of the air, or the pathways it takes through the body (i.e.: shocks that travel across the core of the body and, especially, the heart are more dangerous than those limited to the extremities), shocks as low as one joule have been reported to cause death, although in most instances they may not even leave a burn. Shocks over ten joules will generally damage skin, and are usually considered hazardous. Any capacitor that can store 50 joules or more should be considered potentially lethal.<sup id="cite_ref-86" class="reference"><a href="#cite_note-86"><span class="cite-bracket">[</span>84<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-ReferenceA_55-2" class="reference"><a href="#cite_note-ReferenceA-55"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup> </p><p>Capacitors may retain a charge long after power is removed from a circuit; this charge can cause dangerous or even potentially fatal <a href="/wiki/Electric_shock" class="mw-redirect" title="Electric shock">shocks</a> or damage connected equipment. For example, even a seemingly innocuous device such as the <a href="/wiki/Flash_(photography)" title="Flash (photography)">flash</a> of a <a href="/wiki/Disposable_camera" title="Disposable camera">disposable camera</a>, has a <a href="/wiki/Photoflash_capacitor" title="Photoflash capacitor">photoflash capacitor</a> which may contain over 15 joules of energy and be charged to over 300 volts. This is easily capable of delivering a shock. Service procedures for electronic devices usually include instructions to discharge large or high-voltage capacitors, for instance using a <a href="/wiki/Brinkley_stick" title="Brinkley stick">Brinkley stick</a>. Larger capacitors, such as those used in <a href="/wiki/Microwave_oven" title="Microwave oven">microwave ovens</a>, <a href="/wiki/HVAC" class="mw-redirect" title="HVAC">HVAC</a> units and medical <a href="/wiki/Defibrillator" class="mw-redirect" title="Defibrillator">defibrillators</a> may also have built-in discharge resistors to dissipate stored energy to a safe level within a few seconds after power is removed. High-voltage capacitors are stored with the terminals <a href="/wiki/Short_circuit" title="Short circuit">shorted</a>, as protection from potentially dangerous voltages due to <a href="/wiki/Permittivity#Lossy_medium" title="Permittivity">dielectric absorption</a> or from transient voltages the capacitor may pick up from static charges or passing weather events.<sup id="cite_ref-ReferenceA_55-3" class="reference"><a href="#cite_note-ReferenceA-55"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup> </p><p>Some old, large oil-filled paper or plastic film capacitors contain <a href="/wiki/Polychlorinated_biphenyls" class="mw-redirect" title="Polychlorinated biphenyls">polychlorinated biphenyls</a> (PCBs). It is known that waste PCBs can leak into <a href="/wiki/Groundwater" title="Groundwater">groundwater</a> under <a href="/wiki/Landfill" title="Landfill">landfills</a>. Capacitors containing PCBs were labelled as containing "Askarel" and several other trade names. PCB-filled paper capacitors are found in very old (pre-1975) <a href="/wiki/Fluorescent_lamp" title="Fluorescent lamp">fluorescent lamp</a> ballasts, and other applications. </p><p>Capacitors may <a href="/wiki/Catastrophic_failure" title="Catastrophic failure">catastrophically fail</a> when subjected to voltages or currents beyond their rating, or in case of polarized capacitors, applied in a reverse polarity. Failures may create arcing that heats and vaporizes the dielectric fluid, causing a build up of pressurized gas that may result in swelling, rupture, or an explosion. Larger capacitors may have vents or similar mechanism to allow the release of such pressures in the event of failure. Capacitors used in <a href="/wiki/Radio_frequency" title="Radio frequency">RF</a> or sustained high-current applications can overheat, especially in the center of the capacitor rolls. Capacitors used within high-energy capacitor banks can violently explode when a short in one capacitor causes sudden dumping of energy stored in the rest of the bank into the failing unit. High voltage vacuum capacitors can generate soft X-rays even during normal operation. Proper containment, fusing, and preventive maintenance can help to minimize these hazards. </p><p>High-voltage capacitors may benefit from a <a href="/wiki/Pre-charge" title="Pre-charge">pre-charge</a> to limit in-rush currents at power-up of high voltage direct current (HVDC) circuits. This extends the life of the component and may mitigate high-voltage hazards. </p> <ul class="gallery mw-gallery-packed"> <li class="gallerybox" style="width: 162px"> <div class="thumb" style="width: 160px;"><span typeof="mw:File"><a href="/wiki/File:Defekte_Kondensatoren.jpg" class="mw-file-description" title="Swollen electrolytic capacitors. The vent on the tops allows the release of pressurized gas build-up in the event of failure, preventing it from exploding."><img alt="Swollen electrolytic capacitors. The vent on the tops allows the release of pressurized gas build-up in the event of failure, preventing it from exploding." src="//upload.wikimedia.org/wikipedia/commons/thumb/7/76/Defekte_Kondensatoren.jpg/240px-Defekte_Kondensatoren.jpg" decoding="async" width="160" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/76/Defekte_Kondensatoren.jpg/360px-Defekte_Kondensatoren.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/76/Defekte_Kondensatoren.jpg/480px-Defekte_Kondensatoren.jpg 2x" data-file-width="800" data-file-height="600" /></a></span></div> <div class="gallerytext">Swollen electrolytic capacitors. The vent on the tops allows the release of pressurized gas build-up in the event of failure, preventing it from exploding.</div> </li> <li class="gallerybox" style="width: 92px"> <div class="thumb" style="width: 90px;"><span typeof="mw:File"><a href="/wiki/File:High-energy_capacitor_from_a_defibrillator_42_MFD_@_5000_VDC.jpg" class="mw-file-description" title="This high-energy capacitor from a defibrillator has a resistor connected between the terminals for safety, to dissipate stored energy."><img alt="This high-energy capacitor from a defibrillator has a resistor connected between the terminals for safety, to dissipate stored energy." src="//upload.wikimedia.org/wikipedia/commons/thumb/3/34/High-energy_capacitor_from_a_defibrillator_42_MFD_%40_5000_VDC.jpg/135px-High-energy_capacitor_from_a_defibrillator_42_MFD_%40_5000_VDC.jpg" decoding="async" width="90" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/34/High-energy_capacitor_from_a_defibrillator_42_MFD_%40_5000_VDC.jpg/202px-High-energy_capacitor_from_a_defibrillator_42_MFD_%40_5000_VDC.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/34/High-energy_capacitor_from_a_defibrillator_42_MFD_%40_5000_VDC.jpg/270px-High-energy_capacitor_from_a_defibrillator_42_MFD_%40_5000_VDC.jpg 2x" data-file-width="2736" data-file-height="3648" /></a></span></div> <div class="gallerytext">This high-energy capacitor from a <a href="/wiki/Defibrillator" class="mw-redirect" title="Defibrillator">defibrillator</a> has a resistor connected between the terminals for safety, to dissipate stored energy.</div> </li> <li class="gallerybox" style="width: 107.33333333333px"> <div class="thumb" style="width: 105.33333333333px;"><span typeof="mw:File"><a href="/wiki/File:Exploded_Electrolytic_Capacitor.jpg" class="mw-file-description" title="An exploded electrolytic capacitor, showing fragments of paper and metallic foil"><img alt="An exploded electrolytic capacitor, showing fragments of paper and metallic foil" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e8/Exploded_Electrolytic_Capacitor.jpg/158px-Exploded_Electrolytic_Capacitor.jpg" decoding="async" width="106" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e8/Exploded_Electrolytic_Capacitor.jpg/237px-Exploded_Electrolytic_Capacitor.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e8/Exploded_Electrolytic_Capacitor.jpg/316px-Exploded_Electrolytic_Capacitor.jpg 2x" data-file-width="1139" data-file-height="1299" /></a></span></div> <div class="gallerytext">An exploded electrolytic capacitor, showing fragments of paper and metallic foil</div> </li> </ul> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=55" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1266661725">.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px solid var(--border-color-base,#a2a9b1);padding:0.1em;background:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .portalbox-entry{display:table-row;font-size:85%;line-height:110%;height:1.9em;font-style:italic;font-weight:bold}.mw-parser-output .portalbox-image{display:table-cell;padding:0.2em;vertical-align:middle;text-align:center}.mw-parser-output .portalbox-link{display:table-cell;padding:0.2em 0.2em 0.2em 0.3em;vertical-align:middle}@media(min-width:720px){.mw-parser-output .portalleft{margin:0.5em 1em 0.5em 0}.mw-parser-output .portalright{clear:right;float:right;margin:0.5em 0 0.5em 1em}}</style><ul role="navigation" aria-label="Portals" class="noprint portalbox portalborder portalright"> <li class="portalbox-entry"><span class="portalbox-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Nuvola_apps_ksim.png" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Nuvola_apps_ksim.png/28px-Nuvola_apps_ksim.png" decoding="async" width="28" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Nuvola_apps_ksim.png/42px-Nuvola_apps_ksim.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Nuvola_apps_ksim.png/56px-Nuvola_apps_ksim.png 2x" data-file-width="128" data-file-height="128" /></a></span></span><span class="portalbox-link"><a href="/wiki/Portal:Electronics" title="Portal:Electronics">Electronics portal</a></span></li></ul> <ul><li><a href="/wiki/Capacitance_meter" title="Capacitance meter">Capacitance meter</a></li> <li><a href="/wiki/Capacitor_plague" title="Capacitor plague">Capacitor plague</a></li> <li><a href="/wiki/Electric_displacement_field" title="Electric displacement field">Electric displacement field</a></li> <li><a href="/wiki/Electroluminescence" title="Electroluminescence">Electroluminescence</a></li> <li><a href="/wiki/List_of_capacitor_manufacturers" title="List of capacitor manufacturers">List of capacitor manufacturers</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=56" title="Edit section: Notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-30">^</a></b></span> <span class="reference-text">Most real capacitors may have a small dielectric leakage current that passes through the resistive dielectric layer in between the plates.</span> </li> </ol></div></div><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626" /><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-NB_AmbiguousLetters-74"><span class="mw-cite-backlink"><b><a href="#cite_ref-NB_AmbiguousLetters_74-0">^</a></b></span> <span class="reference-text">In order to reduce the risk for read errors, the letters <code>I</code> and <code>O</code> are not used as their glyphs look similar to other letters and digits.</span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=57" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626" /><div class="reflist reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-duff-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-duff_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-duff_1-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFDuff1916" class="citation book cs1">Duff, Wilmer (1916) [1908]. <a rel="nofollow" class="external text" href="https://archive.org/stream/atextbookphysic00carmgoog#page/n378/mode/2up"><i>A Text-Book of Physics</i></a> (4th ed.). Philadelphia: P. Blakiston's Son & Co. p. 361<span class="reference-accessdate">. Retrieved <span class="nowrap">2016-12-01</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Text-Book+of+Physics&rft.place=Philadelphia&rft.pages=361&rft.edition=4th&rft.pub=P.+Blakiston%27s+Son+%26+Co.&rft.date=1916&rft.aulast=Duff&rft.aufirst=Wilmer&rft_id=https%3A%2F%2Farchive.org%2Fstream%2Fatextbookphysic00carmgoog%23page%2Fn378%2Fmode%2F2up&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFBird2010" class="citation book cs1">Bird, John (2010). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=A1tAHm_5sl0C"><i>Electrical and Electronic Principles and Technology</i></a>. Routledge. pp. <span class="nowrap">63–</span>76. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-08089056-2" title="Special:BookSources/978-0-08089056-2"><bdi>978-0-08089056-2</bdi></a><span class="reference-accessdate">. Retrieved <span class="nowrap">2013-03-17</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Electrical+and+Electronic+Principles+and+Technology&rft.pages=%3Cspan+class%3D%22nowrap%22%3E63-%3C%2Fspan%3E76&rft.pub=Routledge&rft.date=2010&rft.isbn=978-0-08089056-2&rft.aulast=Bird&rft.aufirst=John&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DA1tAHm_5sl0C&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-floyd-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-floyd_3-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFFloyd2005" class="citation book cs1">Floyd, Thomas (2005) [1984]. <i>Electronic Devices</i> (7th ed.). Upper Saddle River, New Jersey, USA: <a href="/wiki/Pearson_Education" title="Pearson Education">Pearson Education</a>. p. 10. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-13-127827-4" title="Special:BookSources/0-13-127827-4"><bdi>0-13-127827-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Electronic+Devices&rft.place=Upper+Saddle+River%2C+New+Jersey%2C+USA&rft.pages=10&rft.edition=7th&rft.pub=Pearson+Education&rft.date=2005&rft.isbn=0-13-127827-4&rft.aulast=Floyd&rft.aufirst=Thomas&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://micro.magnet.fsu.edu/electromag/java/lightning/index.html#:~:text=An+Example+Of+A+Natural,ionizing+radiation,+and+each+other.">"Molecular Expressions: Electricity and Magnetism - Interactive Java Tutorials: Lightning: A Natural Capacitor"</a>. <i>micro.magnet.fsu.edu</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=micro.magnet.fsu.edu&rft.atitle=Molecular+Expressions%3A+Electricity+and+Magnetism+-+Interactive+Java+Tutorials%3A+Lightning%3A+A+Natural+Capacitor&rft_id=https%3A%2F%2Fmicro.magnet.fsu.edu%2Felectromag%2Fjava%2Flightning%2Findex.html%23%3A~%3Atext%3DAn%2BExample%2BOf%2BA%2BNatural%2Cionizing%2Bradiation%2C%2Band%2Beach%2Bother.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFWilliams" class="citation web cs1">Williams, Henry Smith. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20071024034729/http://www.worldwideschool.org/library/books/sci/history/AHistoryofScienceVolumeII/chap49.html">"A History of Science Volume II, Part VI: The Leyden Jar Discovered"</a>. Archived from <a rel="nofollow" class="external text" href="http://www.worldwideschool.org/library/books/sci/history/AHistoryofScienceVolumeII/chap49.html">the original</a> on 2007-10-24<span class="reference-accessdate">. Retrieved <span class="nowrap">2013-03-17</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=A+History+of+Science+Volume+II%2C+Part+VI%3A+The+Leyden+Jar+Discovered&rft.aulast=Williams&rft.aufirst=Henry+Smith&rft_id=http%3A%2F%2Fwww.worldwideschool.org%2Flibrary%2Fbooks%2Fsci%2Fhistory%2FAHistoryofScienceVolumeII%2Fchap49.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFKeithley1999" class="citation book cs1">Keithley, Joseph F. (1999). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=uwgNAtqSHuQC&pg=PA23"><i>The Story of Electrical and Magnetic Measurements: From 500 BC to the 1940s</i></a>. John Wiley & Sons. p. 23. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0780311930" title="Special:BookSources/978-0780311930"><bdi>978-0780311930</bdi></a><span class="reference-accessdate">. Retrieved <span class="nowrap">2013-03-17</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Story+of+Electrical+and+Magnetic+Measurements%3A+From+500+BC+to+the+1940s&rft.pages=23&rft.pub=John+Wiley+%26+Sons&rft.date=1999&rft.isbn=978-0780311930&rft.aulast=Keithley&rft.aufirst=Joseph+F.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DuwgNAtqSHuQC%26pg%3DPA23&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFHouston1905" class="citation book cs1">Houston, Edwin J. (1905). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=ko9BAAAAIAAJ&pg=PA71"><i>Electricity in Every-day Life</i></a>. P. F. Collier & Son. p. 71<span class="reference-accessdate">. Retrieved <span class="nowrap">2013-03-17</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Electricity+in+Every-day+Life&rft.pages=71&rft.pub=P.+F.+Collier+%26+Son&rft.date=1905&rft.aulast=Houston&rft.aufirst=Edwin+J.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dko9BAAAAIAAJ%26pg%3DPA71&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-Benjamin1895-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-Benjamin1895_8-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFBenjamin1895" class="citation book cs1">Benjamin, Park (1895). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=hkMPAAAAMAAJ&pg=PA523"><i>A History of Electricity: (The Intellectual Rise in Electricity) from Antiquity to the Days of Benjamin Franklin</i></a>. <a href="/wiki/J._Wiley_%26_Sons" class="mw-redirect" title="J. Wiley & Sons">J. Wiley & Sons</a>. pp. <span class="nowrap">522–</span>524.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+History+of+Electricity%3A+%28The+Intellectual+Rise+in+Electricity%29+from+Antiquity+to+the+Days+of+Benjamin+Franklin&rft.pages=%3Cspan+class%3D%22nowrap%22%3E522-%3C%2Fspan%3E524&rft.pub=J.+Wiley+%26+Sons&rft.date=1895&rft.aulast=Benjamin&rft.aufirst=Park&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DhkMPAAAAMAAJ%26pg%3DPA523&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFIsaacson2003" class="citation book cs1"><a href="/wiki/Walter_Isaacson" title="Walter Isaacson">Isaacson, Walter</a> (2003). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=oIW915dDMBwC&pg=PA135"><i>Benjamin Franklin: An American Life</i></a>. Simon and Schuster. p. 136. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-74326084-8" title="Special:BookSources/978-0-74326084-8"><bdi>978-0-74326084-8</bdi></a><span class="reference-accessdate">. Retrieved <span class="nowrap">2013-03-17</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Benjamin+Franklin%3A+An+American+Life&rft.pages=136&rft.pub=Simon+and+Schuster&rft.date=2003&rft.isbn=978-0-74326084-8&rft.aulast=Isaacson&rft.aufirst=Walter&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DoIW915dDMBwC%26pg%3DPA135&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFFranklin1749" class="citation web cs1">Franklin, Benjamin (1749-04-29). <a rel="nofollow" class="external text" href="http://www.chemteam.info/Chem-History/Franklin-1749/Franklin-1749-all.pdf">"Experiments & Observations on Electricity: Letter IV to Peter Collinson"</a> <span class="cs1-format">(PDF)</span>. p. 28<span class="reference-accessdate">. Retrieved <span class="nowrap">2009-08-09</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Experiments+%26+Observations+on+Electricity%3A+Letter+IV+to+Peter+Collinson&rft.pages=28&rft.date=1749-04-29&rft.aulast=Franklin&rft.aufirst=Benjamin&rft_id=http%3A%2F%2Fwww.chemteam.info%2FChem-History%2FFranklin-1749%2FFranklin-1749-all.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFMorse2004" class="citation web cs1">Morse, Robert A. (September 2004). <a rel="nofollow" class="external text" href="http://www.compadre.org/Repository/document/ServeFile.cfm?ID=3430&DocID=2402&DocFID=3925&Attachment=1">"Franklin and Electrostatics – Ben Franklin as my Lab Partner"</a> <span class="cs1-format">(PDF)</span>. <i>Wright Center for Science Education</i>. Tufts University. p. 23<span class="reference-accessdate">. Retrieved <span class="nowrap">2009-08-10</span></span>. <q>After Volta's discovery of the electrochemical cell in 1800, the term was then applied to a group of electrochemical cells</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Wright+Center+for+Science+Education&rft.atitle=Franklin+and+Electrostatics+%E2%80%93+Ben+Franklin+as+my+Lab+Partner&rft.pages=23&rft.date=2004-09&rft.aulast=Morse&rft.aufirst=Robert+A.&rft_id=http%3A%2F%2Fwww.compadre.org%2FRepository%2Fdocument%2FServeFile.cfm%3FID%3D3430%26DocID%3D2402%26DocFID%3D3925%26Attachment%3D1&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFWolfMcKie1962" class="citation book cs1">Wolf, A; McKie, D. (1962). <a rel="nofollow" class="external text" href="https://archive.org/stream/in.ernet.dli.2015.460063/2015.460063.A-History#page/n261/mode/2up"><i>A history of science, technology and philosophy in the 18th century</i></a> (2nd ed.). London: George Allen & Unwin. p. 224.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+history+of+science%2C+technology+and+philosophy+in+the+18th+century&rft.place=London&rft.pages=224&rft.edition=2nd&rft.pub=George+Allen+%26+Unwin&rft.date=1962&rft.aulast=Wolf&rft.aufirst=A&rft.au=McKie%2C+D.&rft_id=https%3A%2F%2Farchive.org%2Fstream%2Fin.ernet.dli.2015.460063%2F2015.460063.A-History%23page%2Fn261%2Fmode%2F2up&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.efunda.com/glossary/units/units--electric_capacitance--jar.cfm">"eFunda: Glossary: Units: Electric Capacitance: Jar"</a>. eFunda<span class="reference-accessdate">. Retrieved <span class="nowrap">2013-03-17</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=eFunda%3A+Glossary%3A+Units%3A+Electric+Capacitance%3A+Jar&rft.pub=eFunda&rft_id=http%3A%2F%2Fwww.efunda.com%2Fglossary%2Funits%2Funits--electric_capacitance--jar.cfm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFPancaldi2003" class="citation book cs1">Pancaldi, G. (2003). <i>Volta: Science and culture in the Age of Enlightenment</i>. Princeton: Princeton University Press. pp. <span class="nowrap">112–</span>126. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0691096856" title="Special:BookSources/0691096856"><bdi>0691096856</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Volta%3A+Science+and+culture+in+the+Age+of+Enlightenment&rft.place=Princeton&rft.pages=%3Cspan+class%3D%22nowrap%22%3E112-%3C%2Fspan%3E126&rft.pub=Princeton+University+Press&rft.date=2003&rft.isbn=0691096856&rft.aulast=Pancaldi&rft.aufirst=G.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation journal cs1"><a rel="nofollow" class="external text" href="https://books.google.com/books?id=eCADAAAAMBAJ&pg=PA117">"Sketch of Alessandro Volta"</a>. <i>The Popular Science Monthly</i>. New York: Bonnier Corporation: <span class="nowrap">118–</span>119. May 1892. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0161-7370">0161-7370</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Popular+Science+Monthly&rft.atitle=Sketch+of+Alessandro+Volta&rft.pages=%3Cspan+class%3D%22nowrap%22%3E118-%3C%2Fspan%3E119&rft.date=1892-05&rft.issn=0161-7370&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DeCADAAAAMBAJ%26pg%3DPA117&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text">British Engineering Standards Association, <i>British Standard Glossary of Terms in Electrical Engineering</i>, C. Lockwood & Son, 1926</span> </li> <li id="cite_note-Boggs-17"><span class="mw-cite-backlink">^ <a href="#cite_ref-Boggs_17-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Boggs_17-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Boggs_17-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-Boggs_17-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-Boggs_17-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-Boggs_17-5"><sup><i><b>f</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFHoJowBoggs2010" class="citation journal cs1">Ho, Janet; Jow, T. Richard; Boggs, Steven (January 2010). <a rel="nofollow" class="external text" href="https://zenodo.org/record/1232215">"Historical Introduction to Capacitor Technology"</a>. <i>IEEE Electrical Insulation Magazine</i>. <b>26</b> (1): <span class="nowrap">20–</span>25. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2Fmei.2010.5383924">10.1109/mei.2010.5383924</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:23077215">23077215</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Electrical+Insulation+Magazine&rft.atitle=Historical+Introduction+to+Capacitor+Technology&rft.volume=26&rft.issue=1&rft.pages=%3Cspan+class%3D%22nowrap%22%3E20-%3C%2Fspan%3E25&rft.date=2010-01&rft_id=info%3Adoi%2F10.1109%2Fmei.2010.5383924&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A23077215%23id-name%3DS2CID&rft.aulast=Ho&rft.aufirst=Janet&rft.au=Jow%2C+T.+Richard&rft.au=Boggs%2C+Steven&rft_id=https%3A%2F%2Fzenodo.org%2Frecord%2F1232215&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1041539562">.mw-parser-output .citation{word-wrap:break-word}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}</style><span class="citation patent" id="CITEREFBecker,_H._I.1957"><a rel="nofollow" class="external text" href="https://worldwide.espacenet.com/textdoc?DB=EPODOC&IDX=US2800616">US 2800616</a>, Becker, H. I., "Low voltage electrolytic capacitor", issued 1957-07-23</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Apatent&rft.number=2800616&rft.cc=US&rft.title=Low+voltage+electrolytic+capacitor&rft.inventor=Becker%2C+H.+I.&rft.date=1957-07-23"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text">A brief history of supercapacitors AUTUMN 2007 <a rel="nofollow" class="external text" href="http://www.cantecsystems.com/ccrdocs/brief-history-of-supercapacitors.pdf">Batteries & Energy Storage Technology</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20140106032318/http://www.cantecsystems.com/ccrdocs/brief-history-of-supercapacitors.pdf">Archived</a> 2014-01-06 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFSzeLee2012" class="citation book cs1"><a href="/wiki/Simon_Sze" title="Simon Sze">Sze, Simon Min</a>; Lee, Ming-Kwei (May 2012). "MOS Capacitor and MOSFET". <a rel="nofollow" class="external text" href="https://www.oreilly.com/library/view/semiconductor-devices-physics/9780470537947/13_chap05.html"><i>Semiconductor Devices: Physics and Technology</i></a>. <a href="/wiki/John_Wiley_%26_Sons" class="mw-redirect" title="John Wiley & Sons">John Wiley & Sons</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-47053794-7" title="Special:BookSources/978-0-47053794-7"><bdi>978-0-47053794-7</bdi></a><span class="reference-accessdate">. Retrieved <span class="nowrap">2019-10-06</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=MOS+Capacitor+and+MOSFET&rft.btitle=Semiconductor+Devices%3A+Physics+and+Technology&rft.pub=John+Wiley+%26+Sons&rft.date=2012-05&rft.isbn=978-0-47053794-7&rft.aulast=Sze&rft.aufirst=Simon+Min&rft.au=Lee%2C+Ming-Kwei&rft_id=https%3A%2F%2Fwww.oreilly.com%2Flibrary%2Fview%2Fsemiconductor-devices-physics%2F9780470537947%2F13_chap05.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-ibm100-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-ibm100_21-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.ibm.com/ibm/history/ibm100/us/en/icons/dram/">"DRAM"</a>. <i>IBM100</i>. <a href="/wiki/IBM" title="IBM">IBM</a>. 2017-08-09<span class="reference-accessdate">. Retrieved <span class="nowrap">2019-09-20</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=IBM100&rft.atitle=DRAM&rft.date=2017-08-09&rft_id=https%3A%2F%2Fwww.ibm.com%2Fibm%2Fhistory%2Fibm100%2Fus%2Fen%2Ficons%2Fdram%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFSze2002" class="citation book cs1"><a href="/wiki/Simon_Sze" title="Simon Sze">Sze, Simon M.</a> (2002). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20230123184804/http://www.fulviofrisone.com/attachments/article/453/Semiconductor.Devices_Physics.Technology_Sze.2ndEd_Wiley_2002.pdf"><i>Semiconductor Devices: Physics and Technology</i></a> <span class="cs1-format">(PDF)</span> (2nd ed.). <a href="/wiki/Wiley_(publisher)" title="Wiley (publisher)">Wiley</a>. p. 214. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-471-33372-7" title="Special:BookSources/0-471-33372-7"><bdi>0-471-33372-7</bdi></a>. Archived from <a rel="nofollow" class="external text" href="http://www.fulviofrisone.com/attachments/article/453/Semiconductor.Devices_Physics.Technology_Sze.2ndEd_Wiley_2002.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2023-01-23.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Semiconductor+Devices%3A+Physics+and+Technology&rft.pages=214&rft.edition=2nd&rft.pub=Wiley&rft.date=2002&rft.isbn=0-471-33372-7&rft.aulast=Sze&rft.aufirst=Simon+M.&rft_id=http%3A%2F%2Fwww.fulviofrisone.com%2Fattachments%2Farticle%2F453%2FSemiconductor.Devices_Physics.Technology_Sze.2ndEd_Wiley_2002.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTEUlaby1999168-23"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTEUlaby1999168_23-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTEUlaby1999168_23-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFUlaby1999">Ulaby 1999</a>, p. 168.</span> </li> <li id="cite_note-FOOTNOTEUlaby1999157-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEUlaby1999157_24-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFUlaby1999">Ulaby 1999</a>, p. 157.</span> </li> <li id="cite_note-FOOTNOTEUlaby199969-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEUlaby199969_25-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFUlaby1999">Ulaby 1999</a>, p. 69.</span> </li> <li id="cite_note-Pillai1970-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-Pillai1970_26-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFPillai1970" class="citation journal cs1">Pillai, K. P. P. (1970). "Fringing field of finite parallel-plate capacitors". <i>Proceedings of the Institution of Electrical Engineers</i>. <b>117</b> (6): <span class="nowrap">1201–</span>1204. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1049%2Fpiee.1970.0232">10.1049/piee.1970.0232</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proceedings+of+the+Institution+of+Electrical+Engineers&rft.atitle=Fringing+field+of+finite+parallel-plate+capacitors&rft.volume=117&rft.issue=6&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1201-%3C%2Fspan%3E1204&rft.date=1970&rft_id=info%3Adoi%2F10.1049%2Fpiee.1970.0232&rft.aulast=Pillai&rft.aufirst=K.+P.+P.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-Purcell-27"><span class="mw-cite-backlink">^ <a href="#cite_ref-Purcell_27-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Purcell_27-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFPurcell2011" class="citation book cs1">Purcell, Edward (2011). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Z3bkNh6h4WEC&pg=PA110"><i>Electricity and Magnetism, 2nd Ed</i></a>. <a href="/wiki/Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a>. pp. <span class="nowrap">110–</span>111. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-13950355-6" title="Special:BookSources/978-1-13950355-6"><bdi>978-1-13950355-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Electricity+and+Magnetism%2C+2nd+Ed.&rft.pages=%3Cspan+class%3D%22nowrap%22%3E110-%3C%2Fspan%3E111&rft.pub=Cambridge+University+Press&rft.date=2011&rft.isbn=978-1-13950355-6&rft.aulast=Purcell&rft.aufirst=Edward&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DZ3bkNh6h4WEC%26pg%3DPA110&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-Serway-28"><span class="mw-cite-backlink">^ <a href="#cite_ref-Serway_28-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Serway_28-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFSerwayVuille2014" class="citation book cs1">Serway, Raymond A.; Vuille, Chris (2014). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=xETAAgAAQBAJ&pg=PA582"><i>College Physics, 10th Ed</i></a>. Cengage Learning. p. 582. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-30514282-4" title="Special:BookSources/978-1-30514282-4"><bdi>978-1-30514282-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=College+Physics%2C+10th+Ed.&rft.pages=582&rft.pub=Cengage+Learning&rft.date=2014&rft.isbn=978-1-30514282-4&rft.aulast=Serway&rft.aufirst=Raymond+A.&rft.au=Vuille%2C+Chris&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DxETAAgAAQBAJ%26pg%3DPA582&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-Hammond2013-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-Hammond2013_29-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFHammond2013" class="citation book cs1">Hammond, P. (2013). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=-8QgBQAAQBAJ&pg=PA44"><i>Electromagnetism for Engineers: An Introductory Course</i></a>. Elsevier Science. pp. <span class="nowrap">44–</span>45. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-48314978-3" title="Special:BookSources/978-1-48314978-3"><bdi>978-1-48314978-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Electromagnetism+for+Engineers%3A+An+Introductory+Course&rft.pages=%3Cspan+class%3D%22nowrap%22%3E44-%3C%2Fspan%3E45&rft.pub=Elsevier+Science&rft.date=2013&rft.isbn=978-1-48314978-3&rft.aulast=Hammond&rft.aufirst=P.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D-8QgBQAAQBAJ%26pg%3DPA44&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTEDorfSvoboda2001263-31"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEDorfSvoboda2001263_31-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFDorfSvoboda2001">Dorf & Svoboda 2001</a>, p. 263.</span> </li> <li id="cite_note-FOOTNOTEDorfSvoboda2001260-32"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEDorfSvoboda2001260_32-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFDorfSvoboda2001">Dorf & Svoboda 2001</a>, p. 260.</span> </li> <li id="cite_note-ChargingCircuit-33"><span class="mw-cite-backlink"><b><a href="#cite_ref-ChargingCircuit_33-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.allaboutcircuits.com/vol_6/chpt_3/17.html">"Capacitor charging and discharging"</a>. <i>All About Circuits</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2009-02-19</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=All+About+Circuits&rft.atitle=Capacitor+charging+and+discharging&rft_id=http%3A%2F%2Fwww.allaboutcircuits.com%2Fvol_6%2Fchpt_3%2F17.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-34"><span class="mw-cite-backlink"><b><a href="#cite_ref-34">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://www.researchgate.net/publication/313799141_Universality_of_the_emergent_scaling_in_finite_random_binary_percolation_networks">Current percolation through resistors and capacitors</a> PLoS one 2017</span> </li> <li id="cite_note-35"><span class="mw-cite-backlink"><b><a href="#cite_ref-35">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.researchgate.net/publication/313799141">"Universality of the emergent scaling in finite random binary percolation networks"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Universality+of+the+emergent+scaling+in+finite+random+binary+percolation+networks&rft_id=https%3A%2F%2Fwww.researchgate.net%2Fpublication%2F313799141&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTEUlaby1999170-36"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEUlaby1999170_36-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFUlaby1999">Ulaby 1999</a>, p. 170.</span> </li> <li id="cite_note-37"><span class="mw-cite-backlink"><b><a href="#cite_ref-37">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFPaiZhang1995" class="citation book cs1">Pai, S. T.; Zhang, Qi (1995). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=spZ_H4nwIN0C&pg=PA47"><i>Introduction to High Power Pulse Technology</i></a>. Advanced Series in Electrical and Computer Engineering. Vol. 10. World Scientific. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-9810217143" title="Special:BookSources/978-9810217143"><bdi>978-9810217143</bdi></a><span class="reference-accessdate">. Retrieved <span class="nowrap">2013-03-17</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+High+Power+Pulse+Technology&rft.series=Advanced+Series+in+Electrical+and+Computer+Engineering&rft.pub=World+Scientific&rft.date=1995&rft.isbn=978-9810217143&rft.aulast=Pai&rft.aufirst=S.+T.&rft.au=Zhang%2C+Qi&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DspZ_H4nwIN0C%26pg%3DPA47&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-38"><span class="mw-cite-backlink"><b><a href="#cite_ref-38">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFDyer2004" class="citation book cs1">Dyer, Stephen A. (2004). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Wr6l42rEizUC&pg=PA397"><i>Wiley Survey of Instrumentation and Measurement</i></a>. <a href="/wiki/John_Wiley_%26_Sons" class="mw-redirect" title="John Wiley & Sons">John Wiley & Sons</a>. p. 397. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-47122165-4" title="Special:BookSources/978-0-47122165-4"><bdi>978-0-47122165-4</bdi></a><span class="reference-accessdate">. Retrieved <span class="nowrap">2013-03-17</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Wiley+Survey+of+Instrumentation+and+Measurement&rft.pages=397&rft.pub=John+Wiley+%26+Sons&rft.date=2004&rft.isbn=978-0-47122165-4&rft.aulast=Dyer&rft.aufirst=Stephen+A.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DWr6l42rEizUC%26pg%3DPA397&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-39"><span class="mw-cite-backlink"><b><a href="#cite_ref-39">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFScherz2006" class="citation book cs1">Scherz, Paul (2006). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=C9pL3iL6eSMC&pg=PA100"><i>Practical Electronics for Inventors</i></a> (2nd ed.). <a href="/wiki/McGraw_Hill_Professional" class="mw-redirect" title="McGraw Hill Professional">McGraw Hill Professional</a>. p. 100. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07177644-8" title="Special:BookSources/978-0-07177644-8"><bdi>978-0-07177644-8</bdi></a><span class="reference-accessdate">. Retrieved <span class="nowrap">2013-03-17</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Practical+Electronics+for+Inventors&rft.pages=100&rft.edition=2nd&rft.pub=McGraw+Hill+Professional&rft.date=2006&rft.isbn=978-0-07177644-8&rft.aulast=Scherz&rft.aufirst=Paul&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DC9pL3iL6eSMC%26pg%3DPA100&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-40"><span class="mw-cite-backlink"><b><a href="#cite_ref-40">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFInuishiPowers1957" class="citation journal cs1">Inuishi, Y.; Powers, D. A. (1957). "Electric breakdown and conduction through Mylar films". <i>Journal of Applied Physics</i>. <b>28</b> (9): <span class="nowrap">1017–</span>1022. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1957JAP....28.1017I">1957JAP....28.1017I</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.1722899">10.1063/1.1722899</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Applied+Physics&rft.atitle=Electric+breakdown+and+conduction+through+Mylar+films&rft.volume=28&rft.issue=9&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1017-%3C%2Fspan%3E1022&rft.date=1957&rft_id=info%3Adoi%2F10.1063%2F1.1722899&rft_id=info%3Abibcode%2F1957JAP....28.1017I&rft.aulast=Inuishi&rft.aufirst=Y.&rft.au=Powers%2C+D.+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-41"><span class="mw-cite-backlink"><b><a href="#cite_ref-41">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFReedCichanowski1994" class="citation journal cs1">Reed, C. W.; Cichanowski, S. W. (1994). "The fundamentals of aging in HV polymer-film capacitors". <i><a href="/wiki/IEEE_Transactions_on_Dielectrics_and_Electrical_Insulation" title="IEEE Transactions on Dielectrics and Electrical Insulation">IEEE Transactions on Dielectrics and Electrical Insulation</a></i>. <b>1</b> (5): <span class="nowrap">904–</span>922. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2F94.326658">10.1109/94.326658</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Transactions+on+Dielectrics+and+Electrical+Insulation&rft.atitle=The+fundamentals+of+aging+in+HV+polymer-film+capacitors&rft.volume=1&rft.issue=5&rft.pages=%3Cspan+class%3D%22nowrap%22%3E904-%3C%2Fspan%3E922&rft.date=1994&rft_id=info%3Adoi%2F10.1109%2F94.326658&rft.aulast=Reed&rft.aufirst=C.+W.&rft.au=Cichanowski%2C+S.+W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-42"><span class="mw-cite-backlink"><b><a href="#cite_ref-42">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFKleinGafni1966" class="citation journal cs1">Klein, N.; Gafni, H. (1966). "The maximum dielectric strength of thin silicon oxide films". <i>IEEE Transactions on Electron Devices</i>. <b>13</b> (2): <span class="nowrap">281–</span>289. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1966ITED...13..281K">1966ITED...13..281K</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FT-ED.1966.15681">10.1109/T-ED.1966.15681</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Transactions+on+Electron+Devices&rft.atitle=The+maximum+dielectric+strength+of+thin+silicon+oxide+films&rft.volume=13&rft.issue=2&rft.pages=%3Cspan+class%3D%22nowrap%22%3E281-%3C%2Fspan%3E289&rft.date=1966&rft_id=info%3Adoi%2F10.1109%2FT-ED.1966.15681&rft_id=info%3Abibcode%2F1966ITED...13..281K&rft.aulast=Klein&rft.aufirst=N.&rft.au=Gafni%2C+H.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-43"><span class="mw-cite-backlink"><b><a href="#cite_ref-43">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFBelkin2017" class="citation journal cs1">Belkin, A.; et al. (2017). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5430567">"Recovery of alumina nanocapacitors after high voltage breakdown"</a>. <i>Scientific Reports</i>. <b>7</b> (1): 932. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2017NatSR...7..932B">2017NatSR...7..932B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2Fs41598-017-01007-9">10.1038/s41598-017-01007-9</a>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5430567">5430567</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/28428625">28428625</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Scientific+Reports&rft.atitle=Recovery+of+alumina+nanocapacitors+after+high+voltage+breakdown&rft.volume=7&rft.issue=1&rft.pages=932&rft.date=2017&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC5430567%23id-name%3DPMC&rft_id=info%3Apmid%2F28428625&rft_id=info%3Adoi%2F10.1038%2Fs41598-017-01007-9&rft_id=info%3Abibcode%2F2017NatSR...7..932B&rft.aulast=Belkin&rft.aufirst=A.&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC5430567&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-44"><span class="mw-cite-backlink"><b><a href="#cite_ref-44">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFBird2007" class="citation book cs1">Bird, John (2007). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Q9zpWdgQeM4C&pg=PA501"><i>Electrical Circuit Theory and Technology</i></a>. Routledge. p. 501. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-75068139-1" title="Special:BookSources/978-0-75068139-1"><bdi>978-0-75068139-1</bdi></a><span class="reference-accessdate">. Retrieved <span class="nowrap">2013-03-17</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Electrical+Circuit+Theory+and+Technology&rft.pages=501&rft.pub=Routledge&rft.date=2007&rft.isbn=978-0-75068139-1&rft.aulast=Bird&rft.aufirst=John&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DQ9zpWdgQeM4C%26pg%3DPA501&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-45"><span class="mw-cite-backlink"><b><a href="#cite_ref-45">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFBisquertGarcia-BelmonteFabregat-Santiago2000" class="citation journal cs1">Bisquert, J.; Garcia-Belmonte, G.; Fabregat-Santiago, F. (2000). <a rel="nofollow" class="external text" href="https://ieeexplore.ieee.org/document/883355">"The role of instrumentation in the process of modeling real capacitors"</a>. <i>IEEE Transactions on Education</i>. <b>43</b> (4): <span class="nowrap">439–</span>442. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2000ITEdu..43..439F">2000ITEdu..43..439F</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2F13.883355">10.1109/13.883355</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1557-9638">1557-9638</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Transactions+on+Education&rft.atitle=The+role+of+instrumentation+in+the+process+of+modeling+real+capacitors&rft.volume=43&rft.issue=4&rft.pages=%3Cspan+class%3D%22nowrap%22%3E439-%3C%2Fspan%3E442&rft.date=2000&rft.issn=1557-9638&rft_id=info%3Adoi%2F10.1109%2F13.883355&rft_id=info%3Abibcode%2F2000ITEdu..43..439F&rft.aulast=Bisquert&rft.aufirst=J.&rft.au=Garcia-Belmonte%2C+G.&rft.au=Fabregat-Santiago%2C+F.&rft_id=https%3A%2F%2Fieeexplore.ieee.org%2Fdocument%2F883355&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTEUlaby1999169-46"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEUlaby1999169_46-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFUlaby1999">Ulaby 1999</a>, p. 169.</span> </li> <li id="cite_note-47"><span class="mw-cite-backlink"><b><a href="#cite_ref-47">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20121226160520/http://www.johansondielectrics.com/technical-notes/general/ceramic-capacitor-aging-made-simple.html">"Ceramic Capacitor Aging Made Simple"</a>. Johanson Dielectrics. 2012-05-21. Archived from <a rel="nofollow" class="external text" href="http://www.johansondielectrics.com/technical-notes/general/ceramic-capacitor-aging-made-simple.html">the original</a> on 2012-12-26<span class="reference-accessdate">. Retrieved <span class="nowrap">2013-03-17</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Ceramic+Capacitor+Aging+Made+Simple&rft.pub=Johanson+Dielectrics&rft.date=2012-05-21&rft_id=http%3A%2F%2Fwww.johansondielectrics.com%2Ftechnical-notes%2Fgeneral%2Fceramic-capacitor-aging-made-simple.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-48"><span class="mw-cite-backlink"><b><a href="#cite_ref-48">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.allaboutcircuits.com/technical-articles/x7r-x5r-c0g...-a-concise-guide-to-ceramic-capacitor-types/">"Concise Guide to Capacitor Types"</a>. EETech Media LLC<span class="reference-accessdate">. Retrieved <span class="nowrap">2023-09-07</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Concise+Guide+to+Capacitor+Types&rft.pub=EETech+Media+LLC&rft_id=https%3A%2F%2Fwww.allaboutcircuits.com%2Ftechnical-articles%2Fx7r-x5r-c0g...-a-concise-guide-to-ceramic-capacitor-types%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-49"><span class="mw-cite-backlink"><b><a href="#cite_ref-49">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20140714134127/http://www.ga.com/websites/ga/images/products/ep/tech-bulletins/voltage-reversal.pdf">"The Effect of Reversal on Capacitor Life"</a> <span class="cs1-format">(PDF)</span>. <i>Engineering Bulletin 96-004</i>. Sorrento Electronics. November 2003. Archived from <a rel="nofollow" class="external text" href="http://www.ga.com/websites/ga/images/products/ep/tech-bulletins/voltage-reversal.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2014-07-14<span class="reference-accessdate">. Retrieved <span class="nowrap">2013-03-17</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Engineering+Bulletin+96-004&rft.atitle=The+Effect+of+Reversal+on+Capacitor+Life&rft.date=2003-11&rft_id=http%3A%2F%2Fwww.ga.com%2Fwebsites%2Fga%2Fimages%2Fproducts%2Fep%2Ftech-bulletins%2Fvoltage-reversal.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-Kaiser2012-50"><span class="mw-cite-backlink"><b><a href="#cite_ref-Kaiser2012_50-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFKaiser2012" class="citation book cs1">Kaiser, Cletus J. (2012-12-06). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=FOatBAAAQBAJ"><i>The Capacitor Handbook</i></a>. Springer Science & Business Media. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-9-40118090-0" title="Special:BookSources/978-9-40118090-0"><bdi>978-9-40118090-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Capacitor+Handbook&rft.pub=Springer+Science+%26+Business+Media&rft.date=2012-12-06&rft.isbn=978-9-40118090-0&rft.aulast=Kaiser&rft.aufirst=Cletus+J.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DFOatBAAAQBAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-51"><span class="mw-cite-backlink"><b><a href="#cite_ref-51">^</a></b></span> <span class="reference-text"><i>Electronics</i>. McGraw-Hill 1960 p. 90</span> </li> <li id="cite_note-52"><span class="mw-cite-backlink"><b><a href="#cite_ref-52">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://donklipstein.com/xesafe.html">Xenon Strobe and Flash Safety Hints</a>. donklipstein.com. 2006-05-29</span> </li> <li id="cite_note-Prutchi2012-53"><span class="mw-cite-backlink"><b><a href="#cite_ref-Prutchi2012_53-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFPrutchi2012" class="citation book cs1">Prutchi, David (2012). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=LLxsnx74KEYC&pg=PA10"><i>Exploring Quantum Physics through Hands-on Projects</i></a>. <a href="/wiki/John_Wiley_%26_Sons" class="mw-redirect" title="John Wiley & Sons">John Wiley & Sons</a>. p. 10. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-11817070-0" title="Special:BookSources/978-1-11817070-0"><bdi>978-1-11817070-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Exploring+Quantum+Physics+through+Hands-on+Projects&rft.pages=10&rft.pub=John+Wiley+%26+Sons&rft.date=2012&rft.isbn=978-1-11817070-0&rft.aulast=Prutchi&rft.aufirst=David&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DLLxsnx74KEYC%26pg%3DPA10&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-DixitYadav2010-54"><span class="mw-cite-backlink"><b><a href="#cite_ref-DixitYadav2010_54-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFDixitYadav2010" class="citation book cs1">Dixit, J. B.; Yadav, Amit (2010). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=lxLWYe5sGMsC&pg=PA63"><i>Electrical Power Quality</i></a>. Laxmi Publications, Ltd. p. 63. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-9-38038674-4" title="Special:BookSources/978-9-38038674-4"><bdi>978-9-38038674-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Electrical+Power+Quality&rft.pages=63&rft.pub=Laxmi+Publications%2C+Ltd.&rft.date=2010&rft.isbn=978-9-38038674-4&rft.aulast=Dixit&rft.aufirst=J.+B.&rft.au=Yadav%2C+Amit&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DlxLWYe5sGMsC%26pg%3DPA63&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-ReferenceA-55"><span class="mw-cite-backlink">^ <a href="#cite_ref-ReferenceA_55-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-ReferenceA_55-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-ReferenceA_55-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-ReferenceA_55-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFWinburn1989" class="citation book cs1">Winburn (1989). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=xx1I5eQybE8C&pg=PA189"><i>Practical Laser Safety, Second Edition</i></a>. <a href="/wiki/CRC_Press" title="CRC Press">CRC Press</a>. p. 189. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-82478240-5" title="Special:BookSources/978-0-82478240-5"><bdi>978-0-82478240-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Practical+Laser+Safety%2C+Second+Edition&rft.pages=189&rft.pub=CRC+Press&rft.date=1989&rft.isbn=978-0-82478240-5&rft.au=Winburn&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dxx1I5eQybE8C%26pg%3DPA189&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-56"><span class="mw-cite-backlink"><b><a href="#cite_ref-56">^</a></b></span> <span class="reference-text"><i>Robinson's Manual of Radio Telegraphy and Telephony by S.S. Robinson -- US Naval Institute 1924 Pg. 170</i></span> </li> <li id="cite_note-57"><span class="mw-cite-backlink"><b><a href="#cite_ref-57">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFGuptaYadavDeVotoMajor2018" class="citation web cs1">Gupta, Anunay; Yadav, Om Prakash; DeVoto, Douglas; Major, Joshua (October 2018). <a rel="nofollow" class="external text" href="https://www.nrel.gov/docs/fy19osti/71386.pdf">"A Review of Degradation Behavior and Modeling of Capacitors"</a> <span class="cs1-format">(PDF)</span>. National Renewable Energy Laboratory. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200605220416/https://www.nrel.gov/docs/fy19osti/71386.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 2020-06-05<span class="reference-accessdate">. Retrieved <span class="nowrap">2021-07-23</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=A+Review+of+Degradation+Behavior+and+Modeling+of+Capacitors&rft.pub=National+Renewable+Energy+Laboratory&rft.date=2018-10&rft.aulast=Gupta&rft.aufirst=Anunay&rft.au=Yadav%2C+Om+Prakash&rft.au=DeVoto%2C+Douglas&rft.au=Major%2C+Joshua&rft_id=https%3A%2F%2Fwww.nrel.gov%2Fdocs%2Ffy19osti%2F71386.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-58"><span class="mw-cite-backlink"><b><a href="#cite_ref-58">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFGuinta" class="citation web cs1">Guinta, Steve. <a rel="nofollow" class="external text" href="http://www.analog.com/library/analogDialogue/Anniversary/21.html">"Ask The Applications Engineer – 21"</a>. Analog Devices<span class="reference-accessdate">. Retrieved <span class="nowrap">2013-03-17</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Ask+The+Applications+Engineer+%E2%80%93+21&rft.pub=Analog+Devices&rft.aulast=Guinta&rft.aufirst=Steve&rft_id=http%3A%2F%2Fwww.analog.com%2Flibrary%2FanalogDialogue%2FAnniversary%2F21.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-Araujo-59"><span class="mw-cite-backlink"><b><a href="#cite_ref-Araujo_59-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFde_AraujoRameshTaylor2001" class="citation book cs1">de Araujo, Carlos Paz; Ramesh, Ramamoorthy; Taylor, George W., eds. (2001). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=QMlOkeJ4qN4C&pg=PA504"><i>Science and Technology of Integrated Ferroelectrics: Selected Papers from Eleven Years of the Proceedings of the International Symposium on Integrated Ferroelectrics</i></a>. <a href="/wiki/CRC_Press" title="CRC Press">CRC Press</a>. Figure 2, p. 504. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/90-5699-704-1" title="Special:BookSources/90-5699-704-1"><bdi>90-5699-704-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Science+and+Technology+of+Integrated+Ferroelectrics%3A+Selected+Papers+from+Eleven+Years+of+the+Proceedings+of+the+International+Symposium+on+Integrated+Ferroelectrics&rft.pages=Figure+2%2C+p.+504&rft.pub=CRC+Press&rft.date=2001&rft.isbn=90-5699-704-1&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DQMlOkeJ4qN4C%26pg%3DPA504&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-Musikant-60"><span class="mw-cite-backlink"><b><a href="#cite_ref-Musikant_60-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFMusikant1991" class="citation book cs1">Musikant, Solomon (1991). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Jc8xRdgdH38C&pg=PA44"><i>What Every Engineer Should Know about Ceramics</i></a>. <a href="/wiki/CRC_Press" title="CRC Press">CRC Press</a>. Figure 3.9, p. 43. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-8247-8498-7" title="Special:BookSources/0-8247-8498-7"><bdi>0-8247-8498-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=What+Every+Engineer+Should+Know+about+Ceramics&rft.pages=Figure+3.9%2C+p.+43&rft.pub=CRC+Press&rft.date=1991&rft.isbn=0-8247-8498-7&rft.aulast=Musikant&rft.aufirst=Solomon&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DJc8xRdgdH38C%26pg%3DPA44&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-Cho-61"><span class="mw-cite-backlink"><b><a href="#cite_ref-Cho_61-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFYasuo_Cho2005" class="citation book cs1">Yasuo Cho (2005). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=wQ09DhMBJroC&pg=PA304"><i>Scanning Nonlinear Dielectric Microscope</i></a> (in <i>Polar Oxides</i>; <a href="/wiki/Rainer_Waser" title="Rainer Waser">R. Waser</a>, U. Böttger & S. Tiedke, editors ed.). Wiley-VCH. Chapter 16. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/3-527-40532-1" title="Special:BookSources/3-527-40532-1"><bdi>3-527-40532-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Scanning+Nonlinear+Dielectric+Microscope&rft.pages=Chapter+16&rft.edition=in+%27%27Polar+Oxides%27%27%3B+R.+Waser%2C+U.+B%C3%B6ttger+%26+S.+Tiedke%2C+editors&rft.pub=Wiley-VCH&rft.date=2005&rft.isbn=3-527-40532-1&rft.au=Yasuo+Cho&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DwQ09DhMBJroC%26pg%3DPA304&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTESzeNg2006217-62"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTESzeNg2006217_62-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTESzeNg2006217_62-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFSzeNg2006">Sze & Ng 2006</a>, p. 217.</span> </li> <li id="cite_note-Giuliani-63"><span class="mw-cite-backlink"><b><a href="#cite_ref-Giuliani_63-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFGiulianiVignale2005" class="citation book cs1">Giuliani, Gabriele; Vignale, Giovanni (2005). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=kFkIKRfgUpsC&pg=PA538"><i>Quantum Theory of the Electron Liquid</i></a>. <a href="/wiki/Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a>. p. 111. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-521-82112-6" title="Special:BookSources/0-521-82112-6"><bdi>0-521-82112-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Quantum+Theory+of+the+Electron+Liquid&rft.pages=111&rft.pub=Cambridge+University+Press&rft.date=2005&rft.isbn=0-521-82112-6&rft.aulast=Giuliani&rft.aufirst=Gabriele&rft.au=Vignale%2C+Giovanni&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DkFkIKRfgUpsC%26pg%3DPA538&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-Rammer-64"><span class="mw-cite-backlink"><b><a href="#cite_ref-Rammer_64-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFRammer2007" class="citation book cs1">Rammer, Jørgen (2007). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=A7TbrAm5Wq0C&pg=PA6"><i>Quantum Field Theory of Non-equilibrium States</i></a>. <a href="/wiki/Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a>. p. 158. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-52187499-1" title="Special:BookSources/978-0-52187499-1"><bdi>978-0-52187499-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Quantum+Field+Theory+of+Non-equilibrium+States&rft.pages=158&rft.pub=Cambridge+University+Press&rft.date=2007&rft.isbn=978-0-52187499-1&rft.aulast=Rammer&rft.aufirst=J%C3%B8rgen&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DA7TbrAm5Wq0C%26pg%3DPA6&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-Handbook-65"><span class="mw-cite-backlink"><b><a href="#cite_ref-Handbook_65-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFCzichosSaitoSmith2006" class="citation book cs1">Czichos, Horst; Saito, Tetsuya; Smith, Leslie (2006). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=8lANaR-Pqi4C&pg=PA1"><i>Springer Handbook of Materials Measurement Methods</i></a>. Springer. p. 475. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/3-540-20785-6" title="Special:BookSources/3-540-20785-6"><bdi>3-540-20785-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Springer+Handbook+of+Materials+Measurement+Methods&rft.pages=475&rft.pub=Springer&rft.date=2006&rft.isbn=3-540-20785-6&rft.aulast=Czichos&rft.aufirst=Horst&rft.au=Saito%2C+Tetsuya&rft.au=Smith%2C+Leslie&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D8lANaR-Pqi4C%26pg%3DPA1&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-Coffey-66"><span class="mw-cite-backlink"><b><a href="#cite_ref-Coffey_66-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFCoffeyKalmykov2006" class="citation book cs1">Coffey, William; Kalmykov, Yu. P. (2006). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=mgtQslaXBc4C&pg=PA18"><i>Fractals, diffusion and relaxation in disordered complex systems. Part A</i></a>. Wiley. p. 17. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-470-04607-4" title="Special:BookSources/0-470-04607-4"><bdi>0-470-04607-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fractals%2C+diffusion+and+relaxation+in+disordered+complex+systems.+Part+A&rft.pages=17&rft.pub=Wiley&rft.date=2006&rft.isbn=0-470-04607-4&rft.aulast=Coffey&rft.aufirst=William&rft.au=Kalmykov%2C+Yu.+P.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DmgtQslaXBc4C%26pg%3DPA18&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-67"><span class="mw-cite-backlink"><b><a href="#cite_ref-67">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation book cs1"><a rel="nofollow" class="external text" href="https://books.google.com/books?id=85I5nQAACAAJ&pg=PA1350"><i>2005 IEEE Instrumentation and Measurement Technology Conference (IMTC): Ottawa, Ontario Canada, 16–19 May 2005</i></a>. IEEE. 2005. pp. <span class="nowrap">1350–</span>1353. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FIMTC.2005.1604368">10.1109/IMTC.2005.1604368</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-78038879-6" title="Special:BookSources/978-0-78038879-6"><bdi>978-0-78038879-6</bdi></a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:37739028">37739028</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=2005+IEEE+Instrumentation+and+Measurement+Technology+Conference+%28IMTC%29%3A+Ottawa%2C+Ontario+Canada%2C+16%E2%80%9319+May+2005&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1350-%3C%2Fspan%3E1353&rft.pub=IEEE&rft.date=2005&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A37739028%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1109%2FIMTC.2005.1604368&rft.isbn=978-0-78038879-6&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D85I5nQAACAAJ%26pg%3DPA1350&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTESchroder2006347-68"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTESchroder2006347_68-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFSchroder2006">Schroder 2006</a>, p. 347.</span> </li> <li id="cite_note-FOOTNOTESchroder2006305-69"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTESchroder2006305_69-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFSchroder2006">Schroder 2006</a>, p. 305.</span> </li> <li id="cite_note-Kasap-70"><span class="mw-cite-backlink"><b><a href="#cite_ref-Kasap_70-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFKasapCapper2006" class="citation book cs1">Kasap, Safa O.; Capper, Peter (2006). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=rVVW22pnzhoC&pg=PA425"><i>Springer Handbook of Electronic and Photonic Materials</i></a>. Springer. Figure 20.22, p. 425.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Springer+Handbook+of+Electronic+and+Photonic+Materials&rft.pages=Figure+20.22%2C+p.+425&rft.pub=Springer&rft.date=2006&rft.aulast=Kasap&rft.aufirst=Safa+O.&rft.au=Capper%2C+Peter&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DrVVW22pnzhoC%26pg%3DPA425&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-Cardona-71"><span class="mw-cite-backlink"><b><a href="#cite_ref-Cardona_71-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFPY_YuCardona2001" class="citation book cs1">PY Yu; Cardona, Manuel (2001). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=W9pdJZoAeyEC&pg=PA244"><i>Fundamentals of Semiconductors</i></a> (3rd ed.). Springer. §6.6 "Modulation Spectroscopy". <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/3-540-25470-6" title="Special:BookSources/3-540-25470-6"><bdi>3-540-25470-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fundamentals+of+Semiconductors&rft.pages=%C2%A76.6+%22Modulation+Spectroscopy%22&rft.edition=3rd&rft.pub=Springer&rft.date=2001&rft.isbn=3-540-25470-6&rft.au=PY+Yu&rft.au=Cardona%2C+Manuel&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DW9pdJZoAeyEC%26pg%3DPA244&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-KaplanWhite2003-72"><span class="mw-cite-backlink"><b><a href="#cite_ref-KaplanWhite2003_72-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFKaplanWhite2003" class="citation book cs1">Kaplan, Daniel M.; White, Christopher G. (2003). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=kNbGGpuJyjMC&pg=PA19"><i>Hands-On Electronics: A Practical Introduction to Analog and Digital Circuits</i></a>. <a href="/wiki/Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a>. p. 19. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-52189351-0" title="Special:BookSources/978-0-52189351-0"><bdi>978-0-52189351-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Hands-On+Electronics%3A+A+Practical+Introduction+to+Analog+and+Digital+Circuits&rft.pages=19&rft.pub=Cambridge+University+Press&rft.date=2003&rft.isbn=978-0-52189351-0&rft.aulast=Kaplan&rft.aufirst=Daniel+M.&rft.au=White%2C+Christopher+G.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DkNbGGpuJyjMC%26pg%3DPA19&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-SIST-EN60062-A1_2019-73"><span class="mw-cite-backlink">^ <a href="#cite_ref-SIST-EN60062-A1_2019_73-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-SIST-EN60062-A1_2019_73-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation book cs1">"Annex B: Special two-character code system for capacitors". <a rel="nofollow" class="external text" href="https://cdn.standards.iteh.ai/samples/67713/7c42aed17a454cdaaff49b69445f0ee8/SIST-EN-60062-2016-A1-2019.pdf"><i>SLOVENSKI STANDARD SIST EN 60062:2016/A1:2019</i></a> <span class="cs1-format">(PDF)</span> (preview). 2019-12-01. pp. <span class="nowrap">3–</span>4. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20220617174351/https://cdn.standards.iteh.ai/samples/67713/7c42aed17a454cdaaff49b69445f0ee8/SIST-EN-60062-2016-A1-2019.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 2022-06-17<span class="reference-accessdate">. Retrieved <span class="nowrap">2022-06-17</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Annex+B%3A+Special+two-character+code+system+for+capacitors&rft.btitle=SLOVENSKI+STANDARD+SIST+EN+60062%3A2016%2FA1%3A2019&rft.pages=%3Cspan+class%3D%22nowrap%22%3E3-%3C%2Fspan%3E4&rft.date=2019-12-01&rft_id=https%3A%2F%2Fcdn.standards.iteh.ai%2Fsamples%2F67713%2F7c42aed17a454cdaaff49b69445f0ee8%2FSIST-EN-60062-2016-A1-2019.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-Zabkar_2011-75"><span class="mw-cite-backlink">^ <a href="#cite_ref-Zabkar_2011_75-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Zabkar_2011_75-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Zabkar_2011_75-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFZabkar2011" class="citation web cs1">Zabkar, Franc (2011-09-15). <a rel="nofollow" class="external text" href="https://www.electronicspoint.com/forums/threads/eia-198-d-capacitance-codes.238921/">"EIA-198-D capacitance codes"</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20220617225054/https://www.electronicspoint.com/forums/threads/eia-198-d-capacitance-codes.238921/">Archived</a> from the original on 2022-06-17<span class="reference-accessdate">. Retrieved <span class="nowrap">2022-06-18</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=EIA-198-D+capacitance+codes&rft.date=2011-09-15&rft.aulast=Zabkar&rft.aufirst=Franc&rft_id=https%3A%2F%2Fwww.electronicspoint.com%2Fforums%2Fthreads%2Feia-198-d-capacitance-codes.238921%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-FoE-1965-76"><span class="mw-cite-backlink">^ <a href="#cite_ref-FoE-1965_76-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FoE-1965_76-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://archive.org/details/FundamentalsOfElectronics93400A1b">"Fundamentals of Electronics, Volume 1b: Basic Electricity, Alternating Current, NAVPERS 93400A-1b"</a>. 1965-04-12 – via Internet Archive.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Fundamentals+of+Electronics%2C+Volume+1b%3A+Basic+Electricity%2C+Alternating+Current%2C+NAVPERS+93400A-1b&rft.date=1965-04-12&rft_id=http%3A%2F%2Farchive.org%2Fdetails%2FFundamentalsOfElectronics93400A1b&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-77"><span class="mw-cite-backlink"><b><a href="#cite_ref-77">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20170711160331/http://www.alliedcatalogs.com/html/catalogs_additional/1930/hr139.html">"1930 Catalog – Capacitors (Condensers)"</a>. <i><a href="/wiki/Allied_Electronics" class="mw-redirect" title="Allied Electronics">Allied Radio</a></i>. p. 139. Archived from <a rel="nofollow" class="external text" href="http://www.alliedcatalogs.com/html/catalogs_additional/1930/hr139.html">the original</a> on 2017-07-11<span class="reference-accessdate">. Retrieved <span class="nowrap">2017-07-11</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Allied+Radio&rft.atitle=1930+Catalog+%E2%80%93+Capacitors+%28Condensers%29&rft.pages=139&rft_id=http%3A%2F%2Fwww.alliedcatalogs.com%2Fhtml%2Fcatalogs_additional%2F1930%2Fhr139.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-78"><span class="mw-cite-backlink"><b><a href="#cite_ref-78">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.justradios.com/MFMMFD.html">"Capacitor MF - MMFD Conversion Chart"</a>. <i>www.justradios.com</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www.justradios.com&rft.atitle=Capacitor+MF+-+MMFD+Conversion+Chart&rft_id=https%3A%2F%2Fwww.justradios.com%2FMFMMFD.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-79"><span class="mw-cite-backlink"><b><a href="#cite_ref-79">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFMiller2011" class="citation book cs1">Miller, Charles (2011). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=RSsJAAAAQBAJ&pg=PA445"><i>Illustrated Guide to the National Electrical Code</i></a>. Cengage Learning. p. 445.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Illustrated+Guide+to+the+National+Electrical+Code&rft.pages=445&rft.pub=Cengage+Learning&rft.date=2011&rft.aulast=Miller&rft.aufirst=Charles&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DRSsJAAAAQBAJ%26pg%3DPA445&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-80"><span class="mw-cite-backlink"><b><a href="#cite_ref-80">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFShinn2012" class="citation journal cs1">Shinn, Eric; et al. (2012). "Nuclear energy conversion with stacks of graphene nanocapacitors". <i>Complexity</i>. <b>18</b> (3): <span class="nowrap">24–</span>27. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2013Cmplx..18c..24S">2013Cmplx..18c..24S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fcplx.21427">10.1002/cplx.21427</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Complexity&rft.atitle=Nuclear+energy+conversion+with+stacks+of+graphene+nanocapacitors&rft.volume=18&rft.issue=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E24-%3C%2Fspan%3E27&rft.date=2012&rft_id=info%3Adoi%2F10.1002%2Fcplx.21427&rft_id=info%3Abibcode%2F2013Cmplx..18c..24S&rft.aulast=Shinn&rft.aufirst=Eric&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-81"><span class="mw-cite-backlink"><b><a href="#cite_ref-81">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFBezryadinBelkin2017" class="citation journal cs1">Bezryadin, A.; Belkin, A.; et al. (2017). "Large energy storage efficiency of the dielectric layer of graphene nanocapacitors". <i>Nanotechnology</i>. <b>28</b> (49): 495401. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/2011.11867">2011.11867</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2017Nanot..28W5401B">2017Nanot..28W5401B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1088%2F1361-6528%2Faa935c">10.1088/1361-6528/aa935c</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/29027908">29027908</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:44693636">44693636</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nanotechnology&rft.atitle=Large+energy+storage+efficiency+of+the+dielectric+layer+of+graphene+nanocapacitors&rft.volume=28&rft.issue=49&rft.pages=495401&rft.date=2017&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A44693636%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2017Nanot..28W5401B&rft_id=info%3Aarxiv%2F2011.11867&rft_id=info%3Apmid%2F29027908&rft_id=info%3Adoi%2F10.1088%2F1361-6528%2Faa935c&rft.aulast=Bezryadin&rft.aufirst=A.&rft.au=Belkin%2C+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-Floyd2017-82"><span class="mw-cite-backlink"><b><a href="#cite_ref-Floyd2017_82-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFFloyd2017" class="citation book cs1">Floyd, Thomas L. (2017). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=vg41vgAACAAJ&pg=PA10"><i>Electronic Devices</i></a>. Pearson. p. 10. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-13441444-7" title="Special:BookSources/978-0-13441444-7"><bdi>978-0-13441444-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Electronic+Devices&rft.pages=10&rft.pub=Pearson&rft.date=2017&rft.isbn=978-0-13441444-7&rft.aulast=Floyd&rft.aufirst=Thomas+L.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dvg41vgAACAAJ%26pg%3DPA10&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-83"><span class="mw-cite-backlink"><b><a href="#cite_ref-83">^</a></b></span> <span class="reference-text"><i>Pulsed Power</i> by Gennady A. Mesyats -- Springer 2005 Page 1--5</span> </li> <li id="cite_note-84"><span class="mw-cite-backlink"><b><a href="#cite_ref-84">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFAlamAzarianOstermanPecht2010" class="citation journal cs1">Alam, Mohammed; Azarian, Michael H.; Osterman, Michael; Pecht, Michael (2010). "Effectiveness of embedded capacitors in reducing the number of surface mount capacitors for decoupling applications". <i>Circuit World</i>. <b>36</b> (1): 22. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1108%2F03056121011015068">10.1108/03056121011015068</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Circuit+World&rft.atitle=Effectiveness+of+embedded+capacitors+in+reducing+the+number+of+surface+mount+capacitors+for+decoupling+applications&rft.volume=36&rft.issue=1&rft.pages=22&rft.date=2010&rft_id=info%3Adoi%2F10.1108%2F03056121011015068&rft.aulast=Alam&rft.aufirst=Mohammed&rft.au=Azarian%2C+Michael+H.&rft.au=Osterman%2C+Michael&rft.au=Pecht%2C+Michael&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> <li id="cite_note-85"><span class="mw-cite-backlink"><b><a href="#cite_ref-85">^</a></b></span> <span class="reference-text">Downie, Neil A and Mathilde Pradier, 'Method and apparatus for monitoring fluid pressure", US Patent 7526961 (2009)</span> </li> <li id="cite_note-86"><span class="mw-cite-backlink"><b><a href="#cite_ref-86">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://donklipstein.com/xesafe.html">"Some Xenon Strobe and Flash Safety Hints"</a>. <i>donklipstein.com</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=donklipstein.com&rft.atitle=Some+Xenon+Strobe+and+Flash+Safety+Hints&rft_id=http%3A%2F%2Fdonklipstein.com%2Fxesafe.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading3"><h3 id="Bibliography">Bibliography</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=58" title="Edit section: Bibliography"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFDorfSvoboda2001" class="citation book cs1">Dorf, Richard C.; Svoboda, James A. (2001). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=l-weAQAAIAAJ"><i>Introduction to Electric Circuits</i></a> (5th ed.). New York: John Wiley & Sons. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-47138689-6" title="Special:BookSources/978-0-47138689-6"><bdi>978-0-47138689-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+Electric+Circuits&rft.place=New+York&rft.edition=5th&rft.pub=John+Wiley+%26+Sons&rft.date=2001&rft.isbn=978-0-47138689-6&rft.aulast=Dorf&rft.aufirst=Richard+C.&rft.au=Svoboda%2C+James+A.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dl-weAQAAIAAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></li> <li>Philosophical Transactions of the Royal Society LXXII, Appendix 8, 1782 (Volta coins the word <i>condenser</i>)</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFUlaby1999" class="citation book cs1">Ulaby, Fawwaz Tayssir (1999). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=a_C8QgAACAAJ"><i>Fundamentals of Applied Electromagnetics</i></a> (2nd ed.). Upper Saddle River, New Jersey, USA: <a href="/wiki/Prentice_Hall" title="Prentice Hall">Prentice Hall</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-13011554-6" title="Special:BookSources/978-0-13011554-6"><bdi>978-0-13011554-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fundamentals+of+Applied+Electromagnetics&rft.place=Upper+Saddle+River%2C+New+Jersey%2C+USA&rft.edition=2nd&rft.pub=Prentice+Hall&rft.date=1999&rft.isbn=978-0-13011554-6&rft.aulast=Ulaby&rft.aufirst=Fawwaz+Tayssir&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Da_C8QgAACAAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFSchroder2006" class="citation book cs1">Schroder, Dieter K. (2006). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=OX2cHKJWCKgC&pg=PA305"><i>Semiconductor Material and Device Characterization</i></a> (3rd ed.). Wiley. p. 270 <i>ff</i>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-47173906-7" title="Special:BookSources/978-0-47173906-7"><bdi>978-0-47173906-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Semiconductor+Material+and+Device+Characterization&rft.pages=270+%27%27ff%27%27&rft.edition=3rd&rft.pub=Wiley&rft.date=2006&rft.isbn=978-0-47173906-7&rft.aulast=Schroder&rft.aufirst=Dieter+K.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DOX2cHKJWCKgC%26pg%3DPA305&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFSzeNg2006" class="citation book cs1">Sze, Simon M.; Ng, Kwok K. (2006). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=o4unkmHBHb8C"><i>Physics of Semiconductor Devices</i></a> (3rd ed.). Wiley. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-47006830-4" title="Special:BookSources/978-0-47006830-4"><bdi>978-0-47006830-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Physics+of+Semiconductor+Devices&rft.edition=3rd&rft.pub=Wiley&rft.date=2006&rft.isbn=978-0-47006830-4&rft.aulast=Sze&rft.aufirst=Simon+M.&rft.au=Ng%2C+Kwok+K.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Do4unkmHBHb8C&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACapacitor" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=59" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><i>Tantalum and Niobium-Based Capacitors – Science, Technology, and Applications</i>; 1st Ed; Yuri Freeman; Springer; 120 pages; 2018; <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-31967869-6" title="Special:BookSources/978-3-31967869-6">978-3-31967869-6</a>.</li> <li><i>Capacitors</i>; 1st Ed; R. P. Deshpande; McGraw-Hill; 342 pages; 2014; <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07184856-5" title="Special:BookSources/978-0-07184856-5">978-0-07184856-5</a>.</li> <li><i>The Capacitor Handbook</i>; 1st Ed; Cletus Kaiser; Van Nostrand Reinhold; 124 pages; 1993; <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-9-40118092-4" title="Special:BookSources/978-9-40118092-4">978-9-40118092-4</a>.</li> <li><i>Understanding Capacitors and their Uses</i>; 1st Ed; William Mullin; Sams Publishing; 96 pages; 1964. <small><a rel="nofollow" class="external text" href="https://worldradiohistory.com/BOOKSHELF-ARH/Sams-Books/Sams-Understanding-Capacitors-And-Their-Uses-1964-Mullin.pdf">(archive)</a></small></li> <li><i>Fixed and Variable Capacitors</i>; 1st Ed; G. W. A. Dummer and Harold Nordenberg; Maple Press; 288 pages; 1960. <small><a rel="nofollow" class="external text" href="https://archive.org/details/FixedAndVariableCapacitors/">(archive)</a></small></li> <li><i>The Electrolytic Capacitor</i>; 1st Ed; Alexander Georgiev; Murray Hill Books; 191 pages; 1945. <small><a rel="nofollow" class="external text" href="https://archive.org/details/TheElectrolyticCapacitor/">(archive)</a></small></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Capacitor&action=edit&section=60" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409" /> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Commons-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/40px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/60px-Commons-logo.svg.png 1.5x" data-file-width="1024" data-file-height="1376" /></a></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <wbr /><i><b><a href="https://commons.wikimedia.org/wiki/Category:Capacitors" class="extiw" title="commons:Category:Capacitors">Capacitors</a></b></i> and <wbr /><i><b><a href="https://commons.wikimedia.org/wiki/Category:Capacitors_(SMD)" class="extiw" title="commons:Category:Capacitors (SMD)">Capacitors (SMD)</a></b></i>.</div></div> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1235681985" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237033735" /><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409" /> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Wikibooks-logo-en-noslogan.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/Wikibooks-logo-en-noslogan.svg/40px-Wikibooks-logo-en-noslogan.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/Wikibooks-logo-en-noslogan.svg/60px-Wikibooks-logo-en-noslogan.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/df/Wikibooks-logo-en-noslogan.svg/80px-Wikibooks-logo-en-noslogan.svg.png 2x" data-file-width="400" data-file-height="400" /></a></span></div> <div class="side-box-text plainlist">The Wikibook <i><a href="https://en.wikibooks.org/wiki/Electronics" class="extiw" title="wikibooks:Electronics">Electronics</a></i> has a page on the topic of: <i><b><a href="https://en.wikibooks.org/wiki/Electronics/Capacitors" class="extiw" title="wikibooks:Electronics/Capacitors">Capacitors</a></b></i></div></div> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1235681985" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237033735" /><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409" /> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Wiktionary-logo-en-v2.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/40px-Wiktionary-logo-en-v2.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/60px-Wiktionary-logo-en-v2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/80px-Wiktionary-logo-en-v2.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span></div> <div class="side-box-text plainlist">Look up <i><b><a href="https://en.wiktionary.org/wiki/Special:Search/capacitor" class="extiw" title="wiktionary:Special:Search/capacitor">capacitor</a></b></i> in Wiktionary, the free dictionary.</div></div> </div> <ul><li><a rel="nofollow" class="external text" href="http://www.sparkmuseum.com/BOOK_LEYDEN.HTM">The First Condenser – A Beer Glass</a> – SparkMuseum</li> <li><a rel="nofollow" class="external text" href="http://electronics.howstuffworks.com/capacitor.htm/printable">How Capacitors Work</a> – Howstuffworks</li> <li><a rel="nofollow" class="external text" href="http://www.robotplatform.com/electronics/capacitor/capacitor.html">Capacitor Tutorial</a></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}</style><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output .navbox-list-with-group{text-align:left;border-left-width:2px;border-left-style:solid}.mw-parser-output tr+tr>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Electronic_components254" style="padding:3px"><table class="nowraplinks mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Electronic_components" title="Template:Electronic components"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Electronic_components" title="Template talk:Electronic components"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Electronic_components" title="Special:EditPage/Template:Electronic components"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Electronic_components254" style="font-size:114%;margin:0 4em"><a href="/wiki/Electronic_component" title="Electronic component">Electronic components</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;"><a href="/wiki/Semiconductor_device" title="Semiconductor device">Semiconductor<br />devices</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/MOSFET" title="MOSFET">MOS <br />transistors</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Transistor" title="Transistor">Transistor</a></li> <li><a href="/wiki/NMOS_logic" title="NMOS logic">NMOS</a></li> <li><a href="/wiki/PMOS_logic" title="PMOS logic">PMOS</a></li> <li><a href="/wiki/BiCMOS" title="BiCMOS">BiCMOS</a></li> <li><a href="/wiki/Bio-FET" title="Bio-FET">BioFET</a></li> <li><a href="/wiki/Chemical_field-effect_transistor" title="Chemical field-effect transistor">Chemical field-effect transistor</a> (ChemFET)</li> <li><a href="/wiki/CMOS" title="CMOS">Complementary MOS</a> (CMOS)</li> <li><a href="/wiki/Depletion-load_NMOS_logic" title="Depletion-load NMOS logic">Depletion-load NMOS</a></li> <li><a href="/wiki/FinFET" class="mw-redirect" title="FinFET">Fin field-effect transistor</a> (FinFET)</li> <li><a href="/wiki/Floating-gate_MOSFET" title="Floating-gate MOSFET">Floating-gate MOSFET</a> (FGMOS)</li> <li><a href="/wiki/Insulated-gate_bipolar_transistor" title="Insulated-gate bipolar transistor">Insulated-gate bipolar transistor</a> (IGBT)</li> <li><a href="/wiki/ISFET" title="ISFET">ISFET</a></li> <li><a href="/wiki/LDMOS" title="LDMOS">LDMOS</a></li> <li><a href="/wiki/MOSFET" title="MOSFET">MOS field-effect transistor</a> (MOSFET)</li> <li><a href="/wiki/Multigate_device" title="Multigate device">Multi-gate field-effect transistor</a> (MuGFET)</li> <li><a href="/wiki/Power_MOSFET" title="Power MOSFET">Power MOSFET</a></li> <li><a href="/wiki/Thin-film_transistor" title="Thin-film transistor">Thin-film transistor</a> (TFT)</li> <li><a href="/wiki/VMOS" title="VMOS">VMOS</a></li> <li><a href="/wiki/Power_MOSFET#UMOS" title="Power MOSFET">UMOS</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Transistor" title="Transistor">Other <br />transistors</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bipolar_junction_transistor" title="Bipolar junction transistor">Bipolar junction transistor</a> (BJT)</li> <li><a href="/wiki/Darlington_transistor" title="Darlington transistor">Darlington transistor</a></li> <li><a href="/wiki/Diffused_junction_transistor" title="Diffused junction transistor">Diffused junction transistor</a></li> <li><a href="/wiki/Field-effect_transistor" title="Field-effect transistor">Field-effect transistor</a> (FET) <ul><li><a href="/wiki/JFET" title="JFET">Junction Gate FET (JFET)</a></li> <li><a href="/wiki/Organic_field-effect_transistor" title="Organic field-effect transistor">Organic FET (OFET)</a></li></ul></li> <li><a href="/wiki/Light-emitting_transistor" title="Light-emitting transistor">Light-emitting transistor</a> (LET) <ul><li><a href="/wiki/Organic_light-emitting_transistor" title="Organic light-emitting transistor">Organic LET (OLET)</a></li></ul></li> <li><a href="/wiki/Pentode_transistor" title="Pentode transistor">Pentode transistor</a></li> <li><a href="/wiki/Point-contact_transistor" title="Point-contact transistor">Point-contact transistor</a></li> <li><a href="/wiki/Programmable_unijunction_transistor" title="Programmable unijunction transistor">Programmable unijunction transistor</a> (PUT)</li> <li><a href="/wiki/Static_induction_transistor" title="Static induction transistor">Static induction transistor</a> (SIT)</li> <li><a href="/wiki/Tetrode_transistor" title="Tetrode transistor">Tetrode transistor</a></li> <li><a href="/wiki/Unijunction_transistor" title="Unijunction transistor">Unijunction transistor</a> (UJT)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Diode" title="Diode">Diodes</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Avalanche_diode" title="Avalanche diode">Avalanche diode</a></li> <li><a href="/wiki/Constant-current_diode" title="Constant-current diode">Constant-current diode</a> (CLD, CRD)</li> <li><a href="/wiki/Gunn_diode" title="Gunn diode">Gunn diode</a></li> <li><a href="/wiki/Laser_diode" title="Laser diode">Laser diode</a> (LD)</li> <li><a href="/wiki/Light-emitting_diode" title="Light-emitting diode">Light-emitting diode</a> (LED)</li> <li><a href="/wiki/OLED" title="OLED">Organic light-emitting diode</a> (OLED)</li> <li><a href="/wiki/Photodiode" title="Photodiode">Photodiode</a></li> <li><a href="/wiki/PIN_diode" title="PIN diode">PIN diode</a></li> <li><a href="/wiki/Schottky_diode" title="Schottky diode">Schottky diode</a></li> <li><a href="/wiki/Step_recovery_diode" title="Step recovery diode">Step recovery diode</a></li> <li><a href="/wiki/Zener_diode" title="Zener diode">Zener diode</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other <br />devices</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Printed_electronics" title="Printed electronics">Printed electronics</a></li> <li><a href="/wiki/Printed_circuit_board" title="Printed circuit board">Printed circuit board</a></li> <li><a href="/wiki/DIAC" title="DIAC">DIAC</a></li> <li><a href="/wiki/Heterostructure_barrier_varactor" title="Heterostructure barrier varactor">Heterostructure barrier varactor</a></li> <li><a href="/wiki/Integrated_circuit" title="Integrated circuit">Integrated circuit</a> (IC)</li> <li><a href="/wiki/Hybrid_integrated_circuit" title="Hybrid integrated circuit">Hybrid integrated circuit</a></li> <li><a href="/wiki/Light_emitting_capacitor" class="mw-redirect" title="Light emitting capacitor">Light emitting capacitor</a> (LEC)</li> <li><a href="/wiki/Memistor" title="Memistor">Memistor</a></li> <li><a href="/wiki/Memristor" title="Memristor">Memristor</a></li> <li><a href="/wiki/Memtransistor" title="Memtransistor">Memtransistor</a></li> <li><a href="/wiki/Memory_cell_(computing)" title="Memory cell (computing)">Memory cell</a></li> <li><a href="/wiki/Metal-oxide_varistor" class="mw-redirect" title="Metal-oxide varistor">Metal-oxide varistor</a> (MOV)</li> <li><a href="/wiki/Mixed-signal_integrated_circuit" title="Mixed-signal integrated circuit">Mixed-signal integrated circuit</a></li> <li><a href="/wiki/MOS_integrated_circuit" class="mw-redirect" title="MOS integrated circuit">MOS integrated circuit</a> (MOS IC)</li> <li><a href="/wiki/Organic_semiconductor" title="Organic semiconductor">Organic semiconductor</a></li> <li><a href="/wiki/Photodetector" title="Photodetector">Photodetector</a></li> <li><a href="/wiki/Quantum_circuit" title="Quantum circuit">Quantum circuit</a></li> <li><a href="/wiki/RF_CMOS" title="RF CMOS">RF CMOS</a></li> <li><a href="/wiki/Silicon_controlled_rectifier" title="Silicon controlled rectifier">Silicon controlled rectifier</a> (SCR)</li> <li><a href="/wiki/Solaristor" title="Solaristor">Solaristor</a></li> <li><a href="/wiki/Static_induction_thyristor" title="Static induction thyristor">Static induction thyristor</a> (SITh)</li> <li><a href="/wiki/Three-dimensional_integrated_circuit" title="Three-dimensional integrated circuit">Three-dimensional integrated circuit</a> (3D IC)</li> <li><a href="/wiki/Thyristor" title="Thyristor">Thyristor</a></li> <li><a href="/wiki/Trancitor" title="Trancitor">Trancitor</a></li> <li><a href="/wiki/TRIAC" title="TRIAC">TRIAC</a></li> <li><a href="/wiki/Varicap" title="Varicap">Varicap</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;"><a href="/wiki/Voltage_regulator" title="Voltage regulator">Voltage regulators</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Linear_regulator" title="Linear regulator">Linear regulator</a></li> <li><a href="/wiki/Low-dropout_regulator" title="Low-dropout regulator">Low-dropout regulator</a></li> <li><a href="/wiki/Switching_regulator" class="mw-redirect" title="Switching regulator">Switching regulator</a></li> <li><a href="/wiki/Buck_converter" title="Buck converter">Buck</a></li> <li><a href="/wiki/Boost_converter" title="Boost converter">Boost</a></li> <li><a href="/wiki/Buck%E2%80%93boost_converter" title="Buck–boost converter">Buck–boost</a></li> <li><a href="/wiki/Split-pi_topology" title="Split-pi topology">Split-pi</a></li> <li><a href="/wiki/%C4%86uk_converter" title="Ćuk converter">Ćuk</a></li> <li><a href="/wiki/Single-ended_primary-inductor_converter" title="Single-ended primary-inductor converter">SEPIC</a></li> <li><a href="/wiki/Charge_pump" title="Charge pump">Charge pump</a></li> <li><a href="/wiki/Switched_capacitor" title="Switched capacitor">Switched capacitor</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;"><a href="/wiki/Vacuum_tube" title="Vacuum tube">Vacuum tubes</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Acorn_tube" title="Acorn tube">Acorn tube</a></li> <li><a href="/wiki/Audion" title="Audion">Audion</a></li> <li><a href="/wiki/Beam_tetrode" title="Beam tetrode">Beam tetrode</a></li> <li><a href="/wiki/Hot-wire_barretter" title="Hot-wire barretter">Barretter</a></li> <li><a href="/wiki/Compactron" title="Compactron">Compactron</a></li> <li><a href="/wiki/Vacuum_diode" class="mw-redirect" title="Vacuum diode">Diode</a></li> <li><a href="/wiki/Fleming_valve" title="Fleming valve">Fleming valve</a></li> <li><a href="/wiki/Neutron_generator" title="Neutron generator">Neutron tube</a></li> <li><a href="/wiki/Nonode" title="Nonode">Nonode</a></li> <li><a href="/wiki/Nuvistor" title="Nuvistor">Nuvistor</a></li> <li><a href="/wiki/Pentagrid_converter" title="Pentagrid converter">Pentagrid</a> (Hexode, Heptode, Octode)</li> <li><a href="/wiki/Pentode" title="Pentode">Pentode</a></li> <li><a href="/wiki/Photomultiplier_tube" title="Photomultiplier tube">Photomultiplier</a></li> <li><a href="/wiki/Phototube" title="Phototube">Phototube</a></li> <li><a href="/wiki/Tetrode" title="Tetrode">Tetrode</a></li> <li><a href="/wiki/Triode" title="Triode">Triode</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;"><a href="/wiki/Vacuum_tube" title="Vacuum tube">Vacuum tubes</a> (<a href="/wiki/Electromagnetic_radiation" title="Electromagnetic radiation">RF</a>)</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Backward-wave_oscillator" title="Backward-wave oscillator">Backward-wave oscillator</a> (BWO)</li> <li><a href="/wiki/Cavity_magnetron" title="Cavity magnetron">Cavity magnetron</a></li> <li><a href="/wiki/Crossed-field_amplifier" title="Crossed-field amplifier">Crossed-field amplifier</a> (CFA)</li> <li><a href="/wiki/Gyrotron" title="Gyrotron">Gyrotron</a></li> <li><a href="/wiki/Inductive_output_tube" title="Inductive output tube">Inductive output tube</a> (IOT)</li> <li><a href="/wiki/Klystron" title="Klystron">Klystron</a></li> <li><a href="/wiki/Maser" title="Maser">Maser</a></li> <li><a href="/wiki/Sutton_tube" title="Sutton tube">Sutton tube</a></li> <li><a href="/wiki/Traveling-wave_tube" title="Traveling-wave tube">Traveling-wave tube</a> (TWT)</li> <li><a href="/wiki/X-ray_tube" title="X-ray tube">X-ray tube</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;"><a href="/wiki/Cathode-ray_tube" title="Cathode-ray tube">Cathode-ray tubes</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Beam_deflection_tube" title="Beam deflection tube">Beam deflection tube</a></li> <li><a href="/wiki/Charactron" title="Charactron">Charactron</a></li> <li><a href="/wiki/Iconoscope" title="Iconoscope">Iconoscope</a></li> <li><a href="/wiki/Magic_eye_tube" title="Magic eye tube">Magic eye tube</a></li> <li><a href="/wiki/Monoscope" title="Monoscope">Monoscope</a></li> <li><a href="/wiki/Selectron_tube" title="Selectron tube">Selectron tube</a></li> <li><a href="/wiki/Storage_tube" title="Storage tube">Storage tube</a></li> <li><a href="/wiki/Trochotron" class="mw-redirect" title="Trochotron">Trochotron</a></li> <li><a href="/wiki/Video_camera_tube" title="Video camera tube">Video camera tube</a></li> <li><a href="/wiki/Williams_tube" title="Williams tube">Williams tube</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;"><a href="/wiki/Gas-filled_tube" title="Gas-filled tube">Gas-filled tubes</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cold_cathode" title="Cold cathode">Cold cathode</a></li> <li><a href="/wiki/Crossatron" title="Crossatron">Crossatron</a></li> <li><a href="/wiki/Dekatron" title="Dekatron">Dekatron</a></li> <li><a href="/wiki/Ignitron" title="Ignitron">Ignitron</a></li> <li><a href="/wiki/Krytron" title="Krytron">Krytron</a></li> <li><a href="/wiki/Mercury-arc_valve" title="Mercury-arc valve">Mercury-arc valve</a></li> <li><a href="/wiki/Neon_lamp" title="Neon lamp">Neon lamp</a></li> <li><a href="/wiki/Nixie_tube" title="Nixie tube">Nixie tube</a></li> <li><a href="/wiki/Thyratron" title="Thyratron">Thyratron</a></li> <li><a href="/wiki/Trigatron" title="Trigatron">Trigatron</a></li> <li><a href="/wiki/Voltage-regulator_tube" title="Voltage-regulator tube">Voltage-regulator tube</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;">Adjustable</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Potentiometer" title="Potentiometer">Potentiometer</a> <ul><li><a href="/wiki/Digital_potentiometer" title="Digital potentiometer">digital</a></li></ul></li> <li><a href="/wiki/Variable_capacitor" title="Variable capacitor">Variable capacitor</a></li> <li><a href="/wiki/Varicap" title="Varicap">Varicap</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;">Passive</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li>Connector <ul><li><a href="/wiki/Audio_and_video_interfaces_and_connectors" title="Audio and video interfaces and connectors">audio and video</a></li> <li><a href="/wiki/AC_power_plugs_and_sockets" title="AC power plugs and sockets">electrical power</a></li> <li><a href="/wiki/RF_connector" title="RF connector">RF</a></li></ul></li> <li><a href="/wiki/Electrolytic_detector" title="Electrolytic detector">Electrolytic detector</a></li> <li><a href="/wiki/Ferrite_core" title="Ferrite core">Ferrite</a></li> <li><a href="/wiki/Antifuse" title="Antifuse">Antifuse</a></li> <li><a href="/wiki/Fuse_(electrical)" title="Fuse (electrical)">Fuse</a> <ul><li><a href="/wiki/Resettable_fuse" title="Resettable fuse">resettable</a></li> <li><a href="/wiki/EFUSE" class="mw-redirect" title="EFUSE">eFUSE</a></li></ul></li> <li><a href="/wiki/Resistor" title="Resistor">Resistor</a></li> <li><a href="/wiki/Switch" title="Switch">Switch</a></li> <li><a href="/wiki/Thermistor" title="Thermistor">Thermistor</a></li> <li><a href="/wiki/Transformer" title="Transformer">Transformer</a></li> <li><a href="/wiki/Varistor" title="Varistor">Varistor</a></li> <li><a href="/wiki/Wire" title="Wire">Wire</a> <ul><li><a href="/wiki/Wollaston_wire" title="Wollaston wire">Wollaston wire</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;"><a href="/wiki/Electrical_reactance" title="Electrical reactance">Reactive</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a class="mw-selflink selflink">Capacitor</a> <ul><li><a href="/wiki/Capacitor_types" title="Capacitor types">types</a></li></ul></li> <li><a href="/wiki/Ceramic_resonator" title="Ceramic resonator">Ceramic resonator</a></li> <li><a href="/wiki/Crystal_oscillator" title="Crystal oscillator">Crystal oscillator</a></li> <li><a href="/wiki/Inductor" title="Inductor">Inductor</a></li> <li><a href="/wiki/Parametron" title="Parametron">Parametron</a></li> <li><a href="/wiki/Relay" title="Relay">Relay</a> <ul><li><a href="/wiki/Reed_relay" title="Reed relay">reed relay</a></li> <li><a href="/wiki/Mercury_relay" title="Mercury relay">mercury relay</a></li></ul></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235" /></div><div role="navigation" class="navbox" aria-labelledby="Digital_electronics118" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231" /><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Digital_electronics" title="Template:Digital electronics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Digital_electronics" title="Template talk:Digital electronics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Digital_electronics" title="Special:EditPage/Template:Digital electronics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Digital_electronics118" style="font-size:114%;margin:0 4em"><a href="/wiki/Digital_electronics" title="Digital electronics">Digital electronics</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;"><a href="/wiki/Electronic_component" title="Electronic component">Components</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Transistor" title="Transistor">Transistor</a></li> <li><a href="/wiki/Resistor" title="Resistor">Resistor</a></li> <li><a href="/wiki/Inductor" title="Inductor">Inductor</a></li> <li><a class="mw-selflink selflink">Capacitor</a></li> <li><a href="/wiki/Printed_electronics" title="Printed electronics">Printed electronics</a></li> <li><a href="/wiki/Printed_circuit_board" title="Printed circuit board">Printed circuit board</a></li> <li><a href="/wiki/Electronic_circuit" title="Electronic circuit">Electronic circuit</a></li> <li><a href="/wiki/Flip-flop_(electronics)" title="Flip-flop (electronics)">Flip-flop</a></li> <li><a href="/wiki/Memory_cell_(computing)" title="Memory cell (computing)">Memory cell</a></li> <li><a href="/wiki/Combinational_logic" title="Combinational logic">Combinational logic</a></li> <li><a href="/wiki/Sequential_logic" title="Sequential logic">Sequential logic</a></li> <li><a href="/wiki/Logic_gate" title="Logic gate">Logic gate</a></li> <li><a href="/wiki/Boolean_circuit" title="Boolean circuit">Boolean circuit</a></li> <li><a href="/wiki/Integrated_circuit" title="Integrated circuit">Integrated circuit</a> (IC)</li> <li><a href="/wiki/Hybrid_integrated_circuit" title="Hybrid integrated circuit">Hybrid integrated circuit</a> (HIC)</li> <li><a href="/wiki/Mixed-signal_integrated_circuit" title="Mixed-signal integrated circuit">Mixed-signal integrated circuit</a></li> <li><a href="/wiki/Three-dimensional_integrated_circuit" title="Three-dimensional integrated circuit">Three-dimensional integrated circuit</a> (3D IC)</li> <li><a href="/wiki/Emitter-coupled_logic" title="Emitter-coupled logic">Emitter-coupled logic</a> (ECL)</li> <li><a href="/wiki/Erasable_programmable_logic_device" class="mw-redirect" title="Erasable programmable logic device">Erasable programmable logic device</a> (EPLD)</li> <li><a href="/wiki/Macrocell_array" title="Macrocell array">Macrocell array</a></li> <li><a href="/wiki/Programmable_logic_array" title="Programmable logic array">Programmable logic array</a> (PLA)</li> <li><a href="/wiki/Programmable_logic_device" title="Programmable logic device">Programmable logic device</a> (PLD)</li> <li><a href="/wiki/Programmable_Array_Logic" title="Programmable Array Logic">Programmable Array Logic</a> (PAL)</li> <li><a href="/wiki/Generic_Array_Logic" title="Generic Array Logic">Generic Array Logic</a> (GAL)</li> <li><a href="/wiki/Complex_programmable_logic_device" title="Complex programmable logic device">Complex programmable logic device</a> (CPLD)</li> <li><a href="/wiki/Field-programmable_gate_array" title="Field-programmable gate array">Field-programmable gate array</a> (FPGA)</li> <li><a href="/wiki/Field-programmable_object_array" title="Field-programmable object array">Field-programmable object array</a> (FPOA)</li> <li><a href="/wiki/Application-specific_integrated_circuit" title="Application-specific integrated circuit">Application-specific integrated circuit</a> (ASIC)</li> <li><a href="/wiki/Tensor_Processing_Unit" title="Tensor Processing Unit">Tensor Processing Unit</a> (TPU)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;">Theory</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Digital_signal" title="Digital signal">Digital signal</a></li> <li><a href="/wiki/Boolean_algebra" title="Boolean algebra">Boolean algebra</a></li> <li><a href="/wiki/Logic_synthesis" title="Logic synthesis">Logic synthesis</a></li> <li><a href="/wiki/Logic_in_computer_science" title="Logic in computer science">Logic in computer science</a></li> <li><a href="/wiki/Computer_architecture" title="Computer architecture">Computer architecture</a></li> <li><a href="/wiki/Digital_signal_(signal_processing)" title="Digital signal (signal processing)">Digital signal</a> <ul><li><a href="/wiki/Digital_signal_processing" title="Digital signal processing">Digital signal processing</a></li></ul></li> <li><a href="/wiki/Circuit_minimization_for_Boolean_functions" class="mw-redirect" title="Circuit minimization for Boolean functions">Circuit minimization</a></li> <li><a href="/wiki/Switching_circuit_theory" title="Switching circuit theory">Switching circuit theory</a></li> <li><a href="/wiki/Gate_equivalent" title="Gate equivalent">Gate equivalent</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;"><a href="/wiki/Electronics_design" class="mw-redirect" title="Electronics design">Design</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Logic_synthesis" title="Logic synthesis">Logic synthesis</a></li> <li><a href="/wiki/Place_and_route" title="Place and route">Place and route</a> <ul><li><a href="/wiki/Placement_(electronic_design_automation)" title="Placement (electronic design automation)">Placement</a></li> <li><a href="/wiki/Routing_(electronic_design_automation)" title="Routing (electronic design automation)">Routing</a></li></ul></li> <li><a href="/wiki/Transaction-level_modeling" title="Transaction-level modeling">Transaction-level modeling</a></li> <li><a href="/wiki/Register-transfer_level" title="Register-transfer level">Register-transfer level</a> <ul><li><a href="/wiki/Hardware_description_language" title="Hardware description language">Hardware description language</a></li> <li><a href="/wiki/High-level_synthesis" title="High-level synthesis">High-level synthesis</a></li></ul></li> <li><a href="/wiki/Formal_equivalence_checking" title="Formal equivalence checking">Formal equivalence checking</a></li> <li><a href="/wiki/Synchronous_circuit" title="Synchronous circuit">Synchronous logic</a></li> <li><a href="/wiki/Asynchronous_circuit" title="Asynchronous circuit">Asynchronous logic</a></li> <li><a href="/wiki/Finite-state_machine" title="Finite-state machine">Finite-state machine</a> <ul><li><a href="/wiki/Hierarchical_state_machine" class="mw-redirect" title="Hierarchical state machine">Hierarchical state machine</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;">Applications</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Computer_hardware" title="Computer hardware">Computer hardware</a> <ul><li><a href="/wiki/Hardware_acceleration" title="Hardware acceleration">Hardware acceleration</a></li></ul></li> <li><a href="/wiki/Digital_audio" title="Digital audio">Digital audio</a> <ul><li><a href="/wiki/Digital_radio" title="Digital radio">radio</a></li></ul></li> <li><a href="/wiki/Digital_photography" title="Digital photography">Digital photography</a></li> <li><a href="/wiki/Telephony#Digital_telephony" title="Telephony">Digital telephone</a></li> <li><a href="/wiki/Digital_video" title="Digital video">Digital video</a> <ul><li><a href="/wiki/Digital_cinematography" title="Digital cinematography">cinematography</a></li> <li><a href="/wiki/Digital_television" title="Digital television">television</a></li></ul></li> <li><a href="/wiki/Electronic_literature" title="Electronic literature">Electronic literature</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;">Design issues</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Metastability_(electronics)" title="Metastability (electronics)">Metastability</a></li> <li><a href="/wiki/Runt_pulse" title="Runt pulse">Runt pulse</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235" /><style data-mw-deduplicate="TemplateStyles:r1038841319">.mw-parser-output .tooltip-dotted{border-bottom:1px dotted;cursor:help}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1038841319" /></div><div role="navigation" class="navbox authority-control" aria-label="Navbox1270" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Help:Authority_control" title="Help:Authority control">Authority control databases</a>: National <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q5322#identifiers" title="Edit this at Wikidata"><img alt="Edit this at Wikidata" src="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4128311-9">Germany</a></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="Capacitors"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/sh85019859">United States</a></span></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb119811121">France</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb119811121">BnF data</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.ndl.go.jp/auth/ndlna/00573017">Japan</a></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="kondenzátory"><a rel="nofollow" class="external text" href="https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=ph121792&CON_LNG=ENG">Czech Republic</a></span></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.nli.org.il/en/authorities/987007283490105171">Israel</a></span></li></ul></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Capacitor&oldid=1281636495">https://en.wikipedia.org/w/index.php?title=Capacitor&oldid=1281636495</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Electrical_components" title="Category:Electrical components">Electrical components</a></li><li><a href="/wiki/Category:Energy_storage" title="Category:Energy storage">Energy storage</a></li><li><a href="/wiki/Category:Capacitors" title="Category:Capacitors">Capacitors</a></li><li><a href="/wiki/Category:Science_and_technology_in_the_Dutch_Republic" title="Category:Science and technology in the Dutch Republic">Science and technology in the Dutch Republic</a></li><li><a href="/wiki/Category:Dutch_inventions" title="Category:Dutch inventions">Dutch inventions</a></li><li><a href="/wiki/Category:18th-century_inventions" title="Category:18th-century inventions">18th-century inventions</a></li><li><a href="/wiki/Category:German_inventions" title="Category:German inventions">German inventions</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:Webarchive_template_wayback_links" title="Category:Webarchive template wayback links">Webarchive template wayback links</a></li><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_is_different_from_Wikidata" title="Category:Short description is different from Wikidata">Short description is different from Wikidata</a></li><li><a href="/wiki/Category:Use_dmy_dates_from_June_2022" title="Category:Use dmy dates from June 2022">Use dmy dates from June 2022</a></li><li><a href="/wiki/Category:All_articles_with_unsourced_statements" title="Category:All articles with unsourced statements">All articles with unsourced statements</a></li><li><a href="/wiki/Category:Articles_with_unsourced_statements_from_January_2020" title="Category:Articles with unsourced statements from January 2020">Articles with unsourced statements from January 2020</a></li><li><a href="/wiki/Category:Articles_with_unsourced_statements_from_September_2023" title="Category:Articles with unsourced statements from September 2023">Articles with unsourced statements from September 2023</a></li><li><a href="/wiki/Category:Articles_with_unsourced_statements_from_October_2020" title="Category:Articles with unsourced statements from October 2020">Articles with unsourced statements from October 2020</a></li><li><a href="/wiki/Category:Articles_with_unsourced_statements_from_November_2016" title="Category:Articles with unsourced statements from November 2016">Articles with unsourced statements from November 2016</a></li><li><a href="/wiki/Category:Articles_containing_potentially_dated_statements_from_2010" title="Category:Articles containing potentially dated statements from 2010">Articles containing potentially dated statements from 2010</a></li><li><a href="/wiki/Category:All_articles_containing_potentially_dated_statements" title="Category:All articles containing potentially dated statements">All articles containing potentially dated statements</a></li><li><a href="/wiki/Category:All_articles_with_vague_or_ambiguous_time" title="Category:All articles with vague or ambiguous time">All articles with vague or ambiguous time</a></li><li><a href="/wiki/Category:Vague_or_ambiguous_time_from_May_2018" title="Category:Vague or ambiguous time from May 2018">Vague or ambiguous time from May 2018</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 21 March 2025, at 15:30<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. By using this site, you agree to the <a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Terms_of_Use" class="extiw" title="foundation:Special:MyLanguage/Policy:Terms of Use">Terms of Use</a> and <a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy" class="extiw" title="foundation:Special:MyLanguage/Policy:Privacy policy">Privacy Policy</a>. Wikipedia® is a registered trademark of the <a rel="nofollow" class="external text" href="https://wikimediafoundation.org/">Wikimedia Foundation, Inc.</a>, a non-profit organization.</li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">Privacy policy</a></li> <li id="footer-places-about"><a href="/wiki/Wikipedia:About">About Wikipedia</a></li> <li id="footer-places-disclaimers"><a href="/wiki/Wikipedia:General_disclaimer">Disclaimers</a></li> <li id="footer-places-contact"><a href="//en.wikipedia.org/wiki/Wikipedia:Contact_us">Contact Wikipedia</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">Code of Conduct</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">Developers</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/en.wikipedia.org">Statistics</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">Cookie statement</a></li> <li id="footer-places-mobileview"><a href="//en.m.wikipedia.org/w/index.php?title=Capacitor&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">Mobile view</a></li> </ul> <ul id="footer-icons" class="noprint"> <li id="footer-copyrightico"><a href="https://wikimediafoundation.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><picture><source media="(min-width: 500px)" srcset="/static/images/footer/wikimedia-button.svg" width="84" height="29"><img src="/static/images/footer/wikimedia.svg" width="25" height="25" alt="Wikimedia Foundation" lang="en" loading="lazy"></picture></a></li> <li id="footer-poweredbyico"><a href="https://www.mediawiki.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><picture><source media="(min-width: 500px)" srcset="/w/resources/assets/poweredby_mediawiki.svg" width="88" height="31"><img src="/w/resources/assets/mediawiki_compact.svg" alt="Powered by MediaWiki" lang="en" width="25" height="25" loading="lazy"></picture></a></li> </ul> </footer> </div> </div> </div> <div class="vector-header-container vector-sticky-header-container"> <div id="vector-sticky-header" class="vector-sticky-header"> <div class="vector-sticky-header-start"> <div class="vector-sticky-header-icon-start vector-button-flush-left vector-button-flush-right" aria-hidden="true"> <button class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-sticky-header-search-toggle" tabindex="-1" data-event-name="ui.vector-sticky-search-form.icon"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Search</span> </button> </div> <div role="search" class="vector-search-box-vue vector-search-box-show-thumbnail vector-search-box"> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail"> <form action="/w/index.php" id="vector-sticky-search-form" class="cdx-search-input cdx-search-input--has-end-button"> <div class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Search Wikipedia"> <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Special:Search"> </div> <button class="cdx-button cdx-search-input__end-button">Search</button> </form> </div> </div> </div> <div class="vector-sticky-header-context-bar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-sticky-header-toc" class="vector-dropdown mw-portlet mw-portlet-sticky-header-toc vector-sticky-header-toc vector-button-flush-left" > <input type="checkbox" id="vector-sticky-header-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-sticky-header-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-sticky-header-toc-label" for="vector-sticky-header-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-sticky-header-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div class="vector-sticky-header-context-bar-primary" aria-hidden="true" ><span class="mw-page-title-main">Capacitor</span></div> </div> </div> <div class="vector-sticky-header-end" aria-hidden="true"> <div class="vector-sticky-header-icons"> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-talk-sticky-header" tabindex="-1" data-event-name="talk-sticky-header"><span class="vector-icon mw-ui-icon-speechBubbles mw-ui-icon-wikimedia-speechBubbles"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-subject-sticky-header" tabindex="-1" data-event-name="subject-sticky-header"><span class="vector-icon mw-ui-icon-article mw-ui-icon-wikimedia-article"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-history-sticky-header" tabindex="-1" data-event-name="history-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-history mw-ui-icon-wikimedia-wikimedia-history"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only mw-watchlink" id="ca-watchstar-sticky-header" tabindex="-1" data-event-name="watch-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-star mw-ui-icon-wikimedia-wikimedia-star"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-edit-sticky-header" tabindex="-1" data-event-name="wikitext-edit-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-wikiText mw-ui-icon-wikimedia-wikimedia-wikiText"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-ve-edit-sticky-header" tabindex="-1" data-event-name="ve-edit-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-edit mw-ui-icon-wikimedia-wikimedia-edit"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-viewsource-sticky-header" tabindex="-1" data-event-name="ve-edit-protected-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-editLock mw-ui-icon-wikimedia-wikimedia-editLock"></span> <span></span> </a> </div> <div class="vector-sticky-header-buttons"> <button class="cdx-button cdx-button--weight-quiet mw-interlanguage-selector" id="p-lang-btn-sticky-header" tabindex="-1" data-event-name="ui.dropdown-p-lang-btn-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-language mw-ui-icon-wikimedia-wikimedia-language"></span> <span>120 languages</span> </button> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive" id="ca-addsection-sticky-header" tabindex="-1" data-event-name="addsection-sticky-header"><span class="vector-icon mw-ui-icon-speechBubbleAdd-progressive mw-ui-icon-wikimedia-speechBubbleAdd-progressive"></span> <span>Add topic</span> </a> </div> <div class="vector-sticky-header-icon-end"> <div class="vector-user-links"> </div> </div> </div> </div> </div> <div class="mw-portlet mw-portlet-dock-bottom emptyPortlet" id="p-dock-bottom"> <ul> </ul> </div> <script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.eqiad.main-75687f9f4b-6tggv","wgBackendResponseTime":304,"wgPageParseReport":{"limitreport":{"cputime":"1.876","walltime":"2.715","ppvisitednodes":{"value":11585,"limit":1000000},"postexpandincludesize":{"value":227489,"limit":2097152},"templateargumentsize":{"value":11455,"limit":2097152},"expansiondepth":{"value":15,"limit":100},"expensivefunctioncount":{"value":30,"limit":500},"unstrip-depth":{"value":1,"limit":20},"unstrip-size":{"value":311585,"limit":5000000},"entityaccesscount":{"value":1,"limit":400},"timingprofile":["100.00% 1772.481 1 -total"," 31.11% 551.443 3 Template:Reflist"," 18.60% 329.768 40 Template:Cite_book"," 7.81% 138.446 12 Template:Sfn"," 6.93% 122.860 1 Template:Short_description"," 6.44% 114.201 3 Template:Navbox"," 6.32% 111.986 1 Template:Electronic_component"," 4.71% 83.395 18 Template:Cite_web"," 4.55% 80.640 2 Template:Pagetype"," 4.52% 80.196 1 Template:Infobox_electronic_component"]},"scribunto":{"limitreport-timeusage":{"value":"0.987","limit":"10.000"},"limitreport-memusage":{"value":12144332,"limit":52428800},"limitreport-logs":"anchor_id_list = table#1 {\n [\"2-char-capacitor-marking-code\"] = 1,\n [\"CITEREFAlamAzarianOstermanPecht2010\"] = 1,\n [\"CITEREFBecker,_H._I.1957\"] = 1,\n [\"CITEREFBelkin2017\"] = 1,\n [\"CITEREFBenjamin1895\"] = 1,\n [\"CITEREFBezryadinBelkin2017\"] = 1,\n [\"CITEREFBird2007\"] = 1,\n [\"CITEREFBird2010\"] = 1,\n [\"CITEREFBisquertGarcia-BelmonteFabregat-Santiago2000\"] = 1,\n [\"CITEREFCoffeyKalmykov2006\"] = 1,\n [\"CITEREFCzichosSaitoSmith2006\"] = 1,\n [\"CITEREFDixitYadav2010\"] = 1,\n [\"CITEREFDorfSvoboda2001\"] = 1,\n [\"CITEREFDuff1916\"] = 1,\n [\"CITEREFDyer2004\"] = 1,\n [\"CITEREFFloyd2005\"] = 1,\n [\"CITEREFFloyd2017\"] = 1,\n [\"CITEREFFranklin1749\"] = 1,\n [\"CITEREFGiulianiVignale2005\"] = 1,\n [\"CITEREFGuinta\"] = 1,\n [\"CITEREFGuptaYadavDeVotoMajor2018\"] = 1,\n [\"CITEREFHammond2013\"] = 1,\n [\"CITEREFHoJowBoggs2010\"] = 1,\n [\"CITEREFHouston1905\"] = 1,\n [\"CITEREFInuishiPowers1957\"] = 1,\n [\"CITEREFIsaacson2003\"] = 1,\n [\"CITEREFKaiser2012\"] = 1,\n [\"CITEREFKaplanWhite2003\"] = 1,\n [\"CITEREFKasapCapper2006\"] = 1,\n [\"CITEREFKeithley1999\"] = 1,\n [\"CITEREFKleinGafni1966\"] = 1,\n [\"CITEREFMiller2011\"] = 1,\n [\"CITEREFMorse2004\"] = 1,\n [\"CITEREFMusikant1991\"] = 1,\n [\"CITEREFPY_YuCardona2001\"] = 1,\n [\"CITEREFPaiZhang1995\"] = 1,\n [\"CITEREFPancaldi2003\"] = 1,\n [\"CITEREFPillai1970\"] = 1,\n [\"CITEREFPrutchi2012\"] = 1,\n [\"CITEREFPurcell2011\"] = 1,\n [\"CITEREFRammer2007\"] = 1,\n [\"CITEREFReedCichanowski1994\"] = 1,\n [\"CITEREFScherz2006\"] = 1,\n [\"CITEREFSchroder2006\"] = 1,\n [\"CITEREFSerwayVuille2014\"] = 1,\n [\"CITEREFShinn2012\"] = 1,\n [\"CITEREFSze2002\"] = 1,\n [\"CITEREFSzeLee2012\"] = 1,\n [\"CITEREFSzeNg2006\"] = 1,\n [\"CITEREFUlaby1999\"] = 1,\n [\"CITEREFWilliams\"] = 1,\n [\"CITEREFWinburn1989\"] = 1,\n [\"CITEREFWolfMcKie1962\"] = 1,\n [\"CITEREFYasuo_Cho2005\"] = 1,\n [\"CITEREFZabkar2011\"] = 1,\n [\"CITEREFde_AraujoRameshTaylor2001\"] = 1,\n [\"Condenser\"] = 1,\n [\"Non-ideal_behavior\"] = 1,\n [\"sparking\"] = 1,\n}\ntemplate_list = table#1 {\n [\"About\"] = 1,\n [\"Anchor\"] = 4,\n [\"As of\"] = 1,\n [\"Authority control\"] = 1,\n [\"Citation needed\"] = 4,\n [\"Cite book\"] = 40,\n [\"Cite journal\"] = 11,\n [\"Cite patent\"] = 1,\n [\"Cite web\"] = 18,\n [\"Clear\"] = 3,\n [\"Commons category multi\"] = 1,\n [\"Digital electronics\"] = 1,\n [\"Electronic component\"] = 1,\n [\"Equation box 1\"] = 1,\n [\"Further\"] = 3,\n [\"Google books\"] = 31,\n [\"ISBN\"] = 3,\n [\"Infobox electronic component\"] = 1,\n [\"Main\"] = 10,\n [\"Math\"] = 25,\n [\"Mono\"] = 3,\n [\"Multiple image\"] = 2,\n [\"Mvar\"] = 14,\n [\"NoteFoot\"] = 1,\n [\"NoteTag\"] = 1,\n [\"Portal\"] = 1,\n [\"Redirect\"] = 1,\n [\"Reflist\"] = 2,\n [\"See also\"] = 5,\n [\"Sfn\"] = 12,\n [\"Sfrac\"] = 1,\n [\"Short description\"] = 1,\n [\"Slink\"] = 1,\n [\"Spaced ndash\"] = 3,\n [\"Sub\"] = 2,\n [\"Sup\"] = 1,\n [\"Ubl\"] = 1,\n [\"Use dmy dates\"] = 1,\n [\"Val\"] = 1,\n [\"Webarchive\"] = 1,\n [\"When\"] = 1,\n [\"Wikibooks\"] = 1,\n [\"Wiktionary\"] = 1,\n}\narticle_whitelist = table#1 {\n}\nciteref_patterns = table#1 {\n}\n"},"cachereport":{"origin":"mw-web.eqiad.main-58c4b96c94-qndf4","timestamp":"20250321153035","ttl":894571,"transientcontent":true}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"Capacitor","url":"https:\/\/en.wikipedia.org\/wiki\/Capacitor","sameAs":"http:\/\/www.wikidata.org\/entity\/Q5322","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q5322","author":{"@type":"Organization","name":"Contributors to Wikimedia projects"},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2001-09-28T00:47:30Z","dateModified":"2025-03-21T15:30:28Z","image":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/b\/b9\/Capacitors_%287189597135%29.jpg","headline":"passive, two-terminal electronic component that stores electrical energy in an electric field"}</script> </body> </html>