CINXE.COM

<!DOCTYPE html> <html class="client-nojs vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-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-toc-available" lang="en" dir="ltr"> <head> <meta charset="UTF-8"> <title>Inductor - Wikipedia</title> <script>(function(){var className="client-js vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-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-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":"88674f0e-65ae-4a72-8614-6711b451e915","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"Inductor","wgTitle":"Inductor","wgCurRevisionId":1257456796,"wgRevisionId":1257456796,"wgArticleId":14896,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["All articles with dead external links","Articles with dead external links from September 2024","Articles with permanently dead external links","Articles with short description","Short description matches Wikidata","Pages using multiple image with auto scaled images","All articles with unsourced statements","Articles with unsourced statements from February 2018","Articles with unsourced statements from September 2022","Commons category link is on Wikidata","Electromagnetic components", "Energy storage","English inventions"],"wgPageViewLanguage":"en","wgPageContentLanguage":"en","wgPageContentModel":"wikitext","wgRelevantPageName":"Inductor","wgRelevantArticleId":14896,"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":60000,"wgRelatedArticlesCompat":[],"wgCentralAuthMobileDomain":false,"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true, "wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q5325","wgCheckUserClientHintsHeadersJsApi":["brands","architecture","bitness","fullVersionList","mobile","model","platform","platformVersion"],"GEHomepageSuggestedEditsEnableTopics":true,"wgGETopicsMatchModeEnabled":false,"wgGEStructuredTaskRejectionReasonTextInputEnabled":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","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.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","wikibase.sidebar.tracking"];</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%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.4"> <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/a/a1/Electronic_component_inductors.jpg"> <meta property="og:image:width" content="1200"> <meta property="og:image:height" content="1065"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a1/Electronic_component_inductors.jpg/800px-Electronic_component_inductors.jpg"> <meta property="og:image:width" content="800"> <meta property="og:image:height" content="710"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a1/Electronic_component_inductors.jpg/640px-Electronic_component_inductors.jpg"> <meta property="og:image:width" content="640"> <meta property="og:image:height" content="568"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="Inductor - 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/Inductor"> <link rel="alternate" type="application/x-wiki" title="Edit this page" href="/w/index.php?title=Inductor&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/Inductor"> <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-Inductor rootpage-Inductor 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" > <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> </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/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_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=Inductor" 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=Inductor" 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/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_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=Inductor" 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=Inductor" 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-Description" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Description"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Description</span> </div> </a> <button aria-controls="toc-Description-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 Description subsection</span> </button> <ul id="toc-Description-sublist" class="vector-toc-list"> <li id="toc-Constitutive_equation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Constitutive_equation"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Constitutive equation</span> </div> </a> <ul id="toc-Constitutive_equation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Lenz's_law" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Lenz's_law"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Lenz's law</span> </div> </a> <ul id="toc-Lenz's_law-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Positive_form_of_current–voltage_relationship" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Positive_form_of_current–voltage_relationship"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Positive form of current–voltage relationship</span> </div> </a> <ul id="toc-Positive_form_of_current–voltage_relationship-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Energy_stored_in_an_inductor" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Energy_stored_in_an_inductor"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4</span> <span>Energy stored in an inductor</span> </div> </a> <ul id="toc-Energy_stored_in_an_inductor-sublist" class="vector-toc-list"> <li id="toc-Derivation" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Derivation"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4.1</span> <span>Derivation</span> </div> </a> <ul id="toc-Derivation-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Voltage_step_response" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Voltage_step_response"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.5</span> <span>Voltage step response</span> </div> </a> <ul id="toc-Voltage_step_response-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ideal_and_real_inductors" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ideal_and_real_inductors"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.6</span> <span>Ideal and real inductors</span> </div> </a> <ul id="toc-Ideal_and_real_inductors-sublist" class="vector-toc-list"> <li id="toc-Q_factor" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Q_factor"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.6.1</span> <span><i>Q</i> factor</span> </div> </a> <ul id="toc-Q_factor-sublist" class="vector-toc-list"> </ul> </li> </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">2</span> <span>Applications</span> </div> </a> <ul id="toc-Applications-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Inductor_construction" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Inductor_construction"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Inductor construction</span> </div> </a> <button aria-controls="toc-Inductor_construction-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 Inductor construction subsection</span> </button> <ul id="toc-Inductor_construction-sublist" class="vector-toc-list"> <li id="toc-Shielded_inductors" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Shielded_inductors"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Shielded inductors</span> </div> </a> <ul id="toc-Shielded_inductors-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Types" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Types"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Types</span> </div> </a> <button aria-controls="toc-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 Types subsection</span> </button> <ul id="toc-Types-sublist" class="vector-toc-list"> <li id="toc-Air-core_inductor" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Air-core_inductor"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Air-core inductor</span> </div> </a> <ul id="toc-Air-core_inductor-sublist" class="vector-toc-list"> <li id="toc-Radio-frequency_inductor" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Radio-frequency_inductor"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1.1</span> <span>Radio-frequency inductor</span> </div> </a> <ul id="toc-Radio-frequency_inductor-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Ferromagnetic-core_inductor" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ferromagnetic-core_inductor"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Ferromagnetic-core inductor</span> </div> </a> <ul id="toc-Ferromagnetic-core_inductor-sublist" class="vector-toc-list"> <li id="toc-Laminated-core_inductor" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Laminated-core_inductor"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2.1</span> <span>Laminated-core inductor</span> </div> </a> <ul id="toc-Laminated-core_inductor-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ferrite-core_inductor" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Ferrite-core_inductor"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2.2</span> <span>Ferrite-core inductor</span> </div> </a> <ul id="toc-Ferrite-core_inductor-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Powdered-iron-core_inductor" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Powdered-iron-core_inductor"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2.3</span> <span>Powdered-iron-core inductor</span> </div> </a> <ul id="toc-Powdered-iron-core_inductor-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Toroidal-core_inductor" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Toroidal-core_inductor"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2.4</span> <span>Toroidal-core inductor</span> </div> </a> <ul id="toc-Toroidal-core_inductor-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Variable_inductor" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Variable_inductor"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Variable inductor</span> </div> </a> <ul id="toc-Variable_inductor-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Choke" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Choke"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>Choke</span> </div> </a> <ul id="toc-Choke-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Circuit_analysis" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Circuit_analysis"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Circuit analysis</span> </div> </a> <button aria-controls="toc-Circuit_analysis-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 Circuit analysis subsection</span> </button> <ul id="toc-Circuit_analysis-sublist" class="vector-toc-list"> <li id="toc-Reactance" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Reactance"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Reactance</span> </div> </a> <ul id="toc-Reactance-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Corner_frequency" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Corner_frequency"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Corner frequency</span> </div> </a> <ul id="toc-Corner_frequency-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">5.3</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-Inductor_networks" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Inductor_networks"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.4</span> <span>Inductor networks</span> </div> </a> <ul id="toc-Inductor_networks-sublist" class="vector-toc-list"> <li id="toc-Mutual_inductance" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Mutual_inductance"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.4.1</span> <span>Mutual inductance</span> </div> </a> <ul id="toc-Mutual_inductance-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Inductance_formulas" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Inductance_formulas"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Inductance formulas</span> </div> </a> <ul id="toc-Inductance_formulas-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">7</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">8</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">9</span> <span>References</span> </div> </a> <ul id="toc-References-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">10</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" > <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">Inductor</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 95 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-95" 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">95 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/Induktor" title="Induktor – Afrikaans" lang="af" hreflang="af" data-title="Induktor" 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/Induktanz" title="Induktanz – Alemannic" lang="gsw" hreflang="gsw" data-title="Induktanz" data-language-autonym="Alemannisch" data-language-local-name="Alemannic" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%8A%A2%E1%8A%95%E1%8B%B3%E1%8A%AD%E1%89%B0%E1%88%AD" title="ኢንዳክተር – Amharic" lang="am" hreflang="am" data-title="ኢንዳክተር" data-language-autonym="አማርኛ" data-language-local-name="Amharic" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%AD%D8%AB" title="محث – Arabic" lang="ar" hreflang="ar" data-title="محث" 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/Inductor" title="Inductor – Aragonese" lang="an" hreflang="an" data-title="Inductor" data-language-autonym="Aragonés" data-language-local-name="Aragonese" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Inductor" title="Inductor – Asturian" lang="ast" hreflang="ast" data-title="Inductor" 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/%C4%B0nduktivlik_%C3%A7arx%C4%B1" title="İnduktivlik çarxı – Azerbaijani" lang="az" hreflang="az" data-title="İnduktivlik çarxı" 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%A7%DB%8C%D9%84%D9%82%D8%A7%DA%86%DB%8C" title="ایلقاچی – South Azerbaijani" lang="azb" hreflang="azb" data-title="ایلقاچی" 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%86%E0%A6%AC%E0%A7%87%E0%A6%B6%E0%A6%95" title="আবেশক – Bangla" lang="bn" hreflang="bn" data-title="আবেশক" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%98%D0%BD%D0%B4%D1%83%D0%BA%D1%82%D0%B8%D0%B2%D0%BB%D1%8B%D2%A1_%D0%BA%D0%B0%D1%82%D1%83%D1%88%D0%BA%D0%B0%D2%BB%D1%8B" title="Индуктивлыҡ катушкаһы – Bashkir" lang="ba" hreflang="ba" data-title="Индуктивлыҡ катушкаһы" 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%A8%D0%BF%D1%83%D0%BB%D1%8F_%D1%96%D0%BD%D0%B4%D1%83%D0%BA%D1%82%D1%8B%D1%9E%D0%BD%D0%B0%D1%81%D1%86%D1%96" title="Шпуля індуктыўнасці – Belarusian" lang="be" hreflang="be" data-title="Шпуля індуктыўнасці" 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%A8%D0%BF%D1%83%D0%BB%D1%8F_%D1%96%D0%BD%D0%B4%D1%83%D0%BA%D1%82%D1%8B%D1%9E%D0%BD%D0%B0%D1%81%D1%8C%D1%86%D1%96" title="Шпуля індуктыўнасьці – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Шпуля індуктыўнасьці" 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-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%98%D0%BD%D0%B4%D1%83%D0%BA%D1%82%D0%B8%D0%B2%D0%B5%D0%BD_%D0%B5%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82" title="Индуктивен елемент – Bulgarian" lang="bg" hreflang="bg" data-title="Индуктивен елемент" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Zavojnica" title="Zavojnica – Bosnian" lang="bs" hreflang="bs" data-title="Zavojnica" 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/Inductor" title="Inductor – Catalan" lang="ca" hreflang="ca" data-title="Inductor" 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/C%C3%ADvka" title="Cívka – Czech" lang="cs" hreflang="cs" data-title="Cívka" 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/Anwythydd" title="Anwythydd – Welsh" lang="cy" hreflang="cy" data-title="Anwythydd" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Induktivit%C3%A4t_(Bauelement)" title="Induktivität (Bauelement) – German" lang="de" hreflang="de" data-title="Induktivität (Bauelement)" 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/Induktiivpool" title="Induktiivpool – Estonian" lang="et" hreflang="et" data-title="Induktiivpool" 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%CE%B7%CE%BD%CE%AF%CE%BF" title="Πηνίο – Greek" lang="el" hreflang="el" data-title="Πηνίο" 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/Inductor" title="Inductor – Spanish" lang="es" hreflang="es" data-title="Inductor" 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/Induktilo" title="Induktilo – Esperanto" lang="eo" hreflang="eo" data-title="Induktilo" 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/Haril" title="Haril – Basque" lang="eu" hreflang="eu" data-title="Haril" 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%A7%D9%84%D9%82%D8%A7%DA%AF%D8%B1" title="القاگر – Persian" lang="fa" hreflang="fa" data-title="القاگر" 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/Inductor" title="Inductor – Fiji Hindi" lang="hif" hreflang="hif" data-title="Inductor" 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/Bobine_(%C3%A9lectricit%C3%A9)" title="Bobine (électricité) – French" lang="fr" hreflang="fr" data-title="Bobine (électricité)" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Indutor" title="Indutor – Galician" lang="gl" hreflang="gl" data-title="Indutor" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%9C%A0%EB%8F%84%EC%9E%90" title="유도자 – Korean" lang="ko" hreflang="ko" data-title="유도자" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A5%87%E0%A4%B0%E0%A4%95" title="प्रेरक – Hindi" lang="hi" hreflang="hi" data-title="प्रेरक" 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%8Dna_zavojnica" title="Električna zavojnica – Croatian" lang="hr" hreflang="hr" data-title="Električna zavojnica" 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/Induktoro" title="Induktoro – Ido" lang="io" hreflang="io" data-title="Induktoro" 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/Induktor" title="Induktor – Indonesian" lang="id" hreflang="id" data-title="Induktor" 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/Inductor" title="Inductor – Interlingua" lang="ia" hreflang="ia" data-title="Inductor" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Spansp%C3%B3la" title="Spanspóla – Icelandic" lang="is" hreflang="is" data-title="Spanspóla" 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/Induttore" title="Induttore – Italian" lang="it" hreflang="it" data-title="Induttore" 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%A1%D7%9C%D7%99%D7%9C_%D7%94%D7%A9%D7%A8%D7%90%D7%94" title="סליל השראה – Hebrew" lang="he" hreflang="he" data-title="סליל השראה" 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/Induktor" title="Induktor – Javanese" lang="jv" hreflang="jv" data-title="Induktor" data-language-autonym="Jawa" data-language-local-name="Javanese" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%98%D0%BD%D0%B4%D1%83%D0%BA%D1%82%D0%BE%D1%80" title="Индуктор – Kazakh" lang="kk" hreflang="kk" data-title="Индуктор" 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/Kidukizi" title="Kidukizi – Swahili" lang="sw" hreflang="sw" data-title="Kidukizi" 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/Bobin_(elektrisite)" title="Bobin (elektrisite) – Haitian Creole" lang="ht" hreflang="ht" data-title="Bobin (elektrisite)" 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/%C3%8Enduktor" title="Înduktor – Kurdish" lang="ku" hreflang="ku" data-title="Înduktor" 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%98%D0%BD%D0%B4%D1%83%D0%BA%D1%82%D0%BE%D1%80" title="Индуктор – Kyrgyz" lang="ky" hreflang="ky" data-title="Индуктор" 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/Inductorium" title="Inductorium – Latin" lang="la" hreflang="la" data-title="Inductorium" 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/Induktivit%C4%81tes_spole" title="Induktivitātes spole – Latvian" lang="lv" hreflang="lv" data-title="Induktivitātes spole" 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/Indukcin%C4%97_rit%C4%97" title="Indukcinė ritė – Lithuanian" lang="lt" hreflang="lt" data-title="Indukcinė ritė" 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/Induttor" title="Induttor – Lombard" lang="lmo" hreflang="lmo" data-title="Induttor" 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/Tekercs_(%C3%A1ramk%C3%B6ri_alkatr%C3%A9sz)" title="Tekercs (áramköri alkatrész) – Hungarian" lang="hu" hreflang="hu" data-title="Tekercs (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%95%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%B8%D1%87%D0%BD%D0%B0_%D0%BD%D0%B0%D0%BC%D0%BE%D1%82%D0%BA%D0%B0" title="Електрична намотка – Macedonian" lang="mk" hreflang="mk" data-title="Електрична намотка" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%87%E0%B5%BB%E0%B4%A1%E0%B4%95%E0%B5%8D%E0%B4%B1%E0%B5%8D%E0%B4%B1%E0%B5%BC" title="ഇൻഡക്റ്റർ – Malayalam" lang="ml" hreflang="ml" data-title="ഇൻഡക്റ്റർ" 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%B5%E0%A4%BF%E0%A4%A6%E0%A5%8D%E0%A4%AF%E0%A5%81%E0%A4%A4%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%B5%E0%A4%B0%E0%A5%8D%E0%A4%A4%E0%A4%95" title="विद्युतप्रवर्तक – Marathi" lang="mr" hreflang="mr" data-title="विद्युतप्रवर्तक" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Peraruh" title="Peraruh – Malay" lang="ms" hreflang="ms" data-title="Peraruh" 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-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%98%D0%BD%D0%B4%D1%83%D0%BA%D1%86%D0%B8%D0%B9%D0%BD_%D0%BE%D1%80%D0%BE%D0%BE%D0%BC%D0%BE%D0%B3" title="Индукцийн ороомог – Mongolian" lang="mn" hreflang="mn" data-title="Индукцийн ороомог" 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%A1%E1%80%84%E1%80%BA%E1%80%92%E1%80%95%E1%80%BA%E1%80%90%E1%80%AC" title="အင်ဒပ်တာ – Burmese" lang="my" hreflang="my" data-title="အင်ဒပ်တာ" 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/Inductor" title="Inductor – Dutch" lang="nl" hreflang="nl" data-title="Inductor" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-new mw-list-item"><a href="https://new.wikipedia.org/wiki/%E0%A4%87%E0%A4%A8%E0%A5%8D%E0%A4%A1%E0%A4%95%E0%A5%8D%E0%A4%9F%E0%A4%B0" title="इन्डक्टर – Newari" lang="new" hreflang="new" data-title="इन्डक्टर" 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%A4%E3%83%B3%E3%83%80%E3%82%AF%E3%82%BF" title="インダクタ – Japanese" lang="ja" hreflang="ja" data-title="インダクタ" 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%98%D0%BD%D0%B4%D1%83%D0%BA%D1%82%D0%B8%D0%B2%D0%BD%D0%BE%D1%81%D1%82%D0%B8%D0%BD_%D1%82%D1%83%D1%8C%D0%BF%D0%BF%D0%B0%D0%BB%D0%B3" title="Индуктивностин туьппалг – Chechen" lang="ce" hreflang="ce" data-title="Индуктивностин туьппалг" 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/Spuul" title="Spuul – Northern Frisian" lang="frr" hreflang="frr" data-title="Spuul" data-language-autonym="Nordfriisk" data-language-local-name="Northern Frisian" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Induktor" title="Induktor – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Induktor" 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/Inductor" title="Inductor – Occitan" lang="oc" hreflang="oc" data-title="Inductor" 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/Indaakterii" title="Indaakterii – Oromo" lang="om" hreflang="om" data-title="Indaakterii" 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/Induktivlik_g%CA%BBaltagi" title="Induktivlik gʻaltagi – Uzbek" lang="uz" hreflang="uz" data-title="Induktivlik gʻaltagi" 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%87%E0%A9%B0%E0%A8%A1%E0%A8%95%E0%A8%9F%E0%A8%B0" title="ਇੰਡਕਟਰ – Punjabi" lang="pa" hreflang="pa" data-title="ਇੰਡਕਟਰ" 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/%D8%A7%D9%86%DA%88%DA%A9%D9%B9%D8%B1" title="انڈکٹر – Western Punjabi" lang="pnb" hreflang="pnb" data-title="انڈکٹر" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Cewka" title="Cewka – Polish" lang="pl" hreflang="pl" data-title="Cewka" 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/Indutor" title="Indutor – Portuguese" lang="pt" hreflang="pt" data-title="Indutor" 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/Bobin%C4%83" title="Bobină – Romanian" lang="ro" hreflang="ro" data-title="Bobină" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Pinchikilla_kurur" title="Pinchikilla kurur – Quechua" lang="qu" hreflang="qu" data-title="Pinchikilla kurur" data-language-autonym="Runa Simi" data-language-local-name="Quechua" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9A%D0%B0%D1%82%D1%83%D1%88%D0%BA%D0%B0_%D0%B8%D0%BD%D0%B4%D1%83%D0%BA%D1%82%D0%B8%D0%B2%D0%BD%D0%BE%D1%81%D1%82%D0%B8" title="Катушка индуктивности – Russian" lang="ru" hreflang="ru" data-title="Катушка индуктивности" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Induktori" title="Induktori – Albanian" lang="sq" hreflang="sq" data-title="Induktori" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Ruccheddu" title="Ruccheddu – Sicilian" lang="scn" hreflang="scn" data-title="Ruccheddu" data-language-autonym="Sicilianu" data-language-local-name="Sicilian" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-si badge-Q70893996 mw-list-item" title=""><a href="https://si.wikipedia.org/wiki/%E0%B6%B4%E0%B7%8A%E2%80%8D%E0%B6%BB%E0%B7%9A%E0%B6%BB%E0%B6%AB%E0%B6%BA_%E0%B6%B4%E0%B7%92%E0%B7%85%E0%B7%92%E0%B6%B6%E0%B6%B3_%E0%B6%AF%E0%B7%85_%E0%B7%80%E0%B7%92%E0%B7%81%E0%B7%8A%E0%B6%BD%E0%B7%9A%E0%B7%82%E0%B6%AB%E0%B6%BA" title="ප්‍රේරණය පිළිබඳ දළ විශ්ලේෂණය – Sinhala" lang="si" hreflang="si" data-title="ප්‍රේරණය පිළිබඳ දළ විශ්ලේෂණය" 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/Inductor" title="Inductor – Simple English" lang="en-simple" hreflang="en-simple" data-title="Inductor" 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-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%D8%A7%D9%86%DA%8A%DA%AA%D9%BD%D8%B1" title="انڊڪٽر – Sindhi" lang="sd" hreflang="sd" data-title="انڊڪٽر" data-language-autonym="سنڌي" data-language-local-name="Sindhi" class="interlanguage-link-target"><span>سنڌي</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Cievka_(elektrotechnika)" title="Cievka (elektrotechnika) – Slovak" lang="sk" hreflang="sk" data-title="Cievka (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/Du%C5%A1ilka" title="Dušilka – Slovenian" lang="sl" hreflang="sl" data-title="Dušilka" 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%97%D0%B0%D0%B2%D0%BE%D1%98%D0%BD%D0%B8%D1%86%D0%B0" title="Завојница – Serbian" lang="sr" hreflang="sr" data-title="Завојница" 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/Induktor" title="Induktor – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Induktor" 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-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Kela_(komponentti)" title="Kela (komponentti) – Finnish" lang="fi" hreflang="fi" data-title="Kela (komponentti)" 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/Induktor" title="Induktor – Swedish" lang="sv" hreflang="sv" data-title="Induktor" 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/Panawit" title="Panawit – Tagalog" lang="tl" hreflang="tl" data-title="Panawit" 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%82%E0%AE%A3%E0%AF%8D%E0%AE%9F%E0%AE%BF" title="மின்தூண்டி – Tamil" lang="ta" hreflang="ta" data-title="மின்தூண்டி" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</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%98%D0%BD%D0%B4%D1%83%D0%BA%D1%82%D0%B8%D0%B2%D0%BB%D1%8B%D0%BA_%D0%BA%D3%99%D1%82%D2%AF%D0%B3%D0%B5" title="Индуктивлык кәтүге – Tatar" lang="tt" hreflang="tt" data-title="Индуктивлык кәтүге" 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%AB%E0%B8%99%E0%B8%B5%E0%B9%88%E0%B8%A2%E0%B8%A7%E0%B8%99%E0%B8%B3" title="ตัวเหนี่ยวนำ – Thai" lang="th" hreflang="th" data-title="ตัวเหนี่ยวนำ" 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/%D2%92%D0%B0%D0%BB%D1%82%D0%B0%D0%BA%D0%B8_%D0%B8%D0%BD%D0%B4%D1%83%D0%BA%D1%82%D0%B8%D0%B2%D3%A3" title="Ғалтаки индуктивӣ – Tajik" lang="tg" hreflang="tg" data-title="Ғалтаки индуктивӣ" 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/%C4%B0nd%C3%BCkt%C3%B6r" title="İndüktör – Turkish" lang="tr" hreflang="tr" data-title="İndüktör" 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%9A%D0%BE%D1%82%D1%83%D1%88%D0%BA%D0%B0_%D1%96%D0%BD%D0%B4%D1%83%D0%BA%D1%82%D0%B8%D0%B2%D0%BD%D0%BE%D1%81%D1%82%D1%96" title="Котушка індуктивності – Ukrainian" lang="uk" hreflang="uk" data-title="Котушка індуктивності" 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/%D8%A7%D9%85%D8%A7%D9%84%DB%81_%DA%AF%D8%B1" title="امالہ گر – Urdu" lang="ur" hreflang="ur" data-title="امالہ گر" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Cu%E1%BB%99n_c%E1%BA%A3m" title="Cuộn cảm – Vietnamese" lang="vi" hreflang="vi" data-title="Cuộn cảm" 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/Inductor" title="Inductor – Waray" lang="war" hreflang="war" data-title="Inductor" 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/Xiirtalukaay" title="Xiirtalukaay – Wolof" lang="wo" hreflang="wo" data-title="Xiirtalukaay" 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%E6%84%9F%E5%85%83%E4%BB%B6" title="电感元件 – Wu" lang="wuu" hreflang="wuu" data-title="电感元件" 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%90%D7%99%D7%A0%D7%93%D7%95%D7%A7%D7%98%D7%90%D7%A8" title="אינדוקטאר – Yiddish" lang="yi" hreflang="yi" data-title="אינדוקטאר" 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%E6%84%9F%E5%99%A8" title="電感器 – Cantonese" lang="yue" hreflang="yue" data-title="電感器" 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-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%94%B5%E6%84%9F%E5%85%83%E4%BB%B6" title="电感元件 – Chinese" lang="zh" hreflang="zh" data-title="电感元件" 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/Q5325#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/Inductor" 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:Inductor" 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/Inductor"><span>Read</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Inductor&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=Inductor&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/Inductor"><span>Read</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Inductor&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=Inductor&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/Inductor" 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/Inductor" 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="/wiki/Wikipedia:File_Upload_Wizard" title="Upload files [u]" accesskey="u"><span>Upload file</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Special:SpecialPages" title="A list of all special pages [q]" accesskey="q"><span>Special pages</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Inductor&oldid=1257456796" 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=Inductor&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=Inductor&id=1257456796&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%2FInductor"><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%2FInductor"><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=Inductor&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=Inductor&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/Inductor" hreflang="en"><span>Wikimedia Commons</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/Q5325" 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 electrical component that stores energy in its magnetic 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">For inductors whose magnetic properties rather than electrical properties matter, see <a href="/wiki/Electromagnet" title="Electromagnet">electromagnet</a>.</div> <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">Inductor</caption><tbody><tr><td colspan="2" class="infobox-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:Electronic_component_inductors.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a1/Electronic_component_inductors.jpg/220px-Electronic_component_inductors.jpg" decoding="async" width="220" height="195" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a1/Electronic_component_inductors.jpg/330px-Electronic_component_inductors.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a1/Electronic_component_inductors.jpg/440px-Electronic_component_inductors.jpg 2x" data-file-width="1170" data-file-height="1038" /></a></span><div class="infobox-caption">A selection of low-value inductors</div></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/Electromagnetic_induction" title="Electromagnetic induction">Electromagnetic induction</a></td></tr><tr><th scope="row" class="infobox-label">Invented</th><td class="infobox-data"><a href="/wiki/Michael_Faraday" title="Michael Faraday">Michael Faraday</a> (1831)</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"><span typeof="mw:File"><a href="/wiki/File:Inductor.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Inductor.svg/100px-Inductor.svg.png" decoding="async" width="100" height="33" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Inductor.svg/150px-Inductor.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Inductor.svg/200px-Inductor.svg.png 2x" data-file-width="45" data-file-height="15" /></a></span></td></tr></tbody></table> <p>An <b>inductor</b>, also called a <b>coil</b>, <b>choke</b>, or <b>reactor</b>, is a <a href="/wiki/Passivity_(engineering)" title="Passivity (engineering)">passive</a> two-terminal <a href="/wiki/Electronic_component" title="Electronic component">electrical component</a> that stores energy in a <a href="/wiki/Magnetic_field" title="Magnetic field">magnetic field</a> when an <a href="/wiki/Electric_current" title="Electric current">electric current</a> flows through it.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> An inductor typically consists of an insulated wire wound into a <a href="/wiki/Electromagnetic_coil" title="Electromagnetic coil">coil</a>. </p><p>When the current flowing through the coil changes, the time-varying magnetic field induces an <a href="/wiki/Electromotive_force" title="Electromotive force">electromotive force</a> (<i>emf</i>) (<a href="/wiki/Voltage" title="Voltage">voltage</a>) in the conductor, described by <a href="/wiki/Faraday%27s_law_of_induction" title="Faraday's law of induction">Faraday's law of induction</a>. According to <a href="/wiki/Lenz%27s_law" title="Lenz's law">Lenz's law</a>, the induced voltage has a polarity (direction) which opposes the change in current that created it. As a result, inductors oppose any changes in current through them. </p><p>An inductor is characterized by its <a href="/wiki/Inductance" title="Inductance">inductance</a>, which is the ratio of the voltage to the rate of change of current. In the <a href="/wiki/International_System_of_Units" title="International System of Units">International System of Units</a> (SI), the unit of inductance is the <a href="/wiki/Henry_(unit)" title="Henry (unit)">henry</a> (H) named for 19th century American scientist <a href="/wiki/Joseph_Henry" title="Joseph Henry">Joseph Henry</a>. In the measurement of magnetic circuits, it is equivalent to <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"><a href="/wiki/Weber_(unit)" title="Weber (unit)">weber</a></span><span class="sr-only">/</span><span class="den"><a href="/wiki/Ampere" title="Ampere">ampere</a></span></span>⁠</span>. Inductors have values that typically range from 1<span class="nowrap"> </span>μH (10<sup>−6</sup><span class="nowrap"> </span>H) to 20<span class="nowrap"> </span>H. Many inductors have a <a href="/wiki/Magnetic_core" title="Magnetic core">magnetic core</a> made of iron or <a href="/wiki/Ferrite_(magnet)" title="Ferrite (magnet)">ferrite</a> inside the coil, which serves to increase the magnetic field and thus the inductance. Along with <a href="/wiki/Capacitor" title="Capacitor">capacitors</a> and <a href="/wiki/Resistor" title="Resistor">resistors</a>, inductors are one of the three passive <a href="/wiki/Linear_circuit" title="Linear circuit">linear</a> <a href="/wiki/Circuit_element" class="mw-redirect" title="Circuit element">circuit elements</a> that make up electronic circuits. Inductors are widely used in <a href="/wiki/Alternating_current" title="Alternating current">alternating current</a> (AC) electronic equipment, particularly in <a href="/wiki/Radio" title="Radio">radio</a> equipment. They are used to block AC while allowing DC to pass; inductors designed for this purpose are called <a href="/wiki/Choke_(electronics)" title="Choke (electronics)">chokes</a>. They are also used in <a href="/wiki/Electronic_filter" title="Electronic filter">electronic filters</a> to separate signals of different <a href="/wiki/Frequency" title="Frequency">frequencies</a>, and in combination with capacitors to make <a href="/wiki/Tuned_circuit" class="mw-redirect" title="Tuned circuit">tuned circuits</a>, used to tune radio and TV receivers. </p><p>The term inductor seems to come from <a href="/wiki/Heinrich_Daniel_Ruhmkorff" title="Heinrich Daniel Ruhmkorff">Heinrich Daniel Ruhmkorff</a>, who called the <a href="/wiki/Induction_coil" title="Induction coil">induction coil</a> he invented in 1851 an inductorium.<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> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Description">Description</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductor&action=edit&section=1" title="Edit section: Description"><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:Electromagnetism.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/91/Electromagnetism.svg/220px-Electromagnetism.svg.png" decoding="async" width="220" height="240" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/91/Electromagnetism.svg/330px-Electromagnetism.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/91/Electromagnetism.svg/440px-Electromagnetism.svg.png 2x" data-file-width="651" data-file-height="709" /></a><figcaption>An electric current <span class="texhtml">I</span> creates a magnetic field <span class="texhtml">B</span> around it</figcaption></figure> <p>An electric current flowing through a <a href="/wiki/Electrical_conductor" title="Electrical conductor">conductor</a> generates a magnetic field surrounding it. The <a href="/wiki/Magnetic_flux" title="Magnetic flux"> magnetic flux linkage</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 \Phi _{\mathbf {B} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Phi _{\mathbf {B} }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/73abebb63f1034f0d39b6e24161750587a1c3c3a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.255ex; height:2.509ex;" alt="{\displaystyle \Phi _{\mathbf {B} }}"></span> generated by a given current <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 I}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/535ea7fc4134a31cbe2251d9d3511374bc41be9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.172ex; height:2.176ex;" alt="{\displaystyle I}"></span> depends on the geometric shape of the circuit. Their ratio defines the 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 L}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/103168b86f781fe6e9a4a87b8ea1cebe0ad4ede8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.583ex; height:2.176ex;" alt="{\displaystyle L}"></span>.<sup id="cite_ref-Singh_3-0" class="reference"><a href="#cite_note-Singh-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Wadhwa_4-0" class="reference"><a href="#cite_note-Wadhwa-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Pelcovits_5-0" class="reference"><a href="#cite_note-Pelcovits-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Purcell_6-0" class="reference"><a href="#cite_note-Purcell-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> Thus </p> <dl><dd><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:={\frac {\Phi _{\mathbf {B} }}{I}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mo>:=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi mathvariant="normal">Φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> </mrow> </msub> <mi>I</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L:={\frac {\Phi _{\mathbf {B} }}{I}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4161d3ebde2e771d431b64bf615604fb91671681" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:9.419ex; height:5.176ex;" alt="{\displaystyle L:={\frac {\Phi _{\mathbf {B} }}{I}}}"></span>.</dd></dl> <p>The inductance of a circuit depends on the geometry of the current path as well as the <a href="/wiki/Magnetic_permeability" class="mw-redirect" title="Magnetic permeability">magnetic permeability</a> of nearby materials. An inductor is a <a href="/wiki/Electronic_component" title="Electronic component">component</a> consisting of a wire or other conductor shaped to increase the magnetic flux through the circuit, usually in the shape of a coil or <a href="/wiki/Helix" title="Helix">helix</a>, with two <a href="/wiki/Terminal_(electronics)" title="Terminal (electronics)">terminals</a>. Winding the wire into a <a href="/wiki/Electromagnetic_coil" title="Electromagnetic coil">coil</a> increases the number of times the <a href="/wiki/Magnetic_flux" title="Magnetic flux">magnetic flux</a> <a href="/wiki/Field_Lines" class="mw-redirect" title="Field Lines">lines</a> link the circuit, increasing the field and thus the inductance. The more turns, the higher the inductance. The inductance also depends on the shape of the coil, separation of the turns, and many other factors. By adding a "magnetic core" made of a <a href="/wiki/Ferromagnetic" class="mw-redirect" title="Ferromagnetic">ferromagnetic</a> material like iron inside the coil, the magnetizing field from the coil will induce <a href="/wiki/Magnetization" title="Magnetization">magnetization</a> in the material, increasing the magnetic flux. The high <a href="/wiki/Magnetic_permeability" class="mw-redirect" title="Magnetic permeability">permeability</a> of a ferromagnetic core can increase the inductance of a coil by a factor of several thousand over what it would be without it. </p> <div class="mw-heading mw-heading3"><h3 id="Constitutive_equation">Constitutive equation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductor&action=edit&section=2" title="Edit section: Constitutive equation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Any change in the current through an inductor creates a changing flux, inducing a voltage across the inductor. By <a href="/wiki/Faraday%27s_law_of_induction" title="Faraday's law of induction">Faraday's law of induction</a>, 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 {\mathcal {E}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">E</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {E}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9c298ed828ff778065aeb5f0f305097f55bb9ae0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.311ex; height:2.176ex;" alt="{\displaystyle {\mathcal {E}}}"></span> induced by any change in magnetic flux through the circuit is given by<sup id="cite_ref-Purcell_6-1" class="reference"><a href="#cite_note-Purcell-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><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 {\mathcal {E}}=-{\frac {d\Phi _{\mathbf {B} }}{dt}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">E</mi> </mrow> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <msub> <mi mathvariant="normal">Φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> </mrow> </msub> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {E}}=-{\frac {d\Phi _{\mathbf {B} }}{dt}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01392ec808b95751785a41f6b9247c701120aed5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:11.524ex; height:5.509ex;" alt="{\displaystyle {\mathcal {E}}=-{\frac {d\Phi _{\mathbf {B} }}{dt}}}"></span>.</dd></dl> <p>Reformulating the definition of <span class="texhtml mvar" style="font-style:italic;">L</span> above, we obtain<sup id="cite_ref-Purcell_6-2" class="reference"><a href="#cite_note-Purcell-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><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 \Phi _{\mathbf {B} }=LI}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> </mrow> </msub> <mo>=</mo> <mi>L</mi> <mi>I</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Phi _{\mathbf {B} }=LI}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ddafe820d6a03b10f6f1eaa3d53f5d05503bd0bb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.108ex; height:2.509ex;" alt="{\displaystyle \Phi _{\mathbf {B} }=LI}"></span>.</dd></dl> <p>It follows that </p> <dl><dd><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 {\mathcal {E}}=-{\frac {d\Phi _{\mathbf {B} }}{dt}}=-{\frac {d}{dt}}(LI)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">E</mi> </mrow> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <msub> <mi mathvariant="normal">Φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> </mrow> </msub> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>d</mi> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo stretchy="false">(</mo> <mi>L</mi> <mi>I</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {E}}=-{\frac {d\Phi _{\mathbf {B} }}{dt}}=-{\frac {d}{dt}}(LI)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/67a420d40ac2f3cea760437199e7c8827c0af85f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:23.886ex; height:5.509ex;" alt="{\displaystyle {\mathcal {E}}=-{\frac {d\Phi _{\mathbf {B} }}{dt}}=-{\frac {d}{dt}}(LI)}"></span></dd></dl> <div class="equation-box" style="margin: ;padding: 0px; border-width:2px; 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 \quad {\mathcal {E}}=-L{\frac {dI}{dt}}\quad }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="1em" /> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">E</mi> </mrow> </mrow> <mo>=</mo> <mo>−</mo> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>I</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mspace width="1em" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \quad {\mathcal {E}}=-L{\frac {dI}{dt}}\quad }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b8bb319410c42e07ca6bfd9a49b2fb6b3955870" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:15.669ex; height:5.509ex;" alt="{\displaystyle \quad {\mathcal {E}}=-L{\frac {dI}{dt}}\quad }"></span> </p> </div> <p>if <span class="texhtml mvar" style="font-style:italic;">L</span> is independent of time, current and magnetic flux linkage. Thus, inductance is also a measure of the amount of <a href="/wiki/Electromotive_force" title="Electromotive force">electromotive force</a> (voltage) generated for a given rate of change of current. This is usually taken to be the <a href="/wiki/Constitutive_relation" class="mw-redirect" title="Constitutive relation">constitutive relation</a> (defining equation) of the inductor. </p> <div class="mw-heading mw-heading3"><h3 id="Lenz's_law"><span id="Lenz.27s_law"></span>Lenz's law</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductor&action=edit&section=3" title="Edit section: Lenz's law"><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/Lenz%27s_Law" class="mw-redirect" title="Lenz's Law">Lenz's Law</a></div> <p>The polarity (direction) of the induced voltage is given by <a href="/wiki/Lenz%27s_law" title="Lenz's law">Lenz's law</a>, which states that the induced voltage will be such as to oppose the change in current.<sup id="cite_ref-Shamos_7-0" class="reference"><a href="#cite_note-Shamos-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> For example, if the current through a 1 henry inductor is increasing at a rate of 1 amperes per second, the induced 1 volt of potential difference will be positive at the current's entrance point and negative at the exit point, tending to oppose the additional current.<sup id="cite_ref-Schmitt_8-0" class="reference"><a href="#cite_note-Schmitt-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Jaffe_9-0" class="reference"><a href="#cite_note-Jaffe-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Lerner_10-0" class="reference"><a href="#cite_note-Lerner-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> The energy from the external circuit necessary to overcome this potential "hill" is being stored in the magnetic field of the inductor. If the current is decreasing, the induced voltage will be negative at the current's entrance point and positive at the exit point, tending to maintain the current. In this case energy from the magnetic field is being returned to the circuit. </p> <div class="mw-heading mw-heading3"><h3 id="Positive_form_of_current–voltage_relationship"><span id="Positive_form_of_current.E2.80.93voltage_relationship"></span>Positive form of current–voltage relationship</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductor&action=edit&section=4" title="Edit section: Positive form of current–voltage relationship"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Inductor-positive-voltage-with-input-current-function-of-time.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/Inductor-positive-voltage-with-input-current-function-of-time.svg/146px-Inductor-positive-voltage-with-input-current-function-of-time.svg.png" decoding="async" width="146" height="205" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/Inductor-positive-voltage-with-input-current-function-of-time.svg/219px-Inductor-positive-voltage-with-input-current-function-of-time.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/60/Inductor-positive-voltage-with-input-current-function-of-time.svg/292px-Inductor-positive-voltage-with-input-current-function-of-time.svg.png 2x" data-file-width="89" data-file-height="125" /></a><figcaption>Schematic using current's exit terminal as reference for voltage</figcaption></figure> <p>Because the induced voltage is positive at the current's entrance terminal, the inductor's current–voltage relationship is often expressed without a negative sign by using the current's exit terminal as the reference point for 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(t)}"> <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> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V(t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/383b47023708ac9df0e198448491048ec7acb2cf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.436ex; height:2.843ex;" alt="{\displaystyle V(t)}"></span> at the current's entrance terminal (as labeled in the schematic). </p><p>The derivative form of this current–voltage relationship is then:<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)=L{\frac {\mathrm {d} I(t)}{\mathrm {d} t}}\,.}"> <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> <mi>L</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> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V(t)=L{\frac {\mathrm {d} I(t)}{\mathrm {d} t}}\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f84ad165a75f9cd8828b9c390117c5458ade178" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:16.101ex; height:5.843ex;" alt="{\displaystyle V(t)=L{\frac {\mathrm {d} I(t)}{\mathrm {d} t}}\,.}"></span>The integral form of this current–voltage relationship, starting at time <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/02d3006c4190b1939b04d9b9bb21006fb4e6fa4a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.894ex; height:2.343ex;" alt="{\displaystyle t_{0}}"></span> with some initial current <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 I(t_{0})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> <mo stretchy="false">(</mo> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I(t_{0})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5ac7f2974144a6ff3f0faf78f1a7bf98014868b7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.875ex; height:2.843ex;" alt="{\displaystyle I(t_{0})}"></span>, is then:<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)=I(t_{0})+{\frac {1}{L}}\int _{t_{0}}^{t}V(\tau )\,\mathrm {d} \tau \,.}"> <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> <mi>I</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>L</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>V</mi> <mo stretchy="false">(</mo> <mi>τ</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>τ</mi> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I(t)=I(t_{0})+{\frac {1}{L}}\int _{t_{0}}^{t}V(\tau )\,\mathrm {d} \tau \,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/164d86ad452f76c2ed61c257473f9184f04de037" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:29.832ex; height:6.509ex;" alt="{\displaystyle I(t)=I(t_{0})+{\frac {1}{L}}\int _{t_{0}}^{t}V(\tau )\,\mathrm {d} \tau \,.}"></span>The <a href="/wiki/Duality_(electrical_circuits)" title="Duality (electrical circuits)">dual</a> of the inductor is the <a href="/wiki/Capacitor" title="Capacitor">capacitor</a>, which <a href="/wiki/Capacitor#Energy_stored_in_a_capacitor" title="Capacitor">stores energy in an electric field</a> rather than a magnetic field. <a href="/wiki/Capacitor#Current–voltage_relation" title="Capacitor">Its current–voltage relation</a> replaces <span class="texhtml mvar" style="font-style:italic;">L</span> with the capacitance <span class="texhtml mvar" style="font-style:italic;">C</span> and has current and voltage swapped from these equations. </p> <div class="mw-heading mw-heading3"><h3 id="Energy_stored_in_an_inductor">Energy stored in an inductor</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductor&action=edit&section=5" title="Edit section: Energy stored in an inductor"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>One intuitive explanation as to why a potential difference is induced on a change of current in an inductor goes as follows: </p><p>When there is a change in current through an inductor there is a change in the strength of the magnetic field. For example, if the current is increased, the magnetic field increases. This, however, does not come without a price. The magnetic field contains <a href="/wiki/Potential_energy" title="Potential energy">potential energy</a>, and increasing the field strength requires more energy to be stored in the field. This energy comes from the electric current through the inductor. The increase in the magnetic potential energy of the field is provided by a corresponding drop in the electric potential energy of the charges flowing through the windings. This appears as a voltage drop across the windings as long as the current increases. Once the current is no longer increased and is held constant, the energy in the magnetic field is constant and no additional energy must be supplied, so the voltage drop across the windings disappears. </p><p>Similarly, if the current through the inductor decreases, the magnetic field strength decreases, and the energy in the magnetic field decreases. This energy is returned to the circuit in the form of an increase in the electrical potential energy of the moving charges, causing a voltage rise across the windings. </p> <div class="mw-heading mw-heading4"><h4 id="Derivation">Derivation</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductor&action=edit&section=6" title="Edit section: Derivation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Work_(physics)" title="Work (physics)">work</a> done per unit charge on the charges passing through the inductor 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 -{\mathcal {E}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">E</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -{\mathcal {E}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/077dcc3184f7158b62178add877a18f79efeb7be" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:3.119ex; height:2.343ex;" alt="{\displaystyle -{\mathcal {E}}}"></span>. The negative sign indicates that the work is done <i>against</i> the emf, and is not done <i>by</i> the emf. The current <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 I}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/535ea7fc4134a31cbe2251d9d3511374bc41be9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.172ex; height:2.176ex;" alt="{\displaystyle I}"></span> is the charge per unit time passing through the inductor. Therefore, the rate of 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 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> done by the charges against the emf, that is the rate of change of energy of the current, is given by </p> <dl><dd><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 {\frac {dW}{dt}}=-{\mathcal {E}}I}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>W</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">E</mi> </mrow> </mrow> <mi>I</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {dW}{dt}}=-{\mathcal {E}}I}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/41c72444a5a7b65da64095d8209df3a9e4406a5c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:11.877ex; height:5.509ex;" alt="{\displaystyle {\frac {dW}{dt}}=-{\mathcal {E}}I}"></span></dd></dl> <p>From the constitutive equation for the inductor, <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 -{\mathcal {E}}=L{\frac {dI}{dt}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">E</mi> </mrow> </mrow> <mo>=</mo> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>I</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -{\mathcal {E}}=L{\frac {dI}{dt}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cbcbbb8b152c80c360c7a5a9bb3428449f0e08b5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:11.024ex; height:5.509ex;" alt="{\displaystyle -{\mathcal {E}}=L{\frac {dI}{dt}}}"></span> so </p> <dl><dd><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 {\frac {dW}{dt}}=L{\frac {dI}{dt}}\cdot I=LI\cdot {\frac {dI}{dt}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>W</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>I</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>⋅</mo> <mi>I</mi> <mo>=</mo> <mi>L</mi> <mi>I</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>I</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {dW}{dt}}=L{\frac {dI}{dt}}\cdot I=LI\cdot {\frac {dI}{dt}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4c3e01daf01cc3a564e1b81805c5ab8636e0ca7b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:25.999ex; height:5.509ex;" alt="{\displaystyle {\frac {dW}{dt}}=L{\frac {dI}{dt}}\cdot I=LI\cdot {\frac {dI}{dt}}}"></span></dd></dl> <dl><dd><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=LI\cdot dI}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>W</mi> <mo>=</mo> <mi>L</mi> <mi>I</mi> <mo>⋅</mo> <mi>d</mi> <mi>I</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dW=LI\cdot dI}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/51aa9864d1f8d74e266678fb24608dea900ca614" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:13.571ex; height:2.176ex;" alt="{\displaystyle dW=LI\cdot dI}"></span></dd></dl> <p>In a ferromagnetic core inductor, when the magnetic field approaches the level at which the core saturates, the inductance will begin to change, it will be a function of the current <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(I)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mo stretchy="false">(</mo> <mi>I</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L(I)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a742039d86b57889c6c89c930300f31e5bccb4b0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.564ex; height:2.843ex;" alt="{\displaystyle L(I)}"></span>. Neglecting losses, the <a href="/wiki/Energy" title="Energy">energy</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 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 by an inductor with a current <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 I_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/893d08e90ea73781dc133414d661529d0651ca80" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.077ex; height:2.509ex;" alt="{\displaystyle I_{0}}"></span> passing through it is equal to the amount of work required to establish the current through the inductor. </p><p>This is given by: <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=\int _{0}^{I_{0}}L_{d}(I)\,I\,dI}"> <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"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </msubsup> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>I</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>I</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>I</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W=\int _{0}^{I_{0}}L_{d}(I)\,I\,dI}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c197a91fcc164465991054455e04e807868b2470" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:20.162ex; height:6.176ex;" alt="{\displaystyle W=\int _{0}^{I_{0}}L_{d}(I)\,I\,dI}"></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 L_{d}(I)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>I</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{d}(I)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5eb10ad6c7b799db1237fe969f1fe84282091a7d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.656ex; height:2.843ex;" alt="{\displaystyle L_{d}(I)}"></span> is the so-called "differential inductance" and 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 L_{d}={\frac {d\Phi _{\mathbf {B} }}{dI}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <msub> <mi mathvariant="normal">Φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> </mrow> </msub> </mrow> <mrow> <mi>d</mi> <mi>I</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{d}={\frac {d\Phi _{\mathbf {B} }}{dI}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/de2860074efd58b0d2770e0c68ec214c684711e9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:11.08ex; height:5.509ex;" alt="{\displaystyle L_{d}={\frac {d\Phi _{\mathbf {B} }}{dI}}}"></span>. In an air core inductor or a ferromagnetic core inductor below saturation, the inductance is constant (and equal to the differential inductance), so the stored energy is </p> <dl><dd><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=L\int _{0}^{I_{0}}I\,dI}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>W</mi> <mo>=</mo> <mi>L</mi> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </msubsup> <mi>I</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>I</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W=L\int _{0}^{I_{0}}I\,dI}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/de3db44c2a5754fd958dca86708fdfc8c61d2a65" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:16.089ex; height:6.176ex;" alt="{\displaystyle W=L\int _{0}^{I_{0}}I\,dI}"></span></dd></dl> <div class="equation-box" style="margin: ;padding: 0px; border-width:2px; 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 \quad W={\frac {1}{2}}L{I_{0}}^{2}\quad }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="1em" /> <mi>W</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>L</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="1em" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \quad W={\frac {1}{2}}L{I_{0}}^{2}\quad }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d461bcad64e7ea27f51af069bdb53be34db1de85" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:16.892ex; height:5.176ex;" alt="{\displaystyle \quad W={\frac {1}{2}}L{I_{0}}^{2}\quad }"></span> </p> </div> <p>For inductors with magnetic cores, the above equation is only valid for <a href="/wiki/Linear_circuit" title="Linear circuit">linear</a> regions of the magnetic flux, at currents below the <a href="/wiki/Magnetic_saturation" class="mw-redirect" title="Magnetic saturation">saturation</a> level of the inductor, where the inductance is approximately constant. Where this is not the case, the integral form must be used 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 L_{d}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{d}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/109c17027235d48b00201addbad2c8125389fdd9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.675ex; height:2.509ex;" alt="{\displaystyle L_{d}}"></span> variable. </p> <div class="mw-heading mw-heading3"><h3 id="Voltage_step_response">Voltage step response</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductor&action=edit&section=7" title="Edit section: Voltage step response"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>When a <a href="/wiki/Step_function" title="Step function">voltage step</a> is applied to an inductor: </p> <ul><li>In the short-time limit, since the current cannot change instantaneously, the initial current is zero. The equivalent circuit of an inductor immediately after the step is applied is an <a href="/wiki/Electrical_circuit" class="mw-redirect" title="Electrical circuit">open circuit</a>.</li> <li>As time passes, the current increases at a constant rate with time until the inductor starts to saturate.</li> <li>In the long-time limit, the transient response of the inductor will die out, the magnetic flux through the inductor will become constant, so no voltage would be induced between the terminals of the inductor. Therefore, assuming the resistance of the windings is negligible, the equivalent circuit of an inductor a long time after the step is applied is a <a href="/wiki/Short_circuit" title="Short circuit">short circuit</a>.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Ideal_and_real_inductors">Ideal and real inductors</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductor&action=edit&section=8" title="Edit section: Ideal and real inductors"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="#Constitutive_equation">constitutive equation</a> describes the behavior of an <i>ideal inductor</i> with 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 L}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/103168b86f781fe6e9a4a87b8ea1cebe0ad4ede8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.583ex; height:2.176ex;" alt="{\displaystyle L}"></span>, and without <a href="/wiki/Electrical_resistance" class="mw-redirect" title="Electrical resistance">resistance</a>, <a href="/wiki/Capacitance" title="Capacitance">capacitance</a>, or energy dissipation. In practice, inductors do not follow this theoretical model; <i>real inductors</i> have a measurable resistance due to the resistance of the wire and energy losses in the core, and <a href="/wiki/Parasitic_element_(electrical_networks)" class="mw-redirect" title="Parasitic element (electrical networks)">parasitic capacitance</a> between turns of the wire.<sup id="cite_ref-Bowick_11-0" class="reference"><a href="#cite_note-Bowick-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Kaiser_12-0" class="reference"><a href="#cite_note-Kaiser-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p><p>A real inductor's <a href="/wiki/Capacitive_reactance" class="mw-redirect" title="Capacitive reactance">capacitive reactance</a> rises with frequency, and at a certain frequency, the inductor will behave as a <a href="/wiki/Resonant_circuit" class="mw-redirect" title="Resonant circuit">resonant circuit</a>. Above this <a href="/wiki/Self-resonant_frequency" class="mw-redirect" title="Self-resonant frequency">self-resonant frequency</a>, the capacitive reactance is the dominant part of the inductor's impedance. At higher frequencies, resistive losses in the windings increase due to the <a href="/wiki/Skin_effect" title="Skin effect">skin effect</a> and <a href="/wiki/Proximity_effect_(electromagnetism)" title="Proximity effect (electromagnetism)">proximity effect</a>. </p><p>Inductors with ferromagnetic cores experience additional energy losses due to <a href="/wiki/Hysteresis" title="Hysteresis">hysteresis</a> and <a href="/wiki/Eddy_current" title="Eddy current">eddy currents</a> in the core, which increase with frequency. At high currents, magnetic core inductors also show sudden departure from ideal behavior due to nonlinearity caused by <a href="/wiki/Magnetic_saturation" class="mw-redirect" title="Magnetic saturation">magnetic saturation</a> of the core. </p><p>Inductors radiate electromagnetic energy into surrounding space and may absorb electromagnetic emissions from other circuits, resulting in potential <a href="/wiki/Electromagnetic_interference" title="Electromagnetic interference">electromagnetic interference</a>. </p><p>An early solid-state electrical switching and amplifying device called a <a href="/wiki/Saturable_reactor" title="Saturable reactor">saturable reactor</a> exploits saturation of the core as a means of stopping the inductive transfer of current via the core. </p> <div class="mw-heading mw-heading4"><h4 id="Q_factor"><i>Q</i> factor</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductor&action=edit&section=9" title="Edit section: Q factor"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The winding resistance appears as a resistance in series with the inductor; it is referred to as DCR (DC resistance). This resistance dissipates some of the reactive energy. The <a href="/wiki/Q_factor" title="Q factor">quality factor</a> (or <i>Q</i>) of an inductor is the ratio of its inductive reactance to its resistance at a given frequency, and is a measure of its efficiency. The higher the Q factor of the inductor, the closer it approaches the behavior of an ideal inductor. High Q inductors are used with capacitors to make resonant circuits in radio transmitters and receivers. The higher the Q is, the narrower the <a href="/wiki/Bandwidth_(signal_processing)" title="Bandwidth (signal processing)">bandwidth</a> of the resonant circuit. </p><p>The Q factor of an inductor is defined as </p> <dl><dd><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={\frac {\omega L}{R}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>ω</mi> <mi>L</mi> </mrow> <mi>R</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q={\frac {\omega L}{R}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/90c5e12e6d6f6792db04eabd0acd98a926cf83d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:8.802ex; height:5.343ex;" alt="{\displaystyle Q={\frac {\omega L}{R}}}"></span></dd></dl> <p>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 L}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/103168b86f781fe6e9a4a87b8ea1cebe0ad4ede8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.583ex; height:2.176ex;" alt="{\displaystyle L}"></span> is the 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 R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}"></span> is the DC resistance, and the product <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 L}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω</mi> <mi>L</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega L}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dee2d6e0feb9171f650ca14d6e9ad67264a0f1e1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.029ex; height:2.176ex;" alt="{\displaystyle \omega L}"></span> is the inductive reactance </p><p><i>Q</i> increases linearly with frequency if <i>L</i> and <i>R</i> are constant. Although they are constant at low frequencies, the parameters vary with frequency. For example, skin effect, <a href="/wiki/Proximity_effect_(electromagnetism)" title="Proximity effect (electromagnetism)">proximity effect</a>, and core losses increase <i>R</i> with frequency; winding capacitance and variations in <a href="/wiki/Permeability_(electromagnetism)" title="Permeability (electromagnetism)">permeability</a> with frequency affect <i>L</i>. </p><p>At low frequencies and within limits, increasing the number of turns <i>N</i> improves <i>Q</i> because <i>L</i> varies as <i>N</i><sup>2</sup> while <i>R</i> varies linearly with <i>N</i>. Similarly increasing the radius <i>r</i> of an inductor improves (or increases) <i>Q</i> because <i>L</i> varies with <i>r</i><sup>2</sup> while <i>R</i> varies linearly with <i>r</i>. So high <i>Q</i> air core inductors often have large diameters and many turns. Both of those examples assume the diameter of the wire stays the same, so both examples use proportionally more wire. If the total mass of wire is held constant, then there would be no advantage to increasing the number of turns or the radius of the turns because the wire would have to be proportionally thinner. </p><p>Using a high permeability <a href="/wiki/Ferromagnetic" class="mw-redirect" title="Ferromagnetic">ferromagnetic</a> core can greatly increase the inductance for the same amount of copper, so the core can also increase the Q. Cores however also introduce losses that increase with frequency. The core material is chosen for best results for the frequency band. High Q inductors must avoid saturation; one way is by using a (physically larger) air core inductor. At <a href="/wiki/VHF" class="mw-redirect" title="VHF">VHF</a> or higher frequencies an air core is likely to be used. A well designed air core inductor may have a Q of several hundred. </p> <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=Inductor&action=edit&section=10" title="Edit section: Applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:InductorSignalFilter1.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2f/InductorSignalFilter1.png/150px-InductorSignalFilter1.png" decoding="async" width="150" height="54" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2f/InductorSignalFilter1.png/225px-InductorSignalFilter1.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2f/InductorSignalFilter1.png/300px-InductorSignalFilter1.png 2x" data-file-width="369" data-file-height="132" /></a><figcaption>Example of signal filtering. In this configuration, the inductor blocks AC current, while allowing DC current to pass.</figcaption></figure> <figure typeof="mw:File/Thumb"><a href="/wiki/File:InductorSignalFilter2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d7/InductorSignalFilter2.png/150px-InductorSignalFilter2.png" decoding="async" width="150" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d7/InductorSignalFilter2.png/225px-InductorSignalFilter2.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d7/InductorSignalFilter2.png/300px-InductorSignalFilter2.png 2x" data-file-width="372" data-file-height="297" /></a><figcaption>Example of signal filtering. In this configuration, the inductor <a href="/wiki/Decoupling_(electronics)" title="Decoupling (electronics)">decouples</a> DC current, while allowing AC current to pass.</figcaption></figure> <p>Inductors are used extensively in <a href="/wiki/Analog_circuit" class="mw-redirect" title="Analog circuit">analog circuits</a> and signal processing. Applications range from the use of large inductors in power supplies, which in conjunction with filter <a href="/wiki/Capacitor" title="Capacitor">capacitors</a> remove <a href="/wiki/Ripple_(electrical)" title="Ripple (electrical)">ripple</a> which is a multiple of the mains frequency (or the switching frequency for switched-mode power supplies) from the direct current output, to the small inductance of the <a href="/wiki/Ferrite_bead" title="Ferrite bead">ferrite bead</a> or <a href="/wiki/Torus" title="Torus">torus</a> installed around a cable to prevent <a href="/wiki/Radio_frequency_interference" class="mw-redirect" title="Radio frequency interference">radio frequency interference</a> from being transmitted down the wire. </p><p>Inductors are used as the energy storage device in many <a href="/wiki/Switched-mode_power_supply" title="Switched-mode power supply">switched-mode power supplies</a> to produce DC current. The inductor supplies energy to the circuit to keep current flowing during the "off" switching periods and enables topographies where the output voltage is higher than the input voltage. </p><p>A <a href="/wiki/Tuned_circuit" class="mw-redirect" title="Tuned circuit">tuned circuit</a>, consisting of an inductor connected to a <a href="/wiki/Capacitor" title="Capacitor">capacitor</a>, acts as a <a href="/wiki/Electrical_resonance" title="Electrical resonance">resonator</a> for oscillating current. Tuned circuits are widely used in <a href="/wiki/Radio_frequency" title="Radio frequency">radio frequency</a> equipment such as radio transmitters and receivers, as narrow <a href="/wiki/Bandpass_filter" class="mw-redirect" title="Bandpass filter">bandpass filters</a> to select a single frequency from a composite signal, and in <a href="/wiki/Electronic_oscillator" title="Electronic oscillator">electronic oscillators</a> to generate sinusoidal signals. </p><p>Two (or more) inductors in proximity that have coupled magnetic flux (<a href="/wiki/Mutual_inductance" class="mw-redirect" title="Mutual inductance">mutual inductance</a>) form a <a href="/wiki/Transformer" title="Transformer">transformer</a>, which is a fundamental component of every <a href="/wiki/Electric_utility" title="Electric utility">electric utility</a> <a href="/wiki/Power_grid" class="mw-redirect" title="Power grid">power grid</a>. The efficiency of a transformer may decrease as the frequency increases due to eddy currents in the core material and skin effect on the windings. The size of the core can be decreased at higher frequencies. For this reason, aircraft use 400 hertz alternating current rather than the usual 50 or 60 hertz, allowing a great saving in weight from the use of smaller transformers.<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> Transformers enable switched-mode power supplies that <a href="/wiki/Galvanic_isolation" title="Galvanic isolation">galvanically isolate</a> the output from the input. </p><p>Inductors are also employed in <a href="/wiki/Electrical_transmission" class="mw-redirect" title="Electrical transmission">electrical transmission</a> systems, where they are used to limit switching currents and <a href="/wiki/Fault_current" class="mw-redirect" title="Fault current">fault currents</a>. In this field, they are more commonly referred to as reactors. </p><p>Inductors have parasitic effects which cause them to depart from ideal behavior. They create and suffer from <a href="/wiki/Electromagnetic_interference" title="Electromagnetic interference">electromagnetic interference</a> (EMI). Their physical size prevents them from being integrated on semiconductor chips. So the use of inductors is declining in modern electronic devices, particularly compact portable devices. Real inductors are increasingly being replaced by active circuits such as the <a href="/wiki/Gyrator" title="Gyrator">gyrator</a> which can <a href="/wiki/Simulated_inductor" class="mw-redirect" title="Simulated inductor">synthesize inductance</a> using capacitors. </p> <div style="clear:both;" class=""></div> <div class="mw-heading mw-heading2"><h2 id="Inductor_construction">Inductor construction</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductor&action=edit&section=11" title="Edit section: Inductor construction"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1237032888/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 img{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .tmulti .multiimageinner img{background-color:white}}</style><div class="thumb tmulti tright"><div class="thumbinner multiimageinner" style="width:543px;max-width:543px"><div class="trow"><div class="tsingle" style="width:128px;max-width:128px"><div class="thumbimage" style="height:148px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/File:Common_mode_choke_2A_with_20mH_inductance.jpg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Common_mode_choke_2A_with_20mH_inductance.jpg/126px-Common_mode_choke_2A_with_20mH_inductance.jpg" decoding="async" width="126" height="149" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Common_mode_choke_2A_with_20mH_inductance.jpg/189px-Common_mode_choke_2A_with_20mH_inductance.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Common_mode_choke_2A_with_20mH_inductance.jpg/252px-Common_mode_choke_2A_with_20mH_inductance.jpg 2x" data-file-width="760" data-file-height="899" /></a></span></div><div class="thumbcaption">A ferrite core inductor with two 20 mH windings.</div></div><div class="tsingle" style="width:209px;max-width:209px"><div class="thumbimage" style="height:148px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/File:Ferrite_bead_no_shell.jpg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/58/Ferrite_bead_no_shell.jpg/207px-Ferrite_bead_no_shell.jpg" decoding="async" width="207" height="149" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/58/Ferrite_bead_no_shell.jpg/311px-Ferrite_bead_no_shell.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/58/Ferrite_bead_no_shell.jpg/414px-Ferrite_bead_no_shell.jpg 2x" data-file-width="982" data-file-height="706" /></a></span></div><div class="thumbcaption">A <a href="/wiki/Ferrite_bead" title="Ferrite bead">ferrite "bead"</a> <a href="/wiki/Choke_(electronics)" title="Choke (electronics)">choke</a>, consisting of an encircling <a href="/wiki/Ferrite_(magnet)" title="Ferrite (magnet)">ferrite</a> cylinder, suppresses electronic noise in a computer power cord.</div></div><div class="tsingle" style="width:200px;max-width:200px"><div class="thumbimage" style="height:148px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/File:Drosselspule_im_Umspannwerk_Bisamberg.jpg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Drosselspule_im_Umspannwerk_Bisamberg.jpg/198px-Drosselspule_im_Umspannwerk_Bisamberg.jpg" decoding="async" width="198" height="149" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Drosselspule_im_Umspannwerk_Bisamberg.jpg/297px-Drosselspule_im_Umspannwerk_Bisamberg.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Drosselspule_im_Umspannwerk_Bisamberg.jpg/396px-Drosselspule_im_Umspannwerk_Bisamberg.jpg 2x" data-file-width="1600" data-file-height="1200" /></a></span></div><div class="thumbcaption">Large 50 <a href="/wiki/Volt-ampere_reactive" class="mw-redirect" title="Volt-ampere reactive">Mvar</a> <a href="/wiki/Three-phase_electric_power" title="Three-phase electric power">three-phase</a> iron-core loading inductor at a utility substation</div></div></div></div></div> <p>An inductor usually consists of a coil of conducting material, typically insulated <a href="/wiki/Copper_wire_and_cable" class="mw-redirect" title="Copper wire and cable">copper wire</a>, wrapped around a <a href="/wiki/Magnetic_core" title="Magnetic core">core</a> either of plastic (to create an air-core inductor) or of a <a href="/wiki/Ferromagnetic" class="mw-redirect" title="Ferromagnetic">ferromagnetic</a> (or <a href="/wiki/Ferrimagnetism" title="Ferrimagnetism">ferrimagnetic</a>) material; the latter is called an "iron core" inductor. The high <a href="/wiki/Permeability_(electromagnetism)" title="Permeability (electromagnetism)">permeability</a> of the ferromagnetic core increases the magnetic field and confines it closely to the inductor, thereby increasing the inductance. Low frequency inductors are constructed like transformers, with cores of <a href="/wiki/Electrical_steel" title="Electrical steel">electrical steel</a> <a href="/wiki/Laminate" class="mw-redirect" title="Laminate">laminated</a> to prevent <a href="/wiki/Eddy_current" title="Eddy current">eddy currents</a>. 'Soft' <a href="/wiki/Ferrite_(magnet)" title="Ferrite (magnet)">ferrites</a> are widely used for cores above <a href="/wiki/Audio_frequency" title="Audio frequency">audio frequencies</a>, since they do not cause the large energy losses at high frequencies that ordinary iron alloys do. Inductors come in many shapes. Some inductors have an adjustable core, which enables changing of the inductance. Inductors used to block very high frequencies are sometimes made by stringing a ferrite bead on a wire. </p><p>Small inductors can be etched directly onto a <a href="/wiki/Printed_circuit_board" title="Printed circuit board">printed circuit board</a> by laying out the trace in a <a href="/wiki/Spiral" title="Spiral">spiral</a> pattern. Some such planar inductors use a <a href="/wiki/Magnetic_core#Planar_core" title="Magnetic core">planar core</a>. Small value inductors can also be built on <a href="/wiki/Integrated_circuit" title="Integrated circuit">integrated circuits</a> using the same processes that are used to make <a href="/wiki/Interconnects_(integrated_circuits)" class="mw-redirect" title="Interconnects (integrated circuits)">interconnects</a>. <a href="/wiki/Aluminium_interconnect" class="mw-redirect" title="Aluminium interconnect">Aluminium interconnect</a> is typically used, laid out in a spiral coil pattern. However, the small dimensions limit the inductance, and it is far more common to use a circuit called a <i><a href="/wiki/Gyrator" title="Gyrator">gyrator</a></i> that uses a <a href="/wiki/Capacitor" title="Capacitor">capacitor</a> and active components to behave similarly to an inductor. Regardless of the design, because of the low inductances and low power dissipation on-die inductors allow, they are currently only commercially used for high frequency RF circuits. </p> <div style="clear:both;" class=""></div> <div class="mw-heading mw-heading3"><h3 id="Shielded_inductors">Shielded inductors</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductor&action=edit&section=12" title="Edit section: Shielded inductors"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Inductors used in power regulation systems, lighting, and other systems that require low-noise operating conditions, are often partially or fully shielded.<sup id="cite_ref-Ott_14-0" class="reference"><a href="#cite_note-Ott-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Violette_15-0" class="reference"><a href="#cite_note-Violette-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> In <a href="/wiki/Telecommunication_circuit" title="Telecommunication circuit">telecommunication circuits</a> employing induction coils and repeating transformers shielding of inductors in close proximity reduces circuit cross-talk. </p> <div class="mw-heading mw-heading2"><h2 id="Types">Types</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductor&action=edit&section=13" title="Edit section: Types"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Air-core_inductor">Air-core inductor</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductor&action=edit&section=14" title="Edit section: Air-core inductor"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237032888/mw-parser-output/.tmulti"><div class="thumb tmulti tright"><div class="thumbinner multiimageinner" style="width:368px;max-width:368px"><div class="trow"><div class="tsingle" style="width:222px;max-width:222px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Radio_transmitter_tank_coil.png" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/Radio_transmitter_tank_coil.png/220px-Radio_transmitter_tank_coil.png" decoding="async" width="220" height="207" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/Radio_transmitter_tank_coil.png/330px-Radio_transmitter_tank_coil.png 1.5x, //upload.wikimedia.org/wikipedia/commons/2/24/Radio_transmitter_tank_coil.png 2x" data-file-width="409" data-file-height="384" /></a></span></div><div class="thumbcaption">High Q tank coil in <a href="/wiki/Tuned_circuit" class="mw-redirect" title="Tuned circuit">tuned circuit</a> of radio transmitter</div></div><div class="tsingle" style="width:142px;max-width:142px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Antenna_tuning_coil_-_station_WOR.jpg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Antenna_tuning_coil_-_station_WOR.jpg/140px-Antenna_tuning_coil_-_station_WOR.jpg" decoding="async" width="140" height="210" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Antenna_tuning_coil_-_station_WOR.jpg/210px-Antenna_tuning_coil_-_station_WOR.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/c/c8/Antenna_tuning_coil_-_station_WOR.jpg 2x" data-file-width="277" data-file-height="415" /></a></span></div><div class="thumbcaption">An <a href="/wiki/Antenna_tuner" title="Antenna tuner">antenna tuning</a> coil at an AM radio station.</div></div></div><div class="trow" style="display:flex"><div class="thumbcaption">These coils illustrate high power <a href="/wiki/Q_factor" title="Q factor">high Q</a> construction: single layer winding with turns spaced apart to reduce <a href="/wiki/Proximity_effect_(electromagnetism)" title="Proximity effect (electromagnetism)">proximity effect</a> losses, made of silver-plated wire or tubing to reduce <a href="/wiki/Skin_effect" title="Skin effect">skin effect</a> losses, supported by narrow insulating strips to reduce <a href="/wiki/Dielectric_losses" class="mw-redirect" title="Dielectric losses">dielectric losses</a></div></div></div></div> <p>The term <i>air core coil</i> describes an inductor that does not use a <a href="/wiki/Magnetic_core" title="Magnetic core">magnetic core</a> made of a ferromagnetic material. The term refers to coils wound on plastic, ceramic, or other nonmagnetic forms, as well as those that have only air inside the windings. Air core coils have lower inductance than ferromagnetic core coils, but are often used at high frequencies because they are free from energy losses called <a href="/wiki/Core_loss" class="mw-redirect" title="Core loss">core losses</a> that occur in ferromagnetic cores, which increase with frequency. A side effect that can occur in air core coils in which the winding is not rigidly supported on a form is 'microphony': mechanical vibration of the windings can cause variations in the inductance. </p> <div class="mw-heading mw-heading4"><h4 id="Radio-frequency_inductor">Radio-frequency inductor</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductor&action=edit&section=15" title="Edit section: Radio-frequency inductor"><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:Hf_spoler_og_transformatorer.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Hf_spoler_og_transformatorer.jpg/330px-Hf_spoler_og_transformatorer.jpg" decoding="async" width="330" height="112" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Hf_spoler_og_transformatorer.jpg/495px-Hf_spoler_og_transformatorer.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Hf_spoler_og_transformatorer.jpg/660px-Hf_spoler_og_transformatorer.jpg 2x" data-file-width="2196" data-file-height="744" /></a><figcaption>Collection of RF inductors, showing techniques to reduce losses. The three top left and the <a href="/wiki/Loop_antenna" title="Loop antenna">ferrite loopstick</a> or rod antenna,<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><sup id="cite_ref-Frost_17-0" class="reference"><a href="#cite_note-Frost-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Poisel_18-0" class="reference"><a href="#cite_note-Poisel-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Yadava_19-0" class="reference"><a href="#cite_note-Yadava-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> bottom, have basket windings.</figcaption></figure> <p>At <a href="/wiki/High_frequency" title="High frequency">high frequencies</a>, particularly <a href="/wiki/Radio_frequency" title="Radio frequency">radio frequencies</a> (RF), inductors have higher resistance and other losses. In addition to causing power loss, in <a href="/wiki/Resonant_circuit" class="mw-redirect" title="Resonant circuit">resonant circuits</a> this can reduce the <a href="/wiki/Q_factor" title="Q factor">Q factor</a> of the circuit, broadening the <a href="/wiki/Bandwidth_(signal_processing)" title="Bandwidth (signal processing)">bandwidth</a>. In RF inductors specialized construction techniques are used to minimize these losses. The losses are due to these effects: </p> <ul><li><b>Skin effect</b>: The resistance of a wire to <a href="/wiki/High_frequency" title="High frequency">high frequency</a> current is higher than its resistance to <a href="/wiki/Direct_current" title="Direct current">direct current</a> because of <a href="/wiki/Skin_effect" title="Skin effect">skin effect</a>.<sup id="cite_ref-Zurek1_20-0" class="reference"><a href="#cite_note-Zurek1-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Kazimierczuk_21-0" class="reference"><a href="#cite_note-Kazimierczuk-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: p.141">: p.141 </span></sup> Due to induced <a href="/wiki/Eddy_current" title="Eddy current">eddy currents</a>, radio frequency alternating current does not penetrate far into the body of a conductor but travels along its surface. For example, at 6 MHz the skin depth of copper wire is about 0.001 inches (25 μm); most of the current is within this depth of the surface. Therefore, in a solid wire, the interior portion of the wire may carry little current, effectively increasing its resistance.</li> <li><b>Proximity effect</b>: Another similar effect that also increases the resistance of the wire at high frequencies is <a href="/wiki/Proximity_effect_(electromagnetism)" title="Proximity effect (electromagnetism)">proximity effect</a>, which occurs in parallel wires that lie close to each other.<sup id="cite_ref-Zurek2_22-0" class="reference"><a href="#cite_note-Zurek2-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Kazimierczuk_21-1" class="reference"><a href="#cite_note-Kazimierczuk-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: p.98">: p.98 </span></sup> The individual magnetic field of adjacent turns induces <a href="/wiki/Eddy_current" title="Eddy current">eddy currents</a> in the wire of the coil, which causes the current density in the conductor to be displaced away from the adjacent surfaces. Like skin effect, this reduces the effective cross-sectional area of the wire conducting current, increasing its resistance.</li> <li><b>Dielectric losses</b>: The high frequency electric field near the conductors in a <a href="/wiki/LC_circuit" title="LC circuit">tank coil</a> can cause the motion of polar molecules in nearby insulating materials, dissipating energy as heat. For this reason, coils used for tuned circuits may be suspended in air, supported by narrow plastic or ceramic strips rather than being wound on coil forms.</li> <li><b>Parasitic capacitance</b>: The capacitance between individual wire turns of the coil, called <a href="/wiki/Parasitic_capacitance" title="Parasitic capacitance">parasitic capacitance</a>, does not cause energy losses but can change the behavior of the coil. Each turn of the coil is at a slightly different potential, so the <a href="/wiki/Electric_field" title="Electric field">electric field</a> between neighboring turns stores charge on the wire, so the coil acts as if it has a capacitor in parallel with it. At a high enough frequency this capacitance can resonate with the inductance of the coil forming a <a href="/wiki/Tuned_circuit" class="mw-redirect" title="Tuned circuit">tuned circuit</a>, causing the coil to become <a href="/wiki/Self-resonant_frequency" class="mw-redirect" title="Self-resonant frequency">self-resonant</a>.</li></ul> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237032888/mw-parser-output/.tmulti"><div class="thumb tmulti tright"><div class="thumbinner multiimageinner" style="width:292px;max-width:292px"><div class="trow"><div class="tsingle" style="width:173px;max-width:173px"><div class="thumbimage" style="height:127px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/File:Spider_coil.jpg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Spider_coil.jpg/171px-Spider_coil.jpg" decoding="async" width="171" height="128" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Spider_coil.jpg/257px-Spider_coil.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Spider_coil.jpg/342px-Spider_coil.jpg 2x" data-file-width="4032" data-file-height="3024" /></a></span></div></div><div class="tsingle" style="width:115px;max-width:115px"><div class="thumbimage" style="height:127px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/File:Kreuzwickelspule.png" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/69/Kreuzwickelspule.png/113px-Kreuzwickelspule.png" decoding="async" width="113" height="128" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/69/Kreuzwickelspule.png/170px-Kreuzwickelspule.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/69/Kreuzwickelspule.png/226px-Kreuzwickelspule.png 2x" data-file-width="514" data-file-height="580" /></a></span></div></div></div><div class="trow" style="display:flex"><div class="thumbcaption"><i>(left)</i> Spiderweb coil <i>(right)</i> Adjustable ferrite slug-tuned RF coil with basketweave winding and litz wire</div></div></div></div> <p>To reduce parasitic capacitance and proximity effect, <a href="/wiki/Q_factor" title="Q factor">high Q</a> RF coils are constructed to avoid having many turns lying close together, parallel to one another. The windings of RF coils are often limited to a single layer, and the turns are spaced apart. To reduce resistance due to skin effect, in high-power inductors such as those used in transmitters the windings are sometimes made of a metal strip or tubing which has a larger surface area, and the surface is silver-plated. </p> <dl><dt>Basket-weave coils</dt> <dd>To reduce proximity effect and parasitic capacitance, multilayer RF coils are wound in patterns in which successive turns are not parallel but crisscrossed at an angle; these are often called <i>honeycomb</i> or <i><a href="/wiki/Basket_winding" title="Basket winding">basket-weave</a></i> coils. These are occasionally wound on a vertical insulating supports with dowels or slots, with the wire weaving in and out through the slots.</dd> <dt>Spiderweb coils</dt> <dd>Another construction technique with similar advantages is flat spiral coils. These are often wound on a flat insulating support with radial spokes or slots, with the wire weaving in and out through the slots; these are called <i>spiderweb</i> coils. The form has an odd number of slots, so successive turns of the spiral lie on opposite sides of the form, increasing separation.</dd> <dt>Litz wire</dt> <dd>To reduce skin effect losses, some coils are wound with a special type of radio frequency wire called <a href="/wiki/Litz_wire" title="Litz wire">litz wire</a>. Instead of a single solid conductor, litz wire consists of a number of smaller wire strands that carry the current. Unlike ordinary <a href="/wiki/Stranded_wire" class="mw-redirect" title="Stranded wire">stranded wire</a>, the strands are insulated from each other, to prevent skin effect from forcing the current to the surface, and are twisted or braided together. The twist pattern ensures that each wire strand spends the same amount of its length on the outside of the wire bundle, so skin effect distributes the current equally between the strands, resulting in a larger cross-sectional conduction area than an equivalent single wire.</dd></dl> <dl><dt>Axial Inductor</dt></dl> <p>Small inductors for low current and low power are made in molded cases resembling resistors. These may be either plain (phenolic) core or ferrite core. An ohmmeter readily distinguishes them from similar-sized resistors by showing the low resistance of the inductor. </p> <div class="mw-heading mw-heading3"><h3 id="Ferromagnetic-core_inductor">Ferromagnetic-core inductor</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductor&action=edit&section=16" title="Edit section: Ferromagnetic-core inductor"><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/Magnetic_core" title="Magnetic core">Magnetic core</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Aplikimi_i_feriteve.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/27/Aplikimi_i_feriteve.png/220px-Aplikimi_i_feriteve.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/27/Aplikimi_i_feriteve.png/330px-Aplikimi_i_feriteve.png 1.5x, //upload.wikimedia.org/wikipedia/commons/2/27/Aplikimi_i_feriteve.png 2x" data-file-width="392" data-file-height="392" /></a><figcaption>A variety of types of ferrite core inductors and transformers</figcaption></figure> <p>Ferromagnetic-core or iron-core inductors use a magnetic core made of a <a href="/wiki/Ferromagnetic" class="mw-redirect" title="Ferromagnetic">ferromagnetic</a> or <a href="/wiki/Ferrimagnetic" class="mw-redirect" title="Ferrimagnetic">ferrimagnetic</a> material such as iron or <a href="/wiki/Ferrite_(magnet)" title="Ferrite (magnet)">ferrite</a> to increase the inductance. A magnetic core can increase the inductance of a coil by a factor of several thousand, by increasing the magnetic field due to its higher <a href="/wiki/Magnetic_permeability" class="mw-redirect" title="Magnetic permeability">magnetic permeability</a>. However the magnetic properties of the core material cause several side effects which alter the behavior of the inductor and require special construction: </p> <pre> <style data-mw-deduplicate="TemplateStyles:r1228772891">.mw-parser-output .glossary dt{margin-top:0.4em}.mw-parser-output .glossary dt+dt{margin-top:-0.2em}.mw-parser-output .glossary .templatequote{margin-top:0;margin-bottom:-0.5em}</style> </pre> <dl class="glossary"> <dt id="core_losses"><dfn><a href="/wiki/Core_loss" class="mw-redirect" title="Core loss">Core losses</a></dfn></dt><dd>A time-varying current in a ferromagnetic inductor, which causes a time-varying magnetic field in its core, causes energy losses in the core material that are dissipated as heat, due to two processes:<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1228772891"> <dl class="glossary"> <dt id="eddy_currents"><dfn><a href="/wiki/Eddy_current" title="Eddy current">Eddy currents</a></dfn></dt><dd>From <a href="/wiki/Faraday%27s_law_of_induction" title="Faraday's law of induction">Faraday's law of induction</a>, the changing magnetic field can induce circulating loops of electric current in the conductive metal core. The energy in these currents is dissipated as heat in the <a href="/wiki/Electrical_resistance" class="mw-redirect" title="Electrical resistance">resistance</a> of the core material. The amount of energy lost increases with the area inside the loop of current.</dd> <dt id="hysteresis"><dfn><a href="/wiki/Hysteresis_loop" class="mw-redirect" title="Hysteresis loop">Hysteresis</a></dfn></dt><dd>Changing or reversing the magnetic field in the core also causes losses due to the motion of the tiny <a href="/wiki/Magnetic_domain" title="Magnetic domain">magnetic domains</a> it is composed of. The energy loss is proportional to the area of the hysteresis loop in the BH graph of the core material. Materials with low <a href="/wiki/Coercivity" title="Coercivity">coercivity</a> have narrow hysteresis loops and so low hysteresis losses.</dd> </dl> Core loss is non-linear with respect to both frequency of magnetic fluctuation and magnetic flux density. Frequency of magnetic fluctuation is the frequency of AC current in the electric circuit; magnetic flux density corresponds to current in the electric circuit. Magnetic fluctuation gives rise to hysteresis, and magnetic flux density causes eddy currents in the core. These nonlinearities are distinguished from the threshold nonlinearity of saturation. Core loss can be approximately modeled with <a href="/wiki/Steinmetz%27s_equation" title="Steinmetz's equation">Steinmetz's equation</a>. At low frequencies and over limited frequency spans (maybe a factor of 10), core loss may be treated as a linear function of frequency with minimal error. However, even in the audio range, nonlinear effects of magnetic core inductors are noticeable and of concern. </dd> <dt id="saturation"><dfn>Saturation</dfn></dt><dd>If the current through a magnetic core coil is high enough that the core <a href="/wiki/Saturation_(magnetic)" title="Saturation (magnetic)">saturates</a>, the inductance will fall and current will rise dramatically. This is a nonlinear threshold phenomenon and results in distortion of the signal. For example, <a href="/wiki/Audio_signal" title="Audio signal">audio signals</a> can suffer <a href="/wiki/Intermodulation_distortion" class="mw-redirect" title="Intermodulation distortion">intermodulation distortion</a> in saturated inductors. To prevent this, in <a href="/wiki/Linear_circuit" title="Linear circuit">linear circuits</a> the current through iron core inductors must be limited below the saturation level. Some laminated cores have a narrow air gap in them for this purpose, and powdered iron cores have a distributed air gap. This allows higher levels of magnetic flux and thus higher currents through the inductor before it saturates.<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup></dd> <dt id="curie_point_demagnetization"><dfn>Curie point demagnetization</dfn></dt><dd>If the temperature of a ferromagnetic or ferrimagnetic core rises to a specified level, the magnetic domains dissociate, and the material becomes paramagnetic, no longer able to support magnetic flux. The inductance falls and current rises dramatically, similarly to what happens during saturation. The effect is reversible: When the temperature falls below the Curie point, magnetic flux resulting from current in the electric circuit will realign the magnetic domains of the core and its magnetic flux will be restored. The Curie point of ferromagnetic materials (iron alloys) is quite high; iron is highest at 770<span class="nowrap"> </span>°C. However, for some ferrimagnetic materials (ceramic iron compounds – <a href="/wiki/Ferrite_(magnet)" title="Ferrite (magnet)">ferrites</a>) the Curie point can be close to ambient temperatures (below 100<span class="nowrap"> </span>°C).<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. (February 2018)">citation needed</span></a></i>]</sup> </dd> </dl> <div class="mw-heading mw-heading4"><h4 id="Laminated-core_inductor">Laminated-core inductor</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductor&action=edit&section=17" title="Edit section: Laminated-core inductor"><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:Vorschaltdrossel_Kvg.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Vorschaltdrossel_Kvg.jpg/180px-Vorschaltdrossel_Kvg.jpg" decoding="async" width="180" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Vorschaltdrossel_Kvg.jpg/270px-Vorschaltdrossel_Kvg.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Vorschaltdrossel_Kvg.jpg/360px-Vorschaltdrossel_Kvg.jpg 2x" data-file-width="669" data-file-height="744" /></a><figcaption>Laminated iron core <a href="/wiki/Ballast_(electrical)" class="mw-redirect" title="Ballast (electrical)">ballast</a> inductor for a <a href="/wiki/Metal_halide_lamp" class="mw-redirect" title="Metal halide lamp">metal halide lamp</a> </figcaption></figure> <p>Low-frequency inductors are often made with <a href="/wiki/Laminated_core" class="mw-redirect" title="Laminated core">laminated cores</a> to prevent eddy currents, using construction similar to <a href="/wiki/Transformer" title="Transformer">transformers</a>. The core is made of stacks of thin steel sheets or <a href="/wiki/Lamination" title="Lamination">laminations</a> oriented parallel to the field, with an insulating coating on the surface. The insulation prevents eddy currents between the sheets, so any remaining currents must be within the cross sectional area of the individual laminations, reducing the area of the loop and thus reducing the energy losses greatly. The laminations are made of low-conductivity <a href="/wiki/Silicon_steel" class="mw-redirect" title="Silicon steel">silicon steel</a> to further reduce eddy current losses. </p> <div class="mw-heading mw-heading4"><h4 id="Ferrite-core_inductor">Ferrite-core inductor</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductor&action=edit&section=18" title="Edit section: Ferrite-core inductor"><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/Ferrite_core" title="Ferrite core">Ferrite core</a></div> <p>For higher frequencies, inductors are made with cores of ferrite. Ferrite is a ceramic ferrimagnetic material that is nonconductive, so eddy currents cannot flow within it. The formulation of ferrite is xxFe<sub>2</sub>O<sub>4</sub> where xx represents various metals. For inductor cores <a href="/wiki/Soft_ferrite" class="mw-redirect" title="Soft ferrite">soft ferrites</a> are used, which have low coercivity and thus low hysteresis losses. </p> <div class="mw-heading mw-heading4"><h4 id="Powdered-iron-core_inductor">Powdered-iron-core inductor <span class="anchor" id="powdered_iron_anchor"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductor&action=edit&section=19" title="Edit section: Powdered-iron-core inductor"><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/Carbonyl_iron" title="Carbonyl iron">Carbonyl iron</a></div> <p>Another material is powdered iron cemented with a binder. <a href="/wiki/Medium_frequency" title="Medium frequency">Medium frequency</a> equipment almost exclusively uses powdered iron cores, and inductors and transformers built for the lower <a href="/wiki/Shortwave" class="mw-redirect" title="Shortwave">shortwaves</a> are made using either cemented powdered iron or <a href="/wiki/Ferrite_core" title="Ferrite core">ferrites</a>.<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. (September 2022)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading4"><h4 id="Toroidal-core_inductor">Toroidal-core inductor</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductor&action=edit&section=20" title="Edit section: Toroidal-core inductor"><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/Toroidal_inductors_and_transformers" title="Toroidal inductors and transformers">Toroidal inductors and transformers</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:3Com_OfficeConnect_ADSL_Wireless_11g_Firewall_Router_2012-10-28-0869.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/3Com_OfficeConnect_ADSL_Wireless_11g_Firewall_Router_2012-10-28-0869.jpg/220px-3Com_OfficeConnect_ADSL_Wireless_11g_Firewall_Router_2012-10-28-0869.jpg" decoding="async" width="220" height="147" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/3Com_OfficeConnect_ADSL_Wireless_11g_Firewall_Router_2012-10-28-0869.jpg/330px-3Com_OfficeConnect_ADSL_Wireless_11g_Firewall_Router_2012-10-28-0869.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/ca/3Com_OfficeConnect_ADSL_Wireless_11g_Firewall_Router_2012-10-28-0869.jpg/440px-3Com_OfficeConnect_ADSL_Wireless_11g_Firewall_Router_2012-10-28-0869.jpg 2x" data-file-width="4752" data-file-height="3168" /></a><figcaption>Toroidal inductor in the power supply of a wireless router</figcaption></figure> <p>In an inductor wound on a straight rod-shaped core, the <a href="/wiki/Magnetic_field_lines" class="mw-redirect" title="Magnetic field lines">magnetic field lines</a> emerging from one end of the core must pass through the air to re-enter the core at the other end. This reduces the field, because much of the magnetic field path is in air rather than the higher permeability core material and is a source of <a href="/wiki/Electromagnetic_interference" title="Electromagnetic interference">electromagnetic interference</a>. A higher magnetic field and inductance can be achieved by forming the core in a closed <a href="/wiki/Magnetic_circuit" title="Magnetic circuit">magnetic circuit</a>. The magnetic field lines form closed loops within the core without leaving the core material. The shape often used is a <a href="/wiki/Toroid" title="Toroid">toroidal</a> or doughnut-shaped ferrite core. Because of their symmetry, toroidal cores allow a minimum of the magnetic flux to escape outside the core (called <i><a href="/wiki/Leakage_flux" class="mw-redirect" title="Leakage flux">leakage flux</a></i>), so they radiate less electromagnetic interference than other shapes. Toroidal core coils are manufactured of various materials, primarily ferrite, powdered iron and laminated cores.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Variable_inductor">Variable inductor</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductor&action=edit&section=21" title="Edit section: Variable inductor"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237032888/mw-parser-output/.tmulti"><div class="thumb tmulti tright"><div class="thumbinner multiimageinner" style="width:222px;max-width:222px"><div class="trow"><div class="tsingle" style="width:94px;max-width:94px"><div class="thumbimage" style="height:160px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/File:Ferrite_slug_tuned_inductor_with_pot_core.JPG" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/08/Ferrite_slug_tuned_inductor_with_pot_core.JPG/92px-Ferrite_slug_tuned_inductor_with_pot_core.JPG" decoding="async" width="92" height="160" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/08/Ferrite_slug_tuned_inductor_with_pot_core.JPG/138px-Ferrite_slug_tuned_inductor_with_pot_core.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/08/Ferrite_slug_tuned_inductor_with_pot_core.JPG/184px-Ferrite_slug_tuned_inductor_with_pot_core.JPG 2x" data-file-width="798" data-file-height="1389" /></a></span></div></div><div class="tsingle" style="width:124px;max-width:124px"><div class="thumbimage" style="height:160px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/File:Variometer.jpg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9f/Variometer.jpg/122px-Variometer.jpg" decoding="async" width="122" height="161" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9f/Variometer.jpg/183px-Variometer.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9f/Variometer.jpg/244px-Variometer.jpg 2x" data-file-width="360" data-file-height="476" /></a></span></div></div></div><div class="trow" style="display:flex"><div class="thumbcaption"><i>(left)</i> Inductor with a threaded ferrite slug <i>(visible at top)</i> that can be turned to move it into or out of the coil, 4.2 cm high. <i>(right)</i> A variometer used in radio receivers in the 1920s</div></div></div></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Rollspule.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Rollspule.jpg/220px-Rollspule.jpg" decoding="async" width="220" height="141" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Rollspule.jpg/330px-Rollspule.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Rollspule.jpg/440px-Rollspule.jpg 2x" data-file-width="720" data-file-height="460" /></a><figcaption>A "roller coil", an adjustable air-core RF inductor used in the <a href="/wiki/Tuned_circuit" class="mw-redirect" title="Tuned circuit">tuned circuits</a> of radio transmitters. One of the contacts to the coil is made by the small grooved wheel, which rides on the wire. Turning the shaft rotates the coil, moving the contact wheel up or down the coil, allowing more or fewer turns of the coil into the circuit, to change the inductance.</figcaption></figure> <p>Probably the most common type of variable inductor today is one with a moveable ferrite magnetic core, which can be slid or screwed in or out of the coil. Moving the core farther into the coil increases the <a href="/wiki/Permeability_(electromagnetism)" title="Permeability (electromagnetism)">permeability</a>, increasing the magnetic field and the inductance. Many inductors used in radio applications (usually less than 100 MHz) use adjustable cores in order to tune such inductors to their desired value, since manufacturing processes have certain tolerances (inaccuracy). Sometimes such cores for frequencies above 100 MHz are made from highly conductive non-magnetic material such as aluminum.<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> They decrease the inductance because the magnetic field must bypass them. </p><p>Air core inductors can use sliding contacts or multiple taps to increase or decrease the number of turns included in the circuit, to change the inductance. A type much used in the past but mostly obsolete today has a spring contact that can slide along the bare surface of the windings. The disadvantage of this type is that the contact usually <a href="/wiki/Short_circuit" title="Short circuit">short-circuits</a> one or more turns. These turns act like a single-turn short-circuited transformer <a href="/wiki/Secondary_winding" class="mw-redirect" title="Secondary winding">secondary winding</a>; the large currents induced in them cause power losses. </p><p>A type of continuously variable air core inductor is the <i>variometer</i>. This consists of two coils with the same number of turns connected in series, one inside the other. The inner coil is mounted on a shaft so its axis can be turned with respect to the outer coil. When the two coils' axes are collinear, with the magnetic fields pointing in the same direction, the fields add and the inductance is maximum. When the inner coil is turned so its axis is at an angle with the outer, the mutual inductance between them is smaller so the total inductance is less. When the inner coil is turned 180° so the coils are collinear with their magnetic fields opposing, the two fields cancel each other and the inductance is very small. This type has the advantage that it is continuously variable over a wide range. It is used in <a href="/wiki/Antenna_tuner" title="Antenna tuner">antenna tuners</a> and matching circuits to match low frequency transmitters to their antennas. </p><p>Another method to control the inductance without any moving parts requires an additional DC current bias winding which controls the permeability of an easily saturable core material. <i>See</i> <a href="/wiki/Magnetic_amplifier" title="Magnetic amplifier">Magnetic amplifier</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Choke">Choke</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductor&action=edit&section=22" title="Edit section: Choke"><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:Two_inductors_(437342545).jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5d/Two_inductors_%28437342545%29.jpg/220px-Two_inductors_%28437342545%29.jpg" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5d/Two_inductors_%28437342545%29.jpg/330px-Two_inductors_%28437342545%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5d/Two_inductors_%28437342545%29.jpg/440px-Two_inductors_%28437342545%29.jpg 2x" data-file-width="2140" data-file-height="1606" /></a><figcaption>An MF or HF radio choke for tenths of an ampere, and a ferrite bead VHF choke for several amperes.</figcaption></figure> <p>A <a href="/wiki/Choke_(electronics)" title="Choke (electronics)">choke</a> is an inductor designed specifically for blocking high-frequency alternating current (AC) in an electrical circuit, while allowing DC or low-frequency signals to pass. Because the inductor restricts or "chokes" the changes in current, this type of inductor is called a choke. It usually consists of a coil of insulated wire wound on a magnetic core, although some consist of a donut-shaped "bead" of ferrite material strung on a wire. Like other inductors, chokes resist changes in current passing through them increasingly with frequency. The difference between chokes and other inductors is that chokes do not require the high <a href="/wiki/Q_factor" title="Q factor">Q factor</a> construction techniques that are used to reduce the resistance in inductors used in tuned circuits. </p> <div class="mw-heading mw-heading2"><h2 id="Circuit_analysis">Circuit analysis</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductor&action=edit&section=23" title="Edit section: Circuit analysis"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The effect of an inductor in a circuit is to oppose changes in current through it by developing a voltage across it proportional to the rate of change of the current. An ideal inductor would offer no resistance to a constant <a href="/wiki/Direct_current" title="Direct current">direct current</a>; however, only <a href="/wiki/Superconductor" class="mw-redirect" title="Superconductor">superconducting</a> inductors have truly zero <a href="/wiki/Electrical_resistance" class="mw-redirect" title="Electrical resistance">electrical resistance</a>. </p><p>The relationship between the time-varying voltage <i>v</i>(<i>t</i>) across an inductor with inductance <i>L</i> and the time-varying current <i>i</i>(<i>t</i>) passing through it is described by the <a href="/wiki/Differential_equation" title="Differential equation">differential equation</a>: </p> <dl><dd><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(t)=L{\frac {di(t)}{dt}}}"> <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> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>i</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v(t)=L{\frac {di(t)}{dt}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffb499f6125dac585f351653651f4fffcff273c1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:13.961ex; height:5.843ex;" alt="{\displaystyle v(t)=L{\frac {di(t)}{dt}}}"></span></dd></dl> <p>When there is a <a href="/wiki/Sinusoidal" class="mw-redirect" title="Sinusoidal">sinusoidal</a> <a href="/wiki/Alternating_current" title="Alternating current">alternating current</a> (AC) through an inductor, a sinusoidal voltage is induced. The amplitude of the voltage is proportional to the product of the amplitude (<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 I_{P}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{P}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62cf73d06c6f73b7ce35ac8ee4e3bc2042c5384c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.49ex; height:2.509ex;" alt="{\displaystyle I_{P}}"></span>) of the current and the angular frequency (<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>) of the current. </p> <dl><dd><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}i(t)&=I_{\mathrm {P} }\sin(\omega t)\\{\frac {di(t)}{dt}}&=I_{\mathrm {P} }\omega \cos(\omega t)\\v(t)&=LI_{\mathrm {P} }\omega \cos(\omega t)\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> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> </mrow> </mrow> </msub> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ω</mi> <mi>t</mi> <mo stretchy="false">)</mo> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>i</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> </mrow> </mrow> </msub> <mi>ω</mi> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ω</mi> <mi>t</mi> <mo stretchy="false">)</mo> </mtd> </mtr> <mtr> <mtd> <mi>v</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>L</mi> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> </mrow> </mrow> </msub> <mi>ω</mi> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ω</mi> <mi>t</mi> <mo stretchy="false">)</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}i(t)&=I_{\mathrm {P} }\sin(\omega t)\\{\frac {di(t)}{dt}}&=I_{\mathrm {P} }\omega \cos(\omega t)\\v(t)&=LI_{\mathrm {P} }\omega \cos(\omega t)\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d0db1ee0ebc31c355ce8c2cac941f51405164eae" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.505ex; width:22.349ex; height:12.009ex;" alt="{\displaystyle {\begin{aligned}i(t)&=I_{\mathrm {P} }\sin(\omega t)\\{\frac {di(t)}{dt}}&=I_{\mathrm {P} }\omega \cos(\omega t)\\v(t)&=LI_{\mathrm {P} }\omega \cos(\omega t)\end{aligned}}}"></span></dd></dl> <p>In this situation, the <a href="/wiki/Phase_(waves)" title="Phase (waves)">phase</a> of the current lags that of the voltage by π/2 (90°). For sinusoids, as the voltage across the inductor goes to its maximum value, the current goes to zero, and as the voltage across the inductor goes to zero, the current through it goes to its maximum value. </p><p>If an inductor is connected to a direct current source with value <i>I</i> via a resistance <i>R</i> (at least the DCR of the inductor), and then the current source is short-circuited, the differential relationship above shows that the current through the inductor will discharge with an <a href="/wiki/Exponential_decay" title="Exponential decay">exponential decay</a>: </p> <dl><dd><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 i(t)=Ie^{-{\frac {R}{L}}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> <mi>I</mi> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>R</mi> <mi>L</mi> </mfrac> </mrow> <mi>t</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i(t)=Ie^{-{\frac {R}{L}}t}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b1b7b2a2bc09898dc4ed036d5ab8b749d6061c46" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.758ex; height:4.176ex;" alt="{\displaystyle i(t)=Ie^{-{\frac {R}{L}}t}}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Reactance">Reactance</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductor&action=edit&section=24" title="Edit section: Reactance"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The ratio of the peak voltage to the peak current in an inductor energised from an AC source is called the <a href="/wiki/Electrical_reactance" title="Electrical reactance">reactance</a> and is denoted <i>X</i><sub>L</sub>. </p> <dl><dd><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_{\mathrm {L} }={\frac {V_{\mathrm {P} }}{I_{\mathrm {P} }}}={\frac {\omega LI_{\mathrm {P} }}{I_{\mathrm {P} }}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">L</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> </mrow> </mrow> </msub> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> </mrow> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>ω</mi> <mi>L</mi> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> </mrow> </mrow> </msub> </mrow> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> </mrow> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X_{\mathrm {L} }={\frac {V_{\mathrm {P} }}{I_{\mathrm {P} }}}={\frac {\omega LI_{\mathrm {P} }}{I_{\mathrm {P} }}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cce2011564b7715f141b7521c73772c32a721e93" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:19.163ex; height:5.509ex;" alt="{\displaystyle X_{\mathrm {L} }={\frac {V_{\mathrm {P} }}{I_{\mathrm {P} }}}={\frac {\omega LI_{\mathrm {P} }}{I_{\mathrm {P} }}}}"></span></dd></dl> <p>Thus, </p> <dl><dd><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_{\mathrm {L} }=\omega L}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">L</mi> </mrow> </mrow> </msub> <mo>=</mo> <mi>ω</mi> <mi>L</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X_{\mathrm {L} }=\omega L}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45863a8f6d55e5a89d7c7ae8c3225f28bd71de95" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.311ex; height:2.509ex;" alt="{\displaystyle X_{\mathrm {L} }=\omega L}"></span></dd></dl> <p>where <i>ω</i> is the <a href="/wiki/Angular_frequency" title="Angular frequency">angular frequency</a>. </p><p>Reactance is measured in ohms but referred to as <i>impedance</i> rather than resistance; energy is stored in the magnetic field as current rises and discharged as current falls. Inductive reactance is proportional to frequency. At low frequency the reactance falls; at DC, the inductor behaves as a short circuit. As frequency increases the reactance increases and at a sufficiently high frequency the reactance approaches that of an open circuit. </p> <div class="mw-heading mw-heading3"><h3 id="Corner_frequency">Corner frequency</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductor&action=edit&section=25" title="Edit section: Corner frequency"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In filtering applications, with respect to a particular load impedance, an inductor has a <a href="/wiki/Corner_frequency" class="mw-redirect" title="Corner frequency">corner frequency</a> defined as: </p> <dl><dd><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 f_{\mathrm {3\,dB} }={\frac {R}{2\pi L}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> <mspace width="thinmathspace" /> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>R</mi> <mrow> <mn>2</mn> <mi>π</mi> <mi>L</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f_{\mathrm {3\,dB} }={\frac {R}{2\pi L}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8b7ee2e16edd33e8f5b4f7f78bd035b3ff932cab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:12.67ex; height:5.176ex;" alt="{\displaystyle f_{\mathrm {3\,dB} }={\frac {R}{2\pi L}}}"></span></dd></dl> <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=Inductor&action=edit&section=26" 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 inductor with no initial current is represented in the <i>s</i> domain by: </p> <dl><dd><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 Z(s)=Ls\,}"> <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> <mi>L</mi> <mi>s</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z(s)=Ls\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ba93fceaa2e60b2bb34ba24ac8f92fadbf5039af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.739ex; height:2.843ex;" alt="{\displaystyle Z(s)=Ls\,}"></span></dd></dl> <p>where </p> <dl><dd><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 L}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/103168b86f781fe6e9a4a87b8ea1cebe0ad4ede8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.583ex; height:2.176ex;" alt="{\displaystyle L}"></span></i> is the inductance, and</dd> <dd><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 s}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>s</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01d131dfd7673938b947072a13a9744fe997e632" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:1.676ex;" alt="{\displaystyle s}"></span></i> is the complex frequency.</dd></dl><p> If the inductor does have initial current, it can be represented by: </p><div><ul><li>adding a voltage source in series with the inductor, having the value: <dl><dd><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 LI_{0}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle LI_{0}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e0787fc430e1eb057592bff3baf5f190c099f87d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.047ex; height:2.509ex;" alt="{\displaystyle LI_{0}\,}"></span></dd></dl> <p>where </p> <dl><dd><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 L}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/103168b86f781fe6e9a4a87b8ea1cebe0ad4ede8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.583ex; height:2.176ex;" alt="{\displaystyle L}"></span></i> is the inductance, and</dd> <dd><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 I_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/893d08e90ea73781dc133414d661529d0651ca80" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.077ex; height:2.509ex;" alt="{\displaystyle I_{0}}"></span></i> is the initial current in the inductor.</dd></dl> (The source should have a polarity that is aligned with the initial current.)</li><li>or by adding a current source in parallel with the inductor, having the value: <dl><dd><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 {\frac {I_{0}}{s}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mi>s</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {I_{0}}{s}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8e144587b406e76766bdf46f4401ae624f4032ad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:2.913ex; height:5.343ex;" alt="{\displaystyle {\frac {I_{0}}{s}}}"></span></dd></dl> where <dl><dd><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 I_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/893d08e90ea73781dc133414d661529d0651ca80" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.077ex; height:2.509ex;" alt="{\displaystyle I_{0}}"></span></i> is the initial current in the inductor.</dd> <dd><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 s}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>s</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01d131dfd7673938b947072a13a9744fe997e632" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:1.676ex;" alt="{\displaystyle s}"></span></i> is the complex frequency.</dd></dl></li></ul></div> <div class="mw-heading mw-heading3"><h3 id="Inductor_networks">Inductor networks</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductor&action=edit&section=27" title="Edit section: Inductor networks"><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/Series_and_parallel_circuits" title="Series and parallel circuits">Series and parallel circuits</a></div> <p>Inductors in a parallel configuration each have the same potential difference (voltage). To find their total equivalent inductance (<i>L</i><sub>eq</sub>): </p> <dl><dd><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:Inductors_in_parallel.svg" class="mw-file-description" title="A diagram of several inductors, side by side, both leads of each connected to the same wires"><img alt="A diagram of several inductors, side by side, both leads of each connected to the same wires" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e8/Inductors_in_parallel.svg/230px-Inductors_in_parallel.svg.png" decoding="async" width="230" height="110" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e8/Inductors_in_parallel.svg/345px-Inductors_in_parallel.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e8/Inductors_in_parallel.svg/460px-Inductors_in_parallel.svg.png 2x" data-file-width="230" data-file-height="110" /></a></span></dd></dl> <dl><dd><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_{\mathrm {eq} }=\left(\sum _{i=1}^{n}{1 \over L_{i}}\right)^{-1}=\left({1 \over L_{1}}+{1 \over L_{2}}+\dots +{1 \over L_{n}}\right)^{-1}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>L</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>L</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>L</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>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mfrac> </mrow> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>L</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> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{\mathrm {eq} }=\left(\sum _{i=1}^{n}{1 \over L_{i}}\right)^{-1}=\left({1 \over L_{1}}+{1 \over L_{2}}+\dots +{1 \over L_{n}}\right)^{-1}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7540a2f87b6e9cf92db3c83fddd740e1d7a48a52" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:50.825ex; height:8.009ex;" alt="{\displaystyle L_{\mathrm {eq} }=\left(\sum _{i=1}^{n}{1 \over L_{i}}\right)^{-1}=\left({1 \over L_{1}}+{1 \over L_{2}}+\dots +{1 \over L_{n}}\right)^{-1}.}"></span></dd></dl> <p>The current through inductors in series stays the same, but the voltage across each inductor can be different. The sum of the potential differences (voltage) is equal to the total voltage. To find their total inductance: </p> <dl><dd><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:Inductors_in_series.svg" class="mw-file-description" title="A diagram of several inductors, connected end to end, with the same amount of current going through each"><img alt="A diagram of several inductors, connected end to end, with the same amount of current going through each" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Inductors_in_series.svg/937px-Inductors_in_series.svg.png" decoding="async" width="937" height="208" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Inductors_in_series.svg/1406px-Inductors_in_series.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Inductors_in_series.svg/1874px-Inductors_in_series.svg.png 2x" data-file-width="937" data-file-height="208" /></a></span></dd></dl> <dl><dd><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_{\mathrm {eq} }=\sum _{i=1}^{n}L_{i}=L_{1}+L_{2}+\cdots +L_{n}.\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>L</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>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>.</mo> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{\mathrm {eq} }=\sum _{i=1}^{n}L_{i}=L_{1}+L_{2}+\cdots +L_{n}.\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/50ff7eff6cc9352a10e7bc8ff920d24dfe245feb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; margin-right: -0.387ex; width:36.1ex; height:6.843ex;" alt="{\displaystyle L_{\mathrm {eq} }=\sum _{i=1}^{n}L_{i}=L_{1}+L_{2}+\cdots +L_{n}.\,\!}"></span></dd></dl> <p>These simple relationships hold true only when there is no mutual coupling of magnetic fields between individual inductors. </p> <div class="mw-heading mw-heading4"><h4 id="Mutual_inductance">Mutual inductance</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductor&action=edit&section=28" title="Edit section: Mutual inductance"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Mutual inductance occurs when the magnetic field of an inductor induces a magnetic field in an adjacent inductor. Mutual induction is the basis of transformer construction. </p> <dl><dd><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 M={\sqrt {L_{1}L_{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M={\sqrt {L_{1}L_{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fab4dff88ad4e405f0f96eb98f8ccba5eecb48e9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:13.139ex; height:3.343ex;" alt="{\displaystyle M={\sqrt {L_{1}L_{2}}}}"></span></dd></dl> <p>where M is the maximum mutual inductance possible between 2 inductors and L<sub>1</sub> and L<sub>2</sub> are the two inductors. In general </p> <dl><dd><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 M\leq {\sqrt {L_{1}L_{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> <mo>≤</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M\leq {\sqrt {L_{1}L_{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a8a1274caa50d6d86aa86103636ae2910d189ca9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:13.139ex; height:3.343ex;" alt="{\displaystyle M\leq {\sqrt {L_{1}L_{2}}}}"></span></dd></dl> <p>as only a fraction of self flux is linked with the other. This fraction is called "Coefficient of flux linkage (K)" or "Coefficient of coupling". </p> <dl><dd><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 M=K{\sqrt {L_{1}L_{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> <mo>=</mo> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M=K{\sqrt {L_{1}L_{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eb62fb4f4a5014a6262e3ce5feea7c4e49c0b915" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:15.205ex; height:3.343ex;" alt="{\displaystyle M=K{\sqrt {L_{1}L_{2}}}}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Inductance_formulas">Inductance formulas</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductor&action=edit&section=29" title="Edit section: Inductance formulas"><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/Inductance#Self-inductance_of_thin_wire_shapes" title="Inductance">Inductance § Self-inductance of thin wire shapes</a></div> <p>The table below lists some common simplified formulas for calculating the approximate inductance of several inductor constructions. </p> <table class="wikitable"> <tbody><tr> <th>Construction </th> <th>Formula </th> <th>Notes </th></tr> <tr> <th>Cylindrical air-core coil<sup id="cite_ref-Nagaoka_26-0" class="reference"><a href="#cite_note-Nagaoka-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> </th> <td><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=\mu _{0}KN^{2}{\frac {A}{\ell }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mo>=</mo> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mi>K</mi> <msup> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>A</mi> <mi>ℓ</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L=\mu _{0}KN^{2}{\frac {A}{\ell }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47c4eb5c895d1f694e2b80f09eb870b1b755ffaa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:14.96ex; height:5.509ex;" alt="{\displaystyle L=\mu _{0}KN^{2}{\frac {A}{\ell }}}"></span> <ul><li><i>L</i> = inductance in <a href="/wiki/Henry_(unit)" title="Henry (unit)">henries</a> (H)</li> <li><i>μ<sub>0</sub></i> = <a href="/wiki/Permeability_of_free_space" class="mw-redirect" title="Permeability of free space">permeability of free space</a> = 4<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 \pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9be4ba0bb8df3af72e90a0535fabcc17431e540a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.332ex; height:1.676ex;" alt="{\displaystyle \pi }"></span></i> × 10<sup>−7</sup> H/m</li> <li><i>K</i> = Nagaoka coefficient<sup id="cite_ref-Nagaoka_26-1" class="reference"><a href="#cite_note-Nagaoka-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>a<span class="cite-bracket">]</span></a></sup></li> <li><i>N</i> = number of turns</li> <li><i>A</i> = area of cross-section of the coil in square metres (m<sup>2</sup>)</li> <li><i>ℓ</i> = length of coil in metres (m)</li></ul> </td> <td><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 K\approx 1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>K</mi> <mo>≈</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K\approx 1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f0af487799451228020feb92785632023548f8fd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.327ex; height:2.176ex;" alt="{\displaystyle K\approx 1}"></span> Calculation of Nagaoka's coefficient (<i>K</i>) is complicated; normally it must be looked up from a table.<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <th rowspan="2">Straight wire conductor<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> </th> <td><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={\frac {\mu _{0}}{2\pi }}\ \ell \left(A\;-\;B\right)+C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mfrac> </mrow> <mtext> </mtext> <mi>ℓ</mi> <mrow> <mo>(</mo> <mrow> <mi>A</mi> <mspace width="thickmathspace" /> <mo>−</mo> <mspace width="thickmathspace" /> <mi>B</mi> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L={\frac {\mu _{0}}{2\pi }}\ \ell \left(A\;-\;B\right)+C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/43d658728e98e8afa0d48d164e3c8693addef4f9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:24.003ex; height:4.843ex;" alt="{\displaystyle L={\frac {\mu _{0}}{2\pi }}\ \ell \left(A\;-\;B\right)+C}"></span>, <p>where: </p> <dl><dd><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}A&=\ln \left({\frac {\ell }{r}}+{\sqrt {\left({\frac {\ell }{r}}\right)^{2}+1}}\right)\\B&={\frac {1}{{\frac {r}{\ell }}+{\sqrt {1+\left({\frac {r}{\ell }}\right)^{2}}}}}\\C&={\text{Im}}\left({\frac {n\rho J_{0}(nr)}{2\pi \omega \mu rJ_{1}(nr)}}\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>A</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>ln</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>ℓ</mi> <mi>r</mi> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>ℓ</mi> <mi>r</mi> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>1</mn> </msqrt> </mrow> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>B</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>r</mi> <mi>ℓ</mi> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>1</mn> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>r</mi> <mi>ℓ</mi> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>C</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>Im</mtext> </mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>n</mi> <mi>ρ</mi> <msub> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>n</mi> <mi>r</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mn>2</mn> <mi>π</mi> <mi>ω</mi> <mi>μ</mi> <mi>r</mi> <msub> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>n</mi> <mi>r</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}A&=\ln \left({\frac {\ell }{r}}+{\sqrt {\left({\frac {\ell }{r}}\right)^{2}+1}}\right)\\B&={\frac {1}{{\frac {r}{\ell }}+{\sqrt {1+\left({\frac {r}{\ell }}\right)^{2}}}}}\\C&={\text{Im}}\left({\frac {n\rho J_{0}(nr)}{2\pi \omega \mu rJ_{1}(nr)}}\right)\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d86b80a103e9addabe53a2d5407058cc47df4e7b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -11.338ex; width:28.649ex; height:23.843ex;" alt="{\displaystyle {\begin{aligned}A&=\ln \left({\frac {\ell }{r}}+{\sqrt {\left({\frac {\ell }{r}}\right)^{2}+1}}\right)\\B&={\frac {1}{{\frac {r}{\ell }}+{\sqrt {1+\left({\frac {r}{\ell }}\right)^{2}}}}}\\C&={\text{Im}}\left({\frac {n\rho J_{0}(nr)}{2\pi \omega \mu rJ_{1}(nr)}}\right)\end{aligned}}}"></span></dd></dl> <ul><li><i>L</i> = inductance</li> <li><i>ℓ</i> = cylinder length</li> <li><i>r</i> = cylinder radius</li> <li><i>μ</i><sub>0</sub> = permeability of free space = 4<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 \pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9be4ba0bb8df3af72e90a0535fabcc17431e540a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.332ex; height:1.676ex;" alt="{\displaystyle \pi }"></span></i> × 10<sup>−7</sup> H/m</li> <li><i>μ</i> = conductor permeability</li> <li><i>ρ</i> = resistivity</li> <li><i>ω</i> = angular frequency</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 n={\sqrt {-i{\frac {\omega \mu }{\rho }}}}=(-1+i){\sqrt {\frac {\omega \mu }{2\rho }}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mo>−</mo> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>ω</mi> <mi>μ</mi> </mrow> <mi>ρ</mi> </mfrac> </mrow> </msqrt> </mrow> <mo>=</mo> <mo stretchy="false">(</mo> <mo>−</mo> <mn>1</mn> <mo>+</mo> <mi>i</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mi>ω</mi> <mi>μ</mi> </mrow> <mrow> <mn>2</mn> <mi>ρ</mi> </mrow> </mfrac> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n={\sqrt {-i{\frac {\omega \mu }{\rho }}}}=(-1+i){\sqrt {\frac {\omega \mu }{2\rho }}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9c5090e1cd04ff35c5130f34eaf97a15b6cb3766" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:30.64ex; height:6.343ex;" alt="{\displaystyle n={\sqrt {-i{\frac {\omega \mu }{\rho }}}}=(-1+i){\sqrt {\frac {\omega \mu }{2\rho }}}}"></span></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 J_{0},J_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle J_{0},J_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/21a8c8219a03b5382d257da6b5979aed8147ef2e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.723ex; height:2.509ex;" alt="{\displaystyle J_{0},J_{1}}"></span> are <a href="/wiki/Bessel_functions_of_the_first_kind" class="mw-redirect" title="Bessel functions of the first kind">Bessel functions</a>.</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 {\tfrac {\mu _{0}}{2\pi }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {\mu _{0}}{2\pi }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7402a7a66adb0f421b14cb88ae68414ece1337a7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:2.659ex; height:3.676ex;" alt="{\displaystyle {\tfrac {\mu _{0}}{2\pi }}}"></span> = 0.2 μH/m, exactly.</li></ul> </td> <td>The term <i>C</i> gives the <i>internal</i> inductance of the wire with skin-effect correction (the imaginary part of the internal impedance of the wire). If ω = 0 (DC) then <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 {\mu }{8\pi }},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>μ</mi> <mrow> <mn>8</mn> <mi>π</mi> </mrow> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C={\frac {\mu }{8\pi }},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3236b5e0314edd1a35f54fc745d86d38862e562a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:8.842ex; height:4.843ex;" alt="{\displaystyle C={\frac {\mu }{8\pi }},}"></span> and as ω approaches ∞, <i>C</i> approaches 0.<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> <p>The term <i>B</i> subtracts rather than adds. </p> </td></tr> <tr> <td><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={\frac {\mu _{0}}{2\pi }}\ \ell \left[\ln \left({\frac {4\ell }{d}}\right)-1\right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mfrac> </mrow> <mtext> </mtext> <mi>ℓ</mi> <mrow> <mo>[</mo> <mrow> <mi>ln</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>4</mn> <mi>ℓ</mi> </mrow> <mi>d</mi> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>−</mo> <mn>1</mn> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L={\frac {\mu _{0}}{2\pi }}\ \ell \left[\ln \left({\frac {4\ell }{d}}\right)-1\right]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/179b5909f1eebeb63ead7ec88aa441c758ce1bd2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:24.736ex; height:6.176ex;" alt="{\displaystyle L={\frac {\mu _{0}}{2\pi }}\ \ell \left[\ln \left({\frac {4\ell }{d}}\right)-1\right]}"></span> (when <span class="nowrap"><i>d</i>² <i>f</i> ≫ 1 mm² MHz</span>) <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 L={\frac {\mu _{0}}{2\pi }}\ \ell \left[\ln \left({\frac {4\ell }{d}}\right)-{\frac {3}{4}}\right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mfrac> </mrow> <mtext> </mtext> <mi>ℓ</mi> <mrow> <mo>[</mo> <mrow> <mi>ln</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>4</mn> <mi>ℓ</mi> </mrow> <mi>d</mi> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> </mrow> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L={\frac {\mu _{0}}{2\pi }}\ \ell \left[\ln \left({\frac {4\ell }{d}}\right)-{\frac {3}{4}}\right]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b966d0d02289adc8a86a9430cf195e36c1686175" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:25.572ex; height:6.176ex;" alt="{\displaystyle L={\frac {\mu _{0}}{2\pi }}\ \ell \left[\ln \left({\frac {4\ell }{d}}\right)-{\frac {3}{4}}\right]}"></span> (when <span class="nowrap"><i>d</i>² <i>f</i> ≪ 1 mm² MHz</span>) </p> <ul><li><i>L</i> = inductance (nH)<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Terman_straight_32-0" class="reference"><a href="#cite_note-Terman_straight-32"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup></li> <li><i>ℓ</i> = length of conductor (mm)</li> <li><i>d</i> = diameter of conductor (mm)</li> <li><i>f</i> = frequency</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 {\tfrac {\mu _{0}}{2\pi }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {\mu _{0}}{2\pi }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7402a7a66adb0f421b14cb88ae68414ece1337a7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:2.659ex; height:3.676ex;" alt="{\displaystyle {\tfrac {\mu _{0}}{2\pi }}}"></span> = 0.2 μH/m, exactly.</li></ul> </td> <td>Requires <i>ℓ</i> > 100 <i>d</i><sup id="cite_ref-Terman_adjust_33-0" class="reference"><a href="#cite_note-Terman_adjust-33"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> <p>For relative permeability <i>μ</i><sub>r</sub> = 1 (e.g., <a href="/wiki/Copper" title="Copper">Cu</a> or <a href="/wiki/Aluminum" class="mw-redirect" title="Aluminum">Al</a>). </p> </td></tr> <tr> <th>Small loop or very short coil<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> </th> <td><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\approx {\frac {\mu _{0}}{2\pi }}N^{2}\pi D\left[\ln \left({\frac {D}{d}}\right)+\left(\ln 8-2\right)\right]+{\sqrt {\frac {\mu _{0}}{2\pi }}}\;{\frac {ND}{d}}{\sqrt {\frac {\mu _{\text{r}}}{2f\sigma }}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mo>≈</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mfrac> </mrow> <msup> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>π</mi> <mi>D</mi> <mrow> <mo>[</mo> <mrow> <mi>ln</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>D</mi> <mi>d</mi> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mrow> <mo>(</mo> <mrow> <mi>ln</mi> <mo>⁡</mo> <mn>8</mn> <mo>−</mo> <mn>2</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mo>]</mo> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mfrac> </msqrt> </mrow> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>N</mi> <mi>D</mi> </mrow> <mi>d</mi> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>r</mtext> </mrow> </msub> <mrow> <mn>2</mn> <mi>f</mi> <mi>σ</mi> </mrow> </mfrac> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L\approx {\frac {\mu _{0}}{2\pi }}N^{2}\pi D\left[\ln \left({\frac {D}{d}}\right)+\left(\ln 8-2\right)\right]+{\sqrt {\frac {\mu _{0}}{2\pi }}}\;{\frac {ND}{d}}{\sqrt {\frac {\mu _{\text{r}}}{2f\sigma }}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2a78c89a4565971b1731a7baae30cdf4ca361364" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:58.444ex; height:6.509ex;" alt="{\displaystyle L\approx {\frac {\mu _{0}}{2\pi }}N^{2}\pi D\left[\ln \left({\frac {D}{d}}\right)+\left(\ln 8-2\right)\right]+{\sqrt {\frac {\mu _{0}}{2\pi }}}\;{\frac {ND}{d}}{\sqrt {\frac {\mu _{\text{r}}}{2f\sigma }}}}"></span> <ul><li><i>L</i> = inductance in the same units as <i>μ</i><sub>0</sub>.</li> <li><i>D</i> = Diameter of the coil (conductor center-to-center)</li> <li><i>d</i> = diameter of the conductor</li> <li><i>N</i> = number of turns</li> <li><i>f</i> = operating frequency (regular <i>f</i>, not <i>ω</i>)</li> <li><i>σ</i> = specific conductivity of the coil conductor</li> <li><i>μ</i><sub>r</sub> = relative permeability of the conductor</li> <li>Total conductor length <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 \ell _{\text{c}}\approx N\pi D}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ℓ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>c</mtext> </mrow> </msub> <mo>≈</mo> <mi>N</mi> <mi>π</mi> <mi>D</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ell _{\text{c}}\approx N\pi D}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/270a9cae710c089b51f8b26f9188abe28ea59381" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.35ex; height:2.509ex;" alt="{\displaystyle \ell _{\text{c}}\approx N\pi D}"></span> should be roughly <style data-mw-deduplicate="TemplateStyles:r1154941027">.mw-parser-output .frac{white-space:nowrap}.mw-parser-output .frac .num,.mw-parser-output .frac .den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.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="frac"><span class="num">1</span>⁄<span class="den">10</span></span> wavelength or smaller.<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></li> <li>Proximity effects are not included: edge-to-edge gap between turns should be 2×<i>d</i> or larger.</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 {\tfrac {\mu _{0}}{2\pi }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {\mu _{0}}{2\pi }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7402a7a66adb0f421b14cb88ae68414ece1337a7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:2.659ex; height:3.676ex;" alt="{\displaystyle {\tfrac {\mu _{0}}{2\pi }}}"></span> = 0.2 μH/m, exactly.</li></ul> </td> <td>Conductor <i>μ</i><sub>r</sub> should be as close to 1 as possible – <a href="/wiki/Copper" title="Copper">copper</a> or <a href="/wiki/Aluminum" class="mw-redirect" title="Aluminum">aluminum</a> rather than a magnetic or paramagnetic metal. </td></tr> <tr> <th>Medium or long air-core cylindrical coil<sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup><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> </th> <td><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={\frac {r^{2}N^{2}}{23r+25\ell }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>23</mn> <mi>r</mi> <mo>+</mo> <mn>25</mn> <mi>ℓ</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L={\frac {r^{2}N^{2}}{23r+25\ell }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d5776cf93d8f55560a61eb687cace9d5aa3940d8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:15.026ex; height:6.009ex;" alt="{\displaystyle L={\frac {r^{2}N^{2}}{23r+25\ell }}}"></span> <ul><li><i>L</i> = inductance (μH)</li> <li><i>r</i> = outer radius of coil (cm)</li> <li><i>ℓ</i> = length of coil (cm)</li> <li><i>N</i> = number of turns</li></ul> </td> <td>Requires cylinder length <i>ℓ</i> > 0.4 <i>r</i>: Length must be at least <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">1</span>⁄<span class="den">5</span></span> of the diameter. Not applicable to single-loop antennas or very short, stubby coils. </td></tr> <tr> <th>Multilayer air-core coil<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> </th> <td><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={\frac {r^{2}N^{2}}{19r+29\ell +32d}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>19</mn> <mi>r</mi> <mo>+</mo> <mn>29</mn> <mi>ℓ</mi> <mo>+</mo> <mn>32</mn> <mi>d</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L={\frac {r^{2}N^{2}}{19r+29\ell +32d}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/58ef0217b3ad1380075b64151ae1e312cffc873e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:21.407ex; height:6.009ex;" alt="{\displaystyle L={\frac {r^{2}N^{2}}{19r+29\ell +32d}}}"></span> <ul><li><i>L</i> = inductance (μH)</li> <li><i>r</i> = mean radius of coil (cm)</li> <li><i>ℓ</i> = physical length of coil winding (cm)</li> <li><i>N</i> = number of turns</li> <li><i>d</i> = depth of coil (outer radius minus inner radius) (cm)</li></ul> </td> <td> </td></tr> <tr> <th rowspan="2">Flat spiral air-core coil<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><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> </th> <td><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={\frac {r^{2}N^{2}}{20r+28d}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>20</mn> <mi>r</mi> <mo>+</mo> <mn>28</mn> <mi>d</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L={\frac {r^{2}N^{2}}{20r+28d}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f65ad66fc1fbe0689a497e0d611a9f8b5a19bd12" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:15.272ex; height:6.009ex;" alt="{\displaystyle L={\frac {r^{2}N^{2}}{20r+28d}}}"></span> <ul><li><i>L</i> = inductance (μH)</li> <li><i>r</i> = mean radius of coil (cm)</li> <li><i>N</i> = number of turns</li> <li><i>d</i> = depth of coil (outer radius minus inner radius) (cm)</li></ul> </td> <td> </td></tr> <tr> <td><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={\frac {r^{2}N^{2}}{8r+11d}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>8</mn> <mi>r</mi> <mo>+</mo> <mn>11</mn> <mi>d</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L={\frac {r^{2}N^{2}}{8r+11d}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9051ef06474b9d872e507c8e412d2c816dc285cd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:14.11ex; height:6.009ex;" alt="{\displaystyle L={\frac {r^{2}N^{2}}{8r+11d}}}"></span> <ul><li><i>L</i> = inductance (μH)</li> <li><i>r</i> = mean radius of coil (in)</li> <li><i>N</i> = number of turns</li> <li><i>d</i> = depth of coil (outer radius minus inner radius) (in)</li></ul> </td> <td>Accurate to within 5 percent for <i>d</i> > 0.2 <i>r</i>.<sup id="cite_ref-Terman1943_42-0" class="reference"><a href="#cite_note-Terman1943-42"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <th rowspan="2">Toroidal air-core (circular cross-section)<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> </th> <td><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=2\pi N^{2}\left(D-{\sqrt {D^{2}-d^{2}}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mo>=</mo> <mn>2</mn> <mi>π</mi> <msup> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mo>(</mo> <mrow> <mi>D</mi> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L=2\pi N^{2}\left(D-{\sqrt {D^{2}-d^{2}}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8a8e0244949841c4dcc1388001d3c8f404c4fe8e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:28.695ex; height:4.843ex;" alt="{\displaystyle L=2\pi N^{2}\left(D-{\sqrt {D^{2}-d^{2}}}\right)}"></span> <ul><li><i>L</i> = inductance (nH)</li> <li><i>d</i> = diameter of coil winding (cm)</li> <li><i>N</i> = number of turns</li> <li><i>D</i> = 2 * radius of revolution (cm)</li></ul> </td> <td> </td></tr> <tr> <td><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\approx \pi {d^{2}N^{2} \over D}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mo>≈</mo> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mi>D</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L\approx \pi {d^{2}N^{2} \over D}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4abfecb79f6088dee81d684721305a75e71a8b00" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:12.299ex; height:5.676ex;" alt="{\displaystyle L\approx \pi {d^{2}N^{2} \over D}}"></span> <ul><li><i>L</i> = inductance (nH)</li> <li><i>d</i> = diameter of coil winding (cm)</li> <li><i>N</i> = number of turns</li> <li><i>D</i> = 2 * radius of revolution (cm)</li></ul> </td> <td>Approximation when <i>d</i> < 0.1 <i>D</i> </td></tr> <tr> <th>Toroidal air-core (rectangular cross-section)<sup id="cite_ref-Terman1943_42-1" class="reference"><a href="#cite_note-Terman1943-42"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> </th> <td><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=2N^{2}h\ln \left({\frac {d_{2}}{d_{1}}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mo>=</mo> <mn>2</mn> <msup> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>h</mi> <mi>ln</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L=2N^{2}h\ln \left({\frac {d_{2}}{d_{1}}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0104b19f2c4abb2fba567f51c7ef616b0a304c83" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:19.207ex; height:6.176ex;" alt="{\displaystyle L=2N^{2}h\ln \left({\frac {d_{2}}{d_{1}}}\right)}"></span> <ul><li><i>L</i> = inductance (nH)</li> <li><i>d<sub>1</sub></i> = inside diameter of toroid (cm)</li> <li><i>d<sub>2</sub></i> = outside diameter of toroid (cm)</li> <li><i>N</i> = number of turns</li> <li><i>h</i> = height of toroid (cm)</li></ul> </td> <td> </td></tr></tbody></table> <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=Inductor&action=edit&section=30" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Bellini%E2%80%93Tosi_direction_finder" title="Bellini–Tosi direction finder">Bellini–Tosi direction finder</a> (radio goniometer)</li> <li><a href="/wiki/Hanna_curve" title="Hanna curve">Hanna curve</a></li> <li><a href="/wiki/Induction_coil" title="Induction coil">Induction coil</a></li> <li><a href="/wiki/Induction_cooking" title="Induction cooking">Induction cooking</a></li> <li><a href="/wiki/Induction_loop" title="Induction loop">Induction loop</a></li> <li><a href="/wiki/LC_circuit" title="LC circuit">LC circuit</a></li> <li><a href="/wiki/RLC_circuit" title="RLC circuit">RLC circuit</a></li> <li><a href="/wiki/Saturable_reactor" title="Saturable reactor">Saturable reactor</a> – a type of adjustable inductor</li> <li><a href="/wiki/Solenoid" title="Solenoid">Solenoid</a></li> <li><a href="/wiki/Accumulator_(energy)" title="Accumulator (energy)">Accumulator (energy)</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=Inductor&action=edit&section=31" 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 reflist-lower-alpha"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-27">^</a></b></span> <span class="reference-text">Nagaoka's coefficient (<i>K</i>) is approximately 1 for a coil which is much longer than its diameter and is tightly wound using small gauge wire (so that it approximates a current sheet).</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=Inductor&action=edit&section=32" 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: 25em;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></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="CITEREFAlexanderSadiku2013" class="citation book cs1">Alexander, Charles K.; Sadiku, Matthew N. O. (2013). <i>Fundamentals of Electric Circuits</i> (5 ed.). McGraw-Hill. p. 226. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-338057-5" title="Special:BookSources/978-0-07-338057-5"><bdi>978-0-07-338057-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fundamentals+of+Electric+Circuits&rft.pages=226&rft.edition=5&rft.pub=McGraw-Hill&rft.date=2013&rft.isbn=978-0-07-338057-5&rft.aulast=Alexander&rft.aufirst=Charles+K.&rft.au=Sadiku%2C+Matthew+N.+O.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductor" 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="CITEREFUrbanitzky1886" class="citation book cs1">Urbanitzky, Alfred Ritter von (1886). <i>Electricity in the Service of Man</i>. Macmillan and Company. p. <a rel="nofollow" class="external text" href="https://archive.org/details/electricityinse01wormgoog/page/194/mode/2up">195</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Electricity+in+the+Service+of+Man&rft.pages=195&rft.pub=Macmillan+and+Company&rft.date=1886&rft.aulast=Urbanitzky&rft.aufirst=Alfred+Ritter+von&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductor" class="Z3988"></span></span> </li> <li id="cite_note-Singh-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-Singh_3-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSingh2011" class="citation book cs1">Singh, Yaduvir (2011). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=0-PfbT49tJMC&q=inductance&pg=PA65"><i>Electro Magnetic Field Theory</i></a>. Pearson India. p. 65. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-8131760611" title="Special:BookSources/978-8131760611"><bdi>978-8131760611</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Electro+Magnetic+Field+Theory&rft.pages=65&rft.pub=Pearson+India&rft.date=2011&rft.isbn=978-8131760611&rft.aulast=Singh&rft.aufirst=Yaduvir&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D0-PfbT49tJMC%26q%3Dinductance%26pg%3DPA65&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductor" class="Z3988"></span></span> </li> <li id="cite_note-Wadhwa-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-Wadhwa_4-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWadhwa2005" class="citation book cs1">Wadhwa, C. L. (2005). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Su3-0UhVF28C&q=inductance&pg=PA18"><i>Electrical Power Systems</i></a>. New Age International. p. 18. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-8122417227" title="Special:BookSources/978-8122417227"><bdi>978-8122417227</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+Systems&rft.pages=18&rft.pub=New+Age+International&rft.date=2005&rft.isbn=978-8122417227&rft.aulast=Wadhwa&rft.aufirst=C.+L.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DSu3-0UhVF28C%26q%3Dinductance%26pg%3DPA18&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductor" class="Z3988"></span></span> </li> <li id="cite_note-Pelcovits-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-Pelcovits_5-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPelcovitsJosh_Farkas2007" class="citation book cs1">Pelcovits, Robert A.; Josh Farkas (2007). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=yON684oSjbEC&q=inductance&pg=PA646"><i>Barron's AP Physics C</i></a>. Barron's Educational Series. p. 646. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0764137105" title="Special:BookSources/978-0764137105"><bdi>978-0764137105</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Barron%27s+AP+Physics+C&rft.pages=646&rft.pub=Barron%27s+Educational+Series&rft.date=2007&rft.isbn=978-0764137105&rft.aulast=Pelcovits&rft.aufirst=Robert+A.&rft.au=Josh+Farkas&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DyON684oSjbEC%26q%3Dinductance%26pg%3DPA646&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductor" class="Z3988"></span></span> </li> <li id="cite_note-Purcell-6"><span class="mw-cite-backlink">^ <a href="#cite_ref-Purcell_6-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Purcell_6-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Purcell_6-2"><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="CITEREFPurcellDavid_J._Morin2013" class="citation book cs1">Purcell, Edward M.; David J. Morin (2013). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=A2rS5vlSFq0C&pg=PA364"><i>Electricity and Magnetism</i></a>. Cambridge Univ. Press. p. 364. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1107014022" title="Special:BookSources/978-1107014022"><bdi>978-1107014022</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&rft.pages=364&rft.pub=Cambridge+Univ.+Press&rft.date=2013&rft.isbn=978-1107014022&rft.aulast=Purcell&rft.aufirst=Edward+M.&rft.au=David+J.+Morin&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DA2rS5vlSFq0C%26pg%3DPA364&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductor" class="Z3988"></span></span> </li> <li id="cite_note-Shamos-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-Shamos_7-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFShamos2012" class="citation book cs1">Shamos, Morris H. (2012-10-16). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=J0fCAgAAQBAJ&q=1834+Lenz%E2%80%99s+Law&pg=PT238"><i>Great Experiments in Physics: Firsthand Accounts from Galileo to Einstein</i></a>. Courier Corporation. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780486139623" title="Special:BookSources/9780486139623"><bdi>9780486139623</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Great+Experiments+in+Physics%3A+Firsthand+Accounts+from+Galileo+to+Einstein&rft.pub=Courier+Corporation&rft.date=2012-10-16&rft.isbn=9780486139623&rft.aulast=Shamos&rft.aufirst=Morris+H.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DJ0fCAgAAQBAJ%26q%3D1834%2BLenz%25E2%2580%2599s%2BLaw%26pg%3DPT238&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductor" class="Z3988"></span></span> </li> <li id="cite_note-Schmitt-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-Schmitt_8-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchmitt2002" class="citation book cs1">Schmitt, Ron (2002). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=7gJ4RocvEskC&q=%22lenz%27s+law%22+energy&pg=PA75"><i>Electromagnetics Explained: A Handbook for Wireless/ RF, EMC, and High-Speed Electronics</i></a>. Elsevier. pp. 75–77. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0080505237" title="Special:BookSources/978-0080505237"><bdi>978-0080505237</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Electromagnetics+Explained%3A+A+Handbook+for+Wireless%2F+RF%2C+EMC%2C+and+High-Speed+Electronics&rft.pages=75-77&rft.pub=Elsevier&rft.date=2002&rft.isbn=978-0080505237&rft.aulast=Schmitt&rft.aufirst=Ron&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D7gJ4RocvEskC%26q%3D%2522lenz%2527s%2Blaw%2522%2Benergy%26pg%3DPA75&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductor" class="Z3988"></span></span> </li> <li id="cite_note-Jaffe-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-Jaffe_9-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJaffeTaylor2018" class="citation book cs1">Jaffe, Robert L.; Taylor, Washington (2018). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=RMhJDwAAQBAJ&q=%22lenz%27s+law%22+energy+stored+inductor+current&pg=PA51"><i>The Physics of Energy</i></a>. Cambridge Univ. Press. p. 51. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1108547895" title="Special:BookSources/978-1108547895"><bdi>978-1108547895</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+Physics+of+Energy&rft.pages=51&rft.pub=Cambridge+Univ.+Press&rft.date=2018&rft.isbn=978-1108547895&rft.aulast=Jaffe&rft.aufirst=Robert+L.&rft.au=Taylor%2C+Washington&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DRMhJDwAAQBAJ%26q%3D%2522lenz%2527s%2Blaw%2522%2Benergy%2Bstored%2Binductor%2Bcurrent%26pg%3DPA51&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductor" class="Z3988"></span></span> </li> <li id="cite_note-Lerner-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-Lerner_10-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLerner1997" class="citation book cs1">Lerner, Lawrence S. (1997). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Nv5GAyAdijoC&q=inductor+energy+%22magnetic+field%22+current&pg=PA856"><i>Physics for Scientists and Engineers, Vol. 2</i></a>. Jones and Bartlet Learning. p. 856. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0763704605" title="Special:BookSources/978-0763704605"><bdi>978-0763704605</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+for+Scientists+and+Engineers%2C+Vol.+2&rft.pages=856&rft.pub=Jones+and+Bartlet+Learning&rft.date=1997&rft.isbn=978-0763704605&rft.aulast=Lerner&rft.aufirst=Lawrence+S.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DNv5GAyAdijoC%26q%3Dinductor%2Benergy%2B%2522magnetic%2Bfield%2522%2Bcurrent%26pg%3DPA856&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductor" class="Z3988"></span></span> </li> <li id="cite_note-Bowick-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-Bowick_11-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBowick2011" class="citation book cs1">Bowick, Christopher (2011). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=zpTnMsiUkmwC&q=inductor+%22parasitic+capacitance%22&pg=PA7"><i>RF Circuit Design, 2nd Ed</i></a>. Newnes. pp. 7–8. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0080553429" title="Special:BookSources/978-0080553429"><bdi>978-0080553429</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=RF+Circuit+Design%2C+2nd+Ed.&rft.pages=7-8&rft.pub=Newnes&rft.date=2011&rft.isbn=978-0080553429&rft.aulast=Bowick&rft.aufirst=Christopher&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DzpTnMsiUkmwC%26q%3Dinductor%2B%2522parasitic%2Bcapacitance%2522%26pg%3DPA7&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductor" class="Z3988"></span></span> </li> <li id="cite_note-Kaiser-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-Kaiser_12-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKaiser2004" class="citation book cs1">Kaiser, Kenneth L. (2004). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=nZzOAsroBIEC&q=inductor+%22parasitic+capacitance%22"><i>Electromagnetic Compatibility Handbook</i></a>. CRC Press. pp. 6.4–6.5. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0849320873" title="Special:BookSources/978-0849320873"><bdi>978-0849320873</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Electromagnetic+Compatibility+Handbook&rft.pages=6.4-6.5&rft.pub=CRC+Press&rft.date=2004&rft.isbn=978-0849320873&rft.aulast=Kaiser&rft.aufirst=Kenneth+L.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DnZzOAsroBIEC%26q%3Dinductor%2B%2522parasitic%2Bcapacitance%2522&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductor" 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="https://www.gotrend.com.tw/ec99/rwd1606/news.asp?newsno=55">"What is an inductor? What is the definition of an inductor? Overview of inductor characteristics, parameters, and types"</a>. GOTREND Technology<span class="reference-accessdate">. Retrieved <span class="nowrap">2010-09-24</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=What+is+an+inductor%3F+What+is+the+definition+of+an+inductor%3F+Overview+of+inductor+characteristics%2C+parameters%2C+and+types.&rft.pub=GOTREND+Technology&rft_id=https%3A%2F%2Fwww.gotrend.com.tw%2Fec99%2Frwd1606%2Fnews.asp%3Fnewsno%3D55&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductor" class="Z3988"></span></span> </li> <li id="cite_note-Ott-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-Ott_14-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFOtt2011" class="citation book cs1">Ott, Henry W. (2011). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=2-4WJKxzzigC&q=shielding+transformer+inductor&pg=PA203"><i>Electromagnetic Compatibility Engineering</i></a>. John Wiley and Sons. p. 203. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1118210659" title="Special:BookSources/978-1118210659"><bdi>978-1118210659</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Electromagnetic+Compatibility+Engineering&rft.pages=203&rft.pub=John+Wiley+and+Sons&rft.date=2011&rft.isbn=978-1118210659&rft.aulast=Ott&rft.aufirst=Henry+W.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D2-4WJKxzzigC%26q%3Dshielding%2Btransformer%2Binductor%26pg%3DPA203&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductor" class="Z3988"></span></span> </li> <li id="cite_note-Violette-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-Violette_15-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFViolette2013" class="citation book cs1">Violette, Norman (2013). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=K7_nCAAAQBAJ&q=shielding+transformer+inductor&pg=PA516"><i>Electromagnetic Compatibility Handbook</i></a>. Springer. pp. 515–516. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-9401771443" title="Special:BookSources/978-9401771443"><bdi>978-9401771443</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Electromagnetic+Compatibility+Handbook&rft.pages=515-516&rft.pub=Springer&rft.date=2013&rft.isbn=978-9401771443&rft.aulast=Violette&rft.aufirst=Norman&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DK7_nCAAAQBAJ%26q%3Dshielding%2Btransformer%2Binductor%26pg%3DPA516&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductor" 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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://radio-timetraveller.blogspot.com/2011/01/unassuming-antenna-ferrite-loopstick.html">"An Unassuming Antenna – The Ferrite Loopstick"</a>. Radio Time Traveller. January 23, 2011<span class="reference-accessdate">. Retrieved <span class="nowrap">March 5,</span> 2014</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=An+Unassuming+Antenna+%E2%80%93+The+Ferrite+Loopstick&rft.pub=Radio+Time+Traveller&rft.date=2011-01-23&rft_id=http%3A%2F%2Fradio-timetraveller.blogspot.com%2F2011%2F01%2Funassuming-antenna-ferrite-loopstick.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductor" class="Z3988"></span></span> </li> <li id="cite_note-Frost-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-Frost_17-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFrost2013" class="citation web cs1">Frost, Phil (December 23, 2013). <a rel="nofollow" class="external text" href="http://ham.stackexchange.com/questions/1156/whats-an-appropriate-core-material-for-a-loopstick-antenna">"What's an appropriate core material for a loopstick antenna?"</a>. <i>Amateur Radio beta</i>. Stack Exchange, Inc<span class="reference-accessdate">. Retrieved <span class="nowrap">March 5,</span> 2014</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Amateur+Radio+beta&rft.atitle=What%27s+an+appropriate+core+material+for+a+loopstick+antenna%3F&rft.date=2013-12-23&rft.aulast=Frost&rft.aufirst=Phil&rft_id=http%3A%2F%2Fham.stackexchange.com%2Fquestions%2F1156%2Fwhats-an-appropriate-core-material-for-a-loopstick-antenna&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductor" class="Z3988"></span></span> </li> <li id="cite_note-Poisel-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-Poisel_18-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPoisel2011" class="citation book cs1">Poisel, Richard (2011). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=1YA1NZuo6u0C&q=%22ferrite+rod+loop+antenna&pg=PA280"><i>Antenna Systems and Electronic Warfare Applications</i></a>. Artech House. p. 280. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1608074846" title="Special:BookSources/978-1608074846"><bdi>978-1608074846</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Antenna+Systems+and+Electronic+Warfare+Applications&rft.pages=280&rft.pub=Artech+House&rft.date=2011&rft.isbn=978-1608074846&rft.aulast=Poisel&rft.aufirst=Richard&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D1YA1NZuo6u0C%26q%3D%2522ferrite%2Brod%2Bloop%2Bantenna%26pg%3DPA280&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductor" class="Z3988"></span></span> </li> <li id="cite_note-Yadava-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-Yadava_19-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFYadava2011" class="citation book cs1">Yadava, R. L. (2011). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=MMtjYYrE2r8C&q=%22ferrite+loop+antenna&pg=PA261"><i>Antenna and Wave Propagation</i></a>. PHI Learning Pvt. Ltd. p. 261. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-8120342910" title="Special:BookSources/978-8120342910"><bdi>978-8120342910</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Antenna+and+Wave+Propagation&rft.pages=261&rft.pub=PHI+Learning+Pvt.+Ltd&rft.date=2011&rft.isbn=978-8120342910&rft.aulast=Yadava&rft.aufirst=R.+L.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DMMtjYYrE2r8C%26q%3D%2522ferrite%2Bloop%2Bantenna%26pg%3DPA261&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductor" class="Z3988"></span></span> </li> <li id="cite_note-Zurek1-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-Zurek1_20-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFZurek2023" class="citation web cs1">Zurek, Stan (2023). <a rel="nofollow" class="external text" href="http://www.e-magnetica.pl/doku.php/proximity_effect">"Skin effect"</a>. <i>Encyclopedia Magnetica website</i><span class="reference-accessdate">. Retrieved <span class="nowrap">21 May</span> 2024</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Encyclopedia+Magnetica+website&rft.atitle=Skin+effect&rft.date=2023&rft.aulast=Zurek&rft.aufirst=Stan&rft_id=http%3A%2F%2Fwww.e-magnetica.pl%2Fdoku.php%2Fproximity_effect&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductor" class="Z3988"></span></span> </li> <li id="cite_note-Kazimierczuk-21"><span class="mw-cite-backlink">^ <a href="#cite_ref-Kazimierczuk_21-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Kazimierczuk_21-1"><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="CITEREFKazimierczuk2011" class="citation book cs1">Kazimierczuk, Marian K. (2011). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=t2TgU-uuNQ0C&pg=PA141"><i>High-Frequency Magnetic Components</i></a>. John Wiley and Sons. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-119-96491-9" title="Special:BookSources/978-1-119-96491-9"><bdi>978-1-119-96491-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=High-Frequency+Magnetic+Components&rft.pub=John+Wiley+and+Sons&rft.date=2011&rft.isbn=978-1-119-96491-9&rft.aulast=Kazimierczuk&rft.aufirst=Marian+K.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dt2TgU-uuNQ0C%26pg%3DPA141&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductor" class="Z3988"></span></span> </li> <li id="cite_note-Zurek2-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-Zurek2_22-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFZurek2023" class="citation web cs1">Zurek, Stan (2023). <a rel="nofollow" class="external text" href="http://www.e-magnetica.pl/doku.php/proximity_effect">"Proximity effect"</a>. <i>Encyclopedia Magnetica website</i><span class="reference-accessdate">. Retrieved <span class="nowrap">21 May</span> 2024</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Encyclopedia+Magnetica+website&rft.atitle=Proximity+effect&rft.date=2023&rft.aulast=Zurek&rft.aufirst=Stan&rft_id=http%3A%2F%2Fwww.e-magnetica.pl%2Fdoku.php%2Fproximity_effect&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductor" class="Z3988"></span></span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</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.newark.com/pdfs/techarticles/vishay/Inductors101.pdf">"Inductors 101"</a> <span class="cs1-format">(PDF)</span>. vishay<span class="reference-accessdate">. Retrieved <span class="nowrap">2010-09-24</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Inductors+101&rft.pub=vishay&rft_id=http%3A%2F%2Fwww.newark.com%2Fpdfs%2Ftecharticles%2Fvishay%2FInductors101.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductor" class="Z3988"></span></span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</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.vishay.com/docs/34053/definit.pdf">"Inductor and Magnetic Product Terminology"</a> <span class="cs1-format">(PDF)</span>. Vishay Dale<span class="reference-accessdate">. Retrieved <span class="nowrap">2012-09-24</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Inductor+and+Magnetic+Product+Terminology&rft.pub=Vishay+Dale&rft_id=http%3A%2F%2Fwww.vishay.com%2Fdocs%2F34053%2Fdefinit.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductor" class="Z3988"></span></span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</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.coilcraft.com/pdfs/uni5.pdf">"page with aluminum cores"</a> <span class="cs1-format">(PDF)</span>. Coilcraft catalog<span class="reference-accessdate">. Retrieved <span class="nowrap">10 July</span> 2015</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=page+with+aluminum+cores&rft.series=Coilcraft+catalog&rft_id=http%3A%2F%2Fwww.coilcraft.com%2Fpdfs%2Funi5.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductor" class="Z3988"></span><sup class="noprint Inline-Template"><span style="white-space: nowrap;">[<i><a href="/wiki/Wikipedia:Link_rot" title="Wikipedia:Link rot"><span title=" Dead link tagged September 2024">permanent dead link</span></a></i><span style="visibility:hidden; color:transparent; padding-left:2px">‍</span>]</span></sup></span> </li> <li id="cite_note-Nagaoka-26"><span class="mw-cite-backlink">^ <a href="#cite_ref-Nagaoka_26-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Nagaoka_26-1"><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="CITEREFNagaoka1909" class="citation journal cs1"><a href="/wiki/Hantaro_Nagaoka" title="Hantaro Nagaoka">Nagaoka, Hantaro</a> (1909-05-06). <a rel="nofollow" class="external text" href="http://www.g3ynh.info/zdocs/refs/Nagaoka1909.pdf">"The Inductance Coefficients of Solenoids"</a> <span class="cs1-format">(PDF)</span>. <i>Journal of the College of Science, Imperial University, Tokyo, Japan</i>. <b>27</b>: 18<span class="reference-accessdate">. Retrieved <span class="nowrap">2011-11-10</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+the+College+of+Science%2C+Imperial+University%2C+Tokyo%2C+Japan&rft.atitle=The+Inductance+Coefficients+of+Solenoids&rft.volume=27&rft.pages=18&rft.date=1909-05-06&rft.aulast=Nagaoka&rft.aufirst=Hantaro&rft_id=http%3A%2F%2Fwww.g3ynh.info%2Fzdocs%2Frefs%2FNagaoka1909.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductor" class="Z3988"></span></span> </li> <li id="cite_note-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-28">^</a></b></span> <span class="reference-text">Kenneth L. Kaiser, <i>Electromagnetic Compatibility Handbook</i>, p. 30.64, CRC Press, 2004 <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/0849320879" title="Special:BookSources/0849320879">0849320879</a>.</span> </li> <li id="cite_note-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-29">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRosa1908" class="citation journal cs1">Rosa, Edward B. (1908). <a rel="nofollow" class="external text" href="http://www.g3ynh.info/zdocs/refs/NBS/Rosa1908.pdf">"The Self and Mutual Inductances of Linear Conductors"</a> <span class="cs1-format">(PDF)</span>. <i>Bulletin of the Bureau of Standards</i>. <b>4</b> (2): 301–344. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.6028%2Fbulletin.088">10.6028/bulletin.088</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bulletin+of+the+Bureau+of+Standards&rft.atitle=The+Self+and+Mutual+Inductances+of+Linear+Conductors&rft.volume=4&rft.issue=2&rft.pages=301-344&rft.date=1908&rft_id=info%3Adoi%2F10.6028%2Fbulletin.088&rft.aulast=Rosa&rft.aufirst=Edward+B.&rft_id=http%3A%2F%2Fwww.g3ynh.info%2Fzdocs%2Frefs%2FNBS%2FRosa1908.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductor" class="Z3988"></span></span> </li> <li id="cite_note-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-30">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSkilling1951" class="citation book cs1">Skilling, Hugh Hildreth (1951). <i>Electric transmission lines : distributed constants, theory, and application</i>. Mcgraw-Hill. pp. 153–159.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Electric+transmission+lines+%3A+distributed+constants%2C+theory%2C+and+application&rft.pages=153-159&rft.pub=Mcgraw-Hill&rft.date=1951&rft.aulast=Skilling&rft.aufirst=Hugh+Hildreth&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductor" class="Z3988"></span></span> </li> <li id="cite_note-31"><span class="mw-cite-backlink"><b><a href="#cite_ref-31">^</a></b></span> <span class="reference-text"><a href="#CITEREFRosa1908">Rosa 1908</a>, equation (11a), subst. radius <i>ρ</i> = d/2 and <a href="/wiki/Cgs" class="mw-redirect" title="Cgs">cgs</a> units</span> </li> <li id="cite_note-Terman_straight-32"><span class="mw-cite-backlink"><b><a href="#cite_ref-Terman_straight_32-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFTerman1943">Terman 1943</a>, pp. 48–49, convert to natural logarithms and inches to mm.</span> </li> <li id="cite_note-Terman_adjust-33"><span class="mw-cite-backlink"><b><a href="#cite_ref-Terman_adjust_33-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFTerman1943">Terman (1943</a>, p. 48) states for <i>ℓ</i> < 100 <i>d</i>, include <i>d</i>/2<i>ℓ</i> within the parentheses.</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">Burger, O. & Dvorský, M. (2015). <i>Magnetic Loop Antenna</i>. Ostrava, Czech Republic: EDUCA TV o.p.s.</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">Values 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 \pi D}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> <mi>D</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi D}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d65462ba4a874ba48f70adbe5dddf739af1ca882" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.256ex; height:2.176ex;" alt="{\displaystyle \pi D}"></span> up to <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">1</span>⁄<span class="den">3</span></span> wavelength are feasible antennas, but for windings that long, this formula will be inaccurate.</span> </li> <li id="cite_note-36"><span class="mw-cite-backlink"><b><a href="#cite_ref-36">^</a></b></span> <span class="reference-text">ARRL Handbook, 66th Ed. American Radio Relay League (1989).</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 class="citation web cs1"><a rel="nofollow" class="external text" href="https://kaizerpowerelectronics.dk/calculators/helical-coil-calculator/">"Helical coil calculator"</a>. <i>Kaizer Power Electronics</i>. 2014-07-09<span class="reference-accessdate">. Retrieved <span class="nowrap">2020-12-29</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Kaizer+Power+Electronics&rft.atitle=Helical+coil+calculator&rft.date=2014-07-09&rft_id=https%3A%2F%2Fkaizerpowerelectronics.dk%2Fcalculators%2Fhelical-coil-calculator%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductor" 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="CITEREFWheeler1928" class="citation journal cs1">Wheeler, H.A. (October 1928). "Simple Inductance Formulas for Radio Coils". <i>Proceedings of the Institute of Radio Engineers</i>. <b>16</b> (10): 1398. <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%2FJRPROC.1928.221309">10.1109/JRPROC.1928.221309</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:51638679">51638679</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+Institute+of+Radio+Engineers&rft.atitle=Simple+Inductance+Formulas+for+Radio+Coils&rft.volume=16&rft.issue=10&rft.pages=1398&rft.date=1928-10&rft_id=info%3Adoi%2F10.1109%2FJRPROC.1928.221309&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A51638679%23id-name%3DS2CID&rft.aulast=Wheeler&rft.aufirst=H.A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductor" 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">For the second formula, <a href="#CITEREFTerman1943">Terman (1943</a>, p. 58) which cites to <a href="#CITEREFWheeler1928">Wheeler 1928</a>.</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 class="citation web cs1"><a rel="nofollow" class="external text" href="http://quantum-technologies.iap.uni-bonn.de/de/diplom-theses.html?task=download&file=302&token=fff191dcc4193aae12b9b5b0e9e199c9">"A Magnetic Elevator for Neutral Atoms into a 2D State-dependent Optical Lattice Experiment"</a>. <i>Uni-Bonn</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2017-08-15</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Uni-Bonn&rft.atitle=A+Magnetic+Elevator+for+Neutral+Atoms+into+a+2D+State-dependent+Optical+Lattice+Experiment&rft_id=http%3A%2F%2Fquantum-technologies.iap.uni-bonn.de%2Fde%2Fdiplom-theses.html%3Ftask%3Ddownload%26file%3D302%26token%3Dfff191dcc4193aae12b9b5b0e9e199c9&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductor" 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 class="citation web cs1"><a rel="nofollow" class="external text" href="https://kaizerpowerelectronics.dk/calculators/spiral-coil-calculator/">"Spiral coil calculator"</a>. <i>Kaizer Power Electronics</i>. 2014-07-10<span class="reference-accessdate">. Retrieved <span class="nowrap">2020-12-29</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Kaizer+Power+Electronics&rft.atitle=Spiral+coil+calculator&rft.date=2014-07-10&rft_id=https%3A%2F%2Fkaizerpowerelectronics.dk%2Fcalculators%2Fspiral-coil-calculator%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductor" class="Z3988"></span></span> </li> <li id="cite_note-Terman1943-42"><span class="mw-cite-backlink">^ <a href="#cite_ref-Terman1943_42-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Terman1943_42-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFTerman1943">Terman 1943</a>, p. 58</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"><a href="#CITEREFTerman1943">Terman 1943</a>, p. 57</span> </li> </ol></div> <dl><dt>Source</dt></dl> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTerman1943" class="citation book cs1"><a href="/wiki/Frederick_Terman" title="Frederick Terman">Terman, Frederick</a> (1943). <i>Radio Engineers' Handbook</i>. McGraw-Hill.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Radio+Engineers%27+Handbook&rft.pub=McGraw-Hill&rft.date=1943&rft.aulast=Terman&rft.aufirst=Frederick&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductor" class="Z3988"></span></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=Inductor&action=edit&section=33" 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"><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="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><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" /></span></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/Inductors" class="extiw" title="wikibooks:Electronics/Inductors">Inductors</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"><span><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" /></span></span></div> <div class="side-box-text plainlist">Look up <i><b><a href="https://en.wiktionary.org/wiki/Special:Search/inductor" class="extiw" title="wiktionary:Special:Search/inductor">inductor</a></b></i> in Wiktionary, the free dictionary.</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"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-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/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Inductors" class="extiw" title="commons:Category:Inductors">Inductors</a></span>.</div></div> </div> <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_components" 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_components" 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 href="/wiki/Capacitor" title="Capacitor">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 class="mw-selflink selflink">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_electronics" 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_electronics" 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 class="mw-selflink selflink">Inductor</a></li> <li><a href="/wiki/Capacitor" title="Capacitor">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"></div><div role="navigation" class="navbox" aria-labelledby="Machines" 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"><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:Machines" title="Template:Machines"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Machines" title="Template talk:Machines"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Machines" title="Special:EditPage/Template:Machines"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Machines" style="font-size:114%;margin:0 4em"><a href="/wiki/Machine" title="Machine">Machines</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Simple_machine" title="Simple machine">Classical simple machines</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/Inclined_plane" title="Inclined plane">Inclined plane</a></li> <li><a href="/wiki/Lever" title="Lever">Lever</a></li> <li><a href="/wiki/Pulley" title="Pulley">Pulley</a></li> <li><a href="/wiki/Screw_(simple_machine)" class="mw-redirect" title="Screw (simple machine)">Screw</a></li> <li><a href="/wiki/Wedge_(mechanical_device)" class="mw-redirect" title="Wedge (mechanical device)">Wedge</a></li> <li><a href="/wiki/Wheel_and_axle" title="Wheel and axle">Wheel and axle</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Clock" title="Clock">Clocks</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/Atomic_clock" title="Atomic clock">Atomic clock</a></li> <li><a href="/wiki/Marine_chronometer" title="Marine chronometer">Chronometer</a></li> <li><a href="/wiki/Pendulum_clock" title="Pendulum clock">Pendulum clock</a></li> <li><a href="/wiki/Quartz_clock" title="Quartz clock">Quartz clock</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Gas_compressor" class="mw-redirect" title="Gas compressor">Compressors</a> and <a href="/wiki/Pump" title="Pump">pumps</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/Archimedes%27_screw" title="Archimedes' screw">Archimedes' screw</a></li> <li><a href="/wiki/Injector" title="Injector">Eductor-jet pump</a></li> <li><a href="/wiki/Hydraulic_ram" title="Hydraulic ram">Hydraulic ram</a></li> <li><a href="/wiki/Pump" title="Pump">Pump</a></li> <li><a href="/wiki/Trompe" title="Trompe">Trompe</a></li> <li><a href="/wiki/Vacuum_pump" title="Vacuum pump">Vacuum pump</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/External_combustion_engine" title="External combustion engine">External combustion engines</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/Steam_engine" title="Steam engine">Steam engine</a></li> <li><a href="/wiki/Stirling_engine" title="Stirling engine">Stirling engine</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Internal_combustion_engine" title="Internal combustion engine">Internal combustion engines</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/Gas_turbine" title="Gas turbine">Gas turbine</a></li> <li><a href="/wiki/Reciprocating_engine" title="Reciprocating engine">Reciprocating engine</a></li> <li><a href="/wiki/Rotary_engine" title="Rotary engine">Rotary engine</a></li> <li><a href="/wiki/Nutating_disc_engine" title="Nutating disc engine">Nutating disc engine</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Linkage_(mechanical)" title="Linkage (mechanical)">Linkages</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/Pantograph" title="Pantograph">Pantograph</a></li> <li><a href="/wiki/Peaucellier%E2%80%93Lipkin_linkage" title="Peaucellier–Lipkin linkage">Peaucellier-Lipkin</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Turbine" title="Turbine">Turbine</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/Gas_turbine" title="Gas turbine">Gas turbine</a></li> <li><a href="/wiki/Jet_engine" title="Jet engine">Jet engine</a></li> <li><a href="/wiki/Quasiturbine" title="Quasiturbine">Quasiturbine</a></li> <li><a href="/wiki/Steam_turbine" title="Steam turbine">Steam turbine</a></li> <li><a href="/wiki/Water_turbine" title="Water turbine">Water turbine</a></li> <li><a href="/wiki/Wind_generator" class="mw-redirect" title="Wind generator">Wind generator</a></li> <li><a href="/wiki/Windmill" title="Windmill">Windmill</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Airfoil" title="Airfoil">Aerofoil</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/Sail" title="Sail">Sail</a></li> <li><a href="/wiki/Wing" title="Wing">Wing</a></li> <li><a href="/wiki/Rudder" title="Rudder">Rudder</a></li> <li><a href="/wiki/Flap_(aircraft)" class="mw-redirect" title="Flap (aircraft)">Flap</a></li> <li><a href="/wiki/Propeller_(aircraft)" class="mw-redirect" title="Propeller (aircraft)">Propeller</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Electronics" title="Electronics">Electronics</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/Vacuum_tube" title="Vacuum tube">Vacuum tube</a></li> <li><a href="/wiki/Transistor" title="Transistor">Transistor</a></li> <li><a href="/wiki/Diode" title="Diode">Diode</a></li> <li><a href="/wiki/Resistor" title="Resistor">Resistor</a></li> <li><a href="/wiki/Capacitor" title="Capacitor">Capacitor</a></li> <li><a class="mw-selflink selflink">Inductor</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Vehicle" title="Vehicle">Vehicles</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/Automobile" class="mw-redirect" title="Automobile">Automobile</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Miscellaneous</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/Mecha" title="Mecha">Mecha</a></li> <li><a href="/wiki/Robot" title="Robot">Robot</a></li> <li><a href="/wiki/List_of_agricultural_machinery" title="List of agricultural machinery">Agricultural</a></li> <li><a href="/wiki/Seed-counting_machine" title="Seed-counting machine">Seed-counting machine</a></li> <li><a href="/wiki/Vending_machine" title="Vending machine">Vending machine</a></li> <li><a href="/wiki/Wind_tunnel" title="Wind tunnel">Wind tunnel</a></li> <li><a href="/wiki/Check_weigher" title="Check weigher">Check weighing machines</a></li> <li><a href="/wiki/Riveting_machines" class="mw-redirect" title="Riveting machines">Riveting machines</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Springs</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/Spring_(device)" title="Spring (device)">Spring (device)</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="Navbox" 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/Q5325#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/4182601-2">Germany</a></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="Electric inductors"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/sh85041716">United States</a></span></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="cívky (elektrotechnika)"><a rel="nofollow" class="external text" href="https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=ph119313&CON_LNG=ENG">Czech Republic</a></span></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://olduli.nli.org.il/F/?func=find-b&local_base=NLX10&find_code=UID&request=987007536062305171">Israel</a></span></li></ul></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" 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=Inductor&oldid=1257456796">https://en.wikipedia.org/w/index.php?title=Inductor&oldid=1257456796</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:Electromagnetic_components" title="Category:Electromagnetic components">Electromagnetic components</a></li><li><a href="/wiki/Category:Energy_storage" title="Category:Energy storage">Energy storage</a></li><li><a href="/wiki/Category:English_inventions" title="Category:English inventions">English 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:All_articles_with_dead_external_links" title="Category:All articles with dead external links">All articles with dead external links</a></li><li><a href="/wiki/Category:Articles_with_dead_external_links_from_September_2024" title="Category:Articles with dead external links from September 2024">Articles with dead external links from September 2024</a></li><li><a href="/wiki/Category:Articles_with_permanently_dead_external_links" title="Category:Articles with permanently dead external links">Articles with permanently dead external 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_matches_Wikidata" title="Category:Short description matches Wikidata">Short description matches Wikidata</a></li><li><a href="/wiki/Category:Pages_using_multiple_image_with_auto_scaled_images" title="Category:Pages using multiple image with auto scaled images">Pages using multiple image with auto scaled images</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_February_2018" title="Category:Articles with unsourced statements from February 2018">Articles with unsourced statements from February 2018</a></li><li><a href="/wiki/Category:Articles_with_unsourced_statements_from_September_2022" title="Category:Articles with unsourced statements from September 2022">Articles with unsourced statements from September 2022</a></li><li><a href="/wiki/Category:Commons_category_link_is_on_Wikidata" title="Category:Commons category link is on Wikidata">Commons category link is on Wikidata</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 15 November 2024, at 00:04<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=Inductor&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"><img src="/static/images/footer/wikimedia-button.svg" width="84" height="29" alt="Wikimedia Foundation" loading="lazy"></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"><img src="/w/resources/assets/poweredby_mediawiki.svg" alt="Powered by MediaWiki" width="88" height="31" loading="lazy"></a></li> </ul> </footer> </div> </div> </div> <div class="vector-settings" id="p-dock-bottom"> <ul></ul> </div><script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.codfw.main-f69cdc8f6-lsb4r","wgBackendResponseTime":236,"wgPageParseReport":{"limitreport":{"cputime":"1.183","walltime":"1.533","ppvisitednodes":{"value":5914,"limit":1000000},"postexpandincludesize":{"value":156046,"limit":2097152},"templateargumentsize":{"value":9999,"limit":2097152},"expansiondepth":{"value":17,"limit":100},"expensivefunctioncount":{"value":19,"limit":500},"unstrip-depth":{"value":1,"limit":20},"unstrip-size":{"value":173143,"limit":5000000},"entityaccesscount":{"value":1,"limit":400},"timingprofile":["100.00% 1064.887 1 -total"," 37.50% 399.328 2 Template:Reflist"," 18.47% 196.657 19 Template:Cite_book"," 10.41% 110.825 4 Template:Navbox"," 9.25% 98.538 1 Template:Electronic_components"," 9.10% 96.877 1 Template:Short_description"," 6.15% 65.525 2 Template:Pagetype"," 5.54% 58.943 3 Template:Sister_project"," 5.34% 56.813 3 Template:Side_box"," 5.02% 53.409 5 Template:Harvnb"]},"scribunto":{"limitreport-timeusage":{"value":"0.599","limit":"10.000"},"limitreport-memusage":{"value":8900055,"limit":52428800},"limitreport-logs":"anchor_id_list = table#1 {\n [\"CITEREFAlexanderSadiku2013\"] = 1,\n [\"CITEREFBowick2011\"] = 1,\n [\"CITEREFFrost2013\"] = 1,\n [\"CITEREFJaffeTaylor2018\"] = 1,\n [\"CITEREFKaiser2004\"] = 1,\n [\"CITEREFKazimierczuk2011\"] = 1,\n [\"CITEREFLerner1997\"] = 1,\n [\"CITEREFNagaoka1909\"] = 1,\n [\"CITEREFOtt2011\"] = 1,\n [\"CITEREFPelcovitsJosh_Farkas2007\"] = 1,\n [\"CITEREFPoisel2011\"] = 1,\n [\"CITEREFPurcellDavid_J._Morin2013\"] = 1,\n [\"CITEREFRosa1908\"] = 1,\n [\"CITEREFSchmitt2002\"] = 1,\n [\"CITEREFShamos2012\"] = 1,\n [\"CITEREFSingh2011\"] = 1,\n [\"CITEREFSkilling1951\"] = 1,\n [\"CITEREFTerman1943\"] = 1,\n [\"CITEREFUrbanitzky1886\"] = 1,\n [\"CITEREFViolette2013\"] = 1,\n [\"CITEREFWadhwa2005\"] = 1,\n [\"CITEREFWheeler1928\"] = 1,\n [\"CITEREFYadava2011\"] = 1,\n [\"CITEREFZurek2023\"] = 2,\n}\ntemplate_list = table#1 {\n [\"Authority control\"] = 1,\n [\"Bulleted list\"] = 1,\n [\"Citation needed\"] = 2,\n [\"Cite book\"] = 19,\n [\"Cite journal\"] = 3,\n [\"Cite web\"] = 11,\n [\"Clear\"] = 2,\n [\"Commons category\"] = 1,\n [\"Dead link\"] = 1,\n [\"Defn\"] = 5,\n [\"Digital electronics\"] = 1,\n [\"Electronic components\"] = 1,\n [\"Equation box 1\"] = 2,\n [\"For\"] = 1,\n [\"Frac\"] = 3,\n [\"Glossary\"] = 2,\n [\"Glossary end\"] = 2,\n [\"Harvnb\"] = 5,\n [\"Harvtxt\"] = 2,\n [\"ISBN\"] = 1,\n [\"Infobox electronic component\"] = 1,\n [\"Machines\"] = 1,\n [\"Main\"] = 4,\n [\"Math\"] = 2,\n [\"Multiple image\"] = 4,\n [\"Mvar\"] = 4,\n [\"Nbsp\"] = 5,\n [\"Notelist\"] = 1,\n [\"Nowrap\"] = 2,\n [\"Reflist\"] = 1,\n [\"Rp\"] = 2,\n [\"See also\"] = 3,\n [\"Sfrac\"] = 1,\n [\"Short description\"] = 1,\n [\"Term\"] = 5,\n [\"Wikibooks\"] = 1,\n [\"Wiktionary\"] = 1,\n}\narticle_whitelist = table#1 {\n}\n"},"cachereport":{"origin":"mw-web.codfw.main-f69cdc8f6-tfkkl","timestamp":"20241122140648","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"Inductor","url":"https:\/\/en.wikipedia.org\/wiki\/Inductor","sameAs":"http:\/\/www.wikidata.org\/entity\/Q5325","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q5325","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":"2001-08-14T19:47:19Z","dateModified":"2024-11-15T00:04:49Z","image":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/a\/a1\/Electronic_component_inductors.jpg","headline":"passive two-terminal electrical component that stores energy in its magnetic field"}</script> </body> </html>