Impedans – Wikipedia

<!DOCTYPE html> <html class="client-nojs vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-sticky-header-enabled vector-toc-available" lang="nb" dir="ltr"> <head> <meta charset="UTF-8"> <title>Impedans – Wikipedia</title> <script>(function(){var className="client-js vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-sticky-header-enabled vector-toc-available";var cookie=document.cookie.match(/(?:^|; )nowikimwclientpreferences=([^;]+)/);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":[",\t."," \t,"],"wgDigitTransformTable":["",""],"wgDefaultDateFormat":"dmy", "wgMonthNames":["","januar","februar","mars","april","mai","juni","juli","august","september","oktober","november","desember"],"wgRequestId":"4d1d0f3c-cab5-4fd4-8441-a8453e06471b","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"Impedans","wgTitle":"Impedans","wgCurRevisionId":24393641,"wgRevisionId":24393641,"wgArticleId":25941,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["Artikler uten kilder","Artikler med autoritetsdatalenker fra Wikidata","Elektrisitet","Fysiske størrelser"],"wgPageViewLanguage":"nb","wgPageContentLanguage":"nb","wgPageContentModel":"wikitext","wgRelevantPageName":"Impedans","wgRelevantArticleId":25941,"wgTempUserName":null,"wgIsProbablyEditable":true,"wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[],"wgRestrictionMove":[],"wgNoticeProject":"wikipedia","wgCiteReferencePreviewsActive":true,"wgMediaViewerOnClick":true, "wgMediaViewerEnabledByDefault":true,"wgPopupsFlags":0,"wgVisualEditor":{"pageLanguageCode":"nb","pageLanguageDir":"ltr","pageVariantFallbacks":"nb"},"wgMFDisplayWikibaseDescriptions":{"search":true,"watchlist":true,"tagline":true,"nearby":true},"wgWMESchemaEditAttemptStepOversample":false,"wgWMEPageLength":10000,"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q179043","wgCheckUserClientHintsHeadersJsApi":["brands","architecture","bitness","fullVersionList","mobile","model","platform","platformVersion"],"GEHomepageSuggestedEditsEnableTopics":true,"wgGETopicsMatchModeEnabled":false,"wgGEStructuredTaskRejectionReasonTextInputEnabled":false,"wgGELevelingUpEnabledForUser":false};RLSTATE={"ext.gadget.InterProjectLinks":"ready","ext.globalCssJs.user.styles":"ready","site.styles":"ready","user.styles":"ready","ext.globalCssJs.user":"ready", "user":"ready","user.options":"loading","ext.math.styles":"ready","skins.vector.search.codex.styles":"ready","skins.vector.styles":"ready","skins.vector.icons":"ready","ext.wikimediamessages.styles":"ready","ext.visualEditor.desktopArticleTarget.noscript":"ready","ext.uls.interlanguage":"ready","wikibase.client.init":"ready"};RLPAGEMODULES=["mediawiki.page.media","site","mediawiki.page.ready","mediawiki.toc","skins.vector.js","ext.centralNotice.geoIP","ext.centralNotice.startUp","ext.gadget.UkensKonkurranse","ext.gadget.link-missing-label","ext.gadget.new-section","ext.gadget.superinterwiki","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","oojs-ui.styles.icons-media","oojs-ui-core.icons"];</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=nb&modules=ext.math.styles%7Cext.uls.interlanguage%7Cext.visualEditor.desktopArticleTarget.noscript%7Cext.wikimediamessages.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=nb&modules=startup&only=scripts&raw=1&skin=vector-2022"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=nb&modules=ext.gadget.InterProjectLinks&only=styles&skin=vector-2022"> <link rel="stylesheet" href="/w/load.php?lang=nb&modules=site.styles&only=styles&skin=vector-2022"> <meta name="generator" content="MediaWiki 1.44.0-wmf.18"> <meta name="referrer" content="origin"> <meta name="referrer" content="origin-when-cross-origin"> <meta name="robots" content="max-image-preview:standard"> <meta name="format-detection" content="telephone=no"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Complex_Impedance.svg/1200px-Complex_Impedance.svg.png"> <meta property="og:image:width" content="1200"> <meta property="og:image:height" content="1200"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Complex_Impedance.svg/800px-Complex_Impedance.svg.png"> <meta property="og:image:width" content="800"> <meta property="og:image:height" content="800"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Complex_Impedance.svg/640px-Complex_Impedance.svg.png"> <meta property="og:image:width" content="640"> <meta property="og:image:height" content="640"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="Impedans – 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="//no.m.wikipedia.org/wiki/Impedans"> <link rel="alternate" type="application/x-wiki" title="Rediger" href="/w/index.php?title=Impedans&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 (nb)"> <link rel="EditURI" type="application/rsd+xml" href="//no.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://no.wikipedia.org/wiki/Impedans"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.no"> <link rel="alternate" type="application/atom+xml" title="Wikipedia Atom-mating" href="/w/index.php?title=Spesial:Siste_endringer&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-Impedans rootpage-Impedans skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Hopp til innhold</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="Nettsted"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" title="Hovedmeny" > <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="Hovedmeny" > <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">Hovedmeny</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">Hovedmeny</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">flytt til sidefeltet</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">skjul</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Navigasjon </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage-description" class="mw-list-item"><a href="/wiki/Forside" title="Gå til hovedsiden [z]" accesskey="z"><span>Forside</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Spesial:Tilfeldig" title="Vis en tilfeldig side [x]" accesskey="x"><span>Tilfeldig side</span></a></li><li id="n-help" class="mw-list-item"><a href="/wiki/Hjelp:Portal" title="Stedet for å få hjelp"><span>Hjelp</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Spesial:Siste_endringer" title="Liste over siste endringer på wikien. [r]" accesskey="r"><span>Siste endringer</span></a></li><li id="n-specialpages" class="mw-list-item"><a href="/wiki/Spesial:Spesialsider"><span>Spesialsider</span></a></li> </ul> </div> </div> <div id="p-prosjekt" class="vector-menu mw-portlet mw-portlet-prosjekt" > <div class="vector-menu-heading"> Prosjekt </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-Prosjektportal" class="mw-list-item"><a href="/wiki/Wikipedia:Portal"><span>Prosjektportal</span></a></li><li id="n-bidra" class="mw-list-item"><a href="/wiki/Wikipedia:Bidra_til_Wikipedia"><span>Hvordan bidra?</span></a></li><li id="n-wikitreff" class="mw-list-item"><a href="/wiki/Wikipedia:Wikitreff"><span>Wikitreff</span></a></li><li id="n-tinget" class="mw-list-item"><a href="/wiki/Wikipedia:Tinget"><span>Tinget</span></a></li><li id="n-torget" class="mw-list-item"><a href="/wiki/Wikipedia:Torget"><span>Torget</span></a></li><li id="n-konkurranser" class="mw-list-item"><a href="/wiki/Wikipedia:Konkurranser"><span>Konkurranser</span></a></li> </ul> </div> </div> <div id="p-Wikipedia" class="vector-menu mw-portlet mw-portlet-Wikipedia" > <div class="vector-menu-heading"> Wikipedia </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-kontakt" class="mw-list-item"><a href="/wiki/Wikipedia:Kontakt"><span>Kontakt Wikipedia</span></a></li><li id="n-wmno" class="mw-list-item"><a href="https://www.wikimedia.no" rel="nofollow" title="Medlemsorganisasjon for wikipedianere"><span>Wikimedia Norge</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Forside" 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="" src="/static/images/mobile/copyright/wikipedia-tagline-no.svg" width="121" height="14" style="width: 7.5625em; height: 0.875em;"> </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/Spesial:S%C3%B8k" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Søk i Wikipedia [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Søk</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="Søk i Wikipedia" aria-label="Søk i Wikipedia" autocapitalize="sentences" title="Søk i 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="Spesial:Søk"> </div> <button class="cdx-button cdx-search-input__end-button">Søk</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Personlig"> <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="Utseende"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Endre skriftstørrelse, bredde og farge på siden." > <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="Utseende" > <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">Utseende</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=no.wikipedia.org&uselang=nb" class=""><span>Doner</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=Spesial:Opprett_konto&returnto=Impedans" title="Du oppfordres til å opprette en konto og logge inn, men det er ikke obligatorisk" class=""><span>Opprett konto</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=Spesial:Logg_inn&returnto=Impedans" title="Du oppfordres til å logge inn, men det er ikke obligatorisk [o]" accesskey="o" class=""><span>Logg inn</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 user-links-collapsible-item" title="Flere alternativer" > <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="Personlig" > <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">Personlig</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="Brukermeny" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=no.wikipedia.org&uselang=nb"><span>Doner</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Spesial:Opprett_konto&returnto=Impedans" title="Du oppfordres til å opprette en konto og logge inn, men det er ikke obligatorisk"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Opprett konto</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Spesial:Logg_inn&returnto=Impedans" title="Du oppfordres til å logge inn, men det er ikke obligatorisk [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Logg inn</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="Nettsted"> <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="Innhold" 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">Innhold</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">flytt til sidefeltet</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">skjul</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">(Til toppen)</div> </a> </li> <li id="toc-Reaktanser_for_komponentene_kapasitet_og_induktivitet" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Reaktanser_for_komponentene_kapasitet_og_induktivitet"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Reaktanser for komponentene kapasitet og induktivitet</span> </div> </a> <ul id="toc-Reaktanser_for_komponentene_kapasitet_og_induktivitet-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Inverse_verdier,_ledningsevner" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Inverse_verdier,_ledningsevner"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Inverse verdier, ledningsevner</span> </div> </a> <ul id="toc-Inverse_verdier,_ledningsevner-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Topoler_med_resistanser_og_reaktanser" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Topoler_med_resistanser_og_reaktanser"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Topoler med resistanser og reaktanser</span> </div> </a> <ul id="toc-Topoler_med_resistanser_og_reaktanser-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Analogier" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Analogier"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Analogier</span> </div> </a> <ul id="toc-Analogier-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Matematisk_grunnlag" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Matematisk_grunnlag"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Matematisk grunnlag</span> </div> </a> <ul id="toc-Matematisk_grunnlag-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Beskrivelse_med_kompleks_matematikk" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Beskrivelse_med_kompleks_matematikk"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Beskrivelse med kompleks matematikk</span> </div> </a> <ul id="toc-Beskrivelse_med_kompleks_matematikk-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Beregning_for_parallellkopling_av_reaktans_og_resistans" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Beregning_for_parallellkopling_av_reaktans_og_resistans"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Beregning for parallellkopling av reaktans og resistans</span> </div> </a> <ul id="toc-Beregning_for_parallellkopling_av_reaktans_og_resistans-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="Innhold" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Innholdsfortegnelse" > <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="Vis/skjul innholdsfortegnelsen" > <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">Vis/skjul innholdsfortegnelsen</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">Impedans</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="Gå til en artikkel på et annet språk. Tilgjengelig på 60 språk" > <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-60" 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">60 språk</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Elektrisk_impedans" title="Elektrisk impedans – norsk nynorsk" lang="nn" hreflang="nn" data-title="Elektrisk impedans" data-language-autonym="Norsk nynorsk" data-language-local-name="norsk nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Impedans" title="Impedans – dansk" lang="da" hreflang="da" data-title="Impedans" data-language-autonym="Dansk" data-language-local-name="dansk" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Impedans" title="Impedans – svensk" lang="sv" hreflang="sv" data-title="Impedans" data-language-autonym="Svenska" data-language-local-name="svensk" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Samvi%C3%B0n%C3%A1m" title="Samviðnám – islandsk" lang="is" hreflang="is" data-title="Samviðnám" data-language-autonym="Íslenska" data-language-local-name="islandsk" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Elektriese_impedansie" title="Elektriese impedansie – afrikaans" lang="af" hreflang="af" data-title="Elektriese impedansie" data-language-autonym="Afrikaans" data-language-local-name="afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%B9%D8%A7%D9%88%D9%82%D8%A9" title="معاوقة – arabisk" lang="ar" hreflang="ar" data-title="معاوقة" data-language-autonym="العربية" data-language-local-name="arabisk" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Impedancia" title="Impedancia – asturisk" lang="ast" hreflang="ast" data-title="Impedancia" data-language-autonym="Asturianu" data-language-local-name="asturisk" 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%B0mpedans" title="İmpedans – aserbajdsjansk" lang="az" hreflang="az" data-title="İmpedans" data-language-autonym="Azərbaycanca" data-language-local-name="aserbajdsjansk" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B8%E0%A6%BE%E0%A6%AE%E0%A6%97%E0%A7%8D%E0%A6%B0%E0%A6%BF%E0%A6%95_%E0%A6%AA%E0%A7%8D%E0%A6%B0%E0%A6%A4%E0%A6%BF%E0%A6%B0%E0%A7%8B%E0%A6%A7_(%E0%A6%AC%E0%A7%88%E0%A6%A6%E0%A7%8D%E0%A6%AF%E0%A7%81%E0%A6%A4%E0%A6%BF%E0%A6%95_%E0%A6%AC%E0%A6%B0%E0%A7%8D%E0%A6%A4%E0%A6%A8%E0%A7%80)" title="সামগ্রিক প্রতিরোধ (বৈদ্যুতিক বর্তনী) – bengali" lang="bn" hreflang="bn" data-title="সামগ্রিক প্রতিরোধ (বৈদ্যুতিক বর্তনী)" data-language-autonym="বাংলা" data-language-local-name="bengali" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Ti%C4%81n-kh%C3%AC_ch%C3%B3%CD%98-kh%C3%B2ng" title="Tiān-khì chó͘-khòng – minnan" lang="nan" hreflang="nan" data-title="Tiān-khì chó͘-khòng" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%98%D0%BC%D0%BF%D0%B5%D0%B4%D0%B0%D0%BD%D1%81" title="Импеданс – bulgarsk" lang="bg" hreflang="bg" data-title="Импеданс" data-language-autonym="Български" data-language-local-name="bulgarsk" 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/Elektri%C4%8Dna_impedansa" title="Električna impedansa – bosnisk" lang="bs" hreflang="bs" data-title="Električna impedansa" data-language-autonym="Bosanski" data-language-local-name="bosnisk" 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/Imped%C3%A0ncia" title="Impedància – katalansk" lang="ca" hreflang="ca" data-title="Impedància" data-language-autonym="Català" data-language-local-name="katalansk" 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/Impedance" title="Impedance – tsjekkisk" lang="cs" hreflang="cs" data-title="Impedance" data-language-autonym="Čeština" data-language-local-name="tsjekkisk" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Elektrische_Impedanz" title="Elektrische Impedanz – tysk" lang="de" hreflang="de" data-title="Elektrische Impedanz" data-language-autonym="Deutsch" data-language-local-name="tysk" 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/N%C3%A4ivtakistus" title="Näivtakistus – estisk" lang="et" hreflang="et" data-title="Näivtakistus" data-language-autonym="Eesti" data-language-local-name="estisk" 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%97%CE%BB%CE%B5%CE%BA%CF%84%CF%81%CE%B9%CE%BA%CE%AE_%CE%B5%CE%BC%CF%80%CE%AD%CE%B4%CE%B7%CF%83%CE%B7" title="Ηλεκτρική εμπέδηση – gresk" lang="el" hreflang="el" data-title="Ηλεκτρική εμπέδηση" data-language-autonym="Ελληνικά" data-language-local-name="gresk" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Electrical_impedance" title="Electrical impedance – engelsk" lang="en" hreflang="en" data-title="Electrical impedance" data-language-autonym="English" data-language-local-name="engelsk" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Impedancia" title="Impedancia – spansk" lang="es" hreflang="es" data-title="Impedancia" data-language-autonym="Español" data-language-local-name="spansk" 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/Elektra_impedanco" title="Elektra impedanco – esperanto" lang="eo" hreflang="eo" data-title="Elektra impedanco" 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/Inpedantzia_elektriko" title="Inpedantzia elektriko – baskisk" lang="eu" hreflang="eu" data-title="Inpedantzia elektriko" data-language-autonym="Euskara" data-language-local-name="baskisk" 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%85%D9%BE%D8%AF%D8%A7%D9%86%D8%B3_%D8%A7%D9%84%DA%A9%D8%AA%D8%B1%DB%8C%DA%A9%DB%8C" title="امپدانس الکتریکی – persisk" lang="fa" hreflang="fa" data-title="امپدانس الکتریکی" data-language-autonym="فارسی" data-language-local-name="persisk" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Imp%C3%A9dance_(%C3%A9lectricit%C3%A9)" title="Impédance (électricité) – fransk" lang="fr" hreflang="fr" data-title="Impédance (électricité)" data-language-autonym="Français" data-language-local-name="fransk" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Coisceas" title="Coisceas – irsk" lang="ga" hreflang="ga" data-title="Coisceas" data-language-autonym="Gaeilge" data-language-local-name="irsk" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%98%A8%EC%A0%80%ED%95%AD" title="온저항 – koreansk" lang="ko" hreflang="ko" data-title="온저항" data-language-autonym="한국어" data-language-local-name="koreansk" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B7%D5%AC%D5%A5%D5%AF%D5%BF%D6%80%D5%A1%D5%AF%D5%A1%D5%B6_%D5%AB%D5%B4%D5%BA%D5%A5%D5%A4%D5%A1%D5%B6%D5%BD" title="Էլեկտրական իմպեդանս – armensk" lang="hy" hreflang="hy" data-title="Էլեկտրական իմպեդանս" data-language-autonym="Հայերեն" data-language-local-name="armensk" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%A4%E0%A4%BF%E0%A4%AC%E0%A4%BE%E0%A4%A7%E0%A4%BE" title="प्रतिबाधा – hindi" lang="hi" hreflang="hi" data-title="प्रतिबाधा" 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_impedancija" title="Električna impedancija – kroatisk" lang="hr" hreflang="hr" data-title="Električna impedancija" data-language-autonym="Hrvatski" data-language-local-name="kroatisk" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Impedansi_listrik" title="Impedansi listrik – indonesisk" lang="id" hreflang="id" data-title="Impedansi listrik" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesisk" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Impedenza" title="Impedenza – italiensk" lang="it" hreflang="it" data-title="Impedenza" data-language-autonym="Italiano" data-language-local-name="italiensk" 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%A2%D7%9B%D7%91%D7%94_%D7%97%D7%A9%D7%9E%D7%9C%D7%99%D7%AA" title="עכבה חשמלית – hebraisk" lang="he" hreflang="he" data-title="עכבה חשמלית" data-language-autonym="עברית" data-language-local-name="hebraisk" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%98%D0%BC%D0%BF%D0%B5%D0%B4%D0%B0%D0%BD%D1%81" title="Импеданс – kasakhisk" lang="kk" hreflang="kk" data-title="Импеданс" data-language-autonym="Қазақша" data-language-local-name="kasakhisk" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Impedansas" title="Impedansas – litauisk" lang="lt" hreflang="lt" data-title="Impedansas" data-language-autonym="Lietuvių" data-language-local-name="litauisk" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Impedancia" title="Impedancia – ungarsk" lang="hu" hreflang="hu" data-title="Impedancia" data-language-autonym="Magyar" data-language-local-name="ungarsk" 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%B8%D0%BC%D0%BF%D0%B5%D0%B4%D0%B0%D0%BD%D1%81%D0%B0" title="Електрична импеданса – makedonsk" lang="mk" hreflang="mk" data-title="Електрична импеданса" data-language-autonym="Македонски" data-language-local-name="makedonsk" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Impedantie" title="Impedantie – nederlandsk" lang="nl" hreflang="nl" data-title="Impedantie" data-language-autonym="Nederlands" data-language-local-name="nederlandsk" class="interlanguage-link-target"><span>Nederlands</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%94%E3%83%BC%E3%83%80%E3%83%B3%E3%82%B9" title="インピーダンス – japansk" lang="ja" hreflang="ja" data-title="インピーダンス" data-language-autonym="日本語" data-language-local-name="japansk" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-nap mw-list-item"><a href="https://nap.wikipedia.org/wiki/Impedenza" title="Impedenza – napolitansk" lang="nap" hreflang="nap" data-title="Impedenza" data-language-autonym="Napulitano" data-language-local-name="napolitansk" class="interlanguage-link-target"><span>Napulitano</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Impedancja" title="Impedancja – polsk" lang="pl" hreflang="pl" data-title="Impedancja" data-language-autonym="Polski" data-language-local-name="polsk" 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/Imped%C3%A2ncia_el%C3%A9trica" title="Impedância elétrica – portugisisk" lang="pt" hreflang="pt" data-title="Impedância elétrica" data-language-autonym="Português" data-language-local-name="portugisisk" 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/Impedan%C8%9B%C4%83_electric%C4%83" title="Impedanță electrică – rumensk" lang="ro" hreflang="ro" data-title="Impedanță electrică" data-language-autonym="Română" data-language-local-name="rumensk" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%AD%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B8%D0%B9_%D0%B8%D0%BC%D0%BF%D0%B5%D0%B4%D0%B0%D0%BD%D1%81" title="Электрический импеданс – russisk" lang="ru" hreflang="ru" data-title="Электрический импеданс" data-language-autonym="Русский" data-language-local-name="russisk" 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/Impedanca_elektrike" title="Impedanca elektrike – albansk" lang="sq" hreflang="sq" data-title="Impedanca elektrike" data-language-autonym="Shqip" data-language-local-name="albansk" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B7%80%E0%B7%92%E0%B6%AF%E0%B7%8A%E2%80%8D%E0%B6%BA%E0%B7%94%E0%B6%AD%E0%B7%8A_%E0%B7%83%E0%B6%B8%E0%B7%8A%E0%B6%B6%E0%B7%8F%E0%B6%B0%E0%B6%B1%E0%B6%BA" title="විද්‍යුත් සම්බාධනය – singalesisk" lang="si" hreflang="si" data-title="විද්‍යුත් සම්බාධනය" data-language-autonym="සිංහල" data-language-local-name="singalesisk" 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/Electrical_impedance" title="Electrical impedance – enkel engelsk" lang="en-simple" hreflang="en-simple" data-title="Electrical impedance" data-language-autonym="Simple English" data-language-local-name="enkel engelsk" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Impedancia" title="Impedancia – slovakisk" lang="sk" hreflang="sk" data-title="Impedancia" data-language-autonym="Slovenčina" data-language-local-name="slovakisk" 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/Impedanca" title="Impedanca – slovensk" lang="sl" hreflang="sl" data-title="Impedanca" data-language-autonym="Slovenščina" data-language-local-name="slovensk" 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%95%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%B8%D1%87%D0%BD%D0%B0_%D0%B8%D0%BC%D0%BF%D0%B5%D0%B4%D0%B0%D0%BD%D1%81%D0%B0" title="Електрична импеданса – serbisk" lang="sr" hreflang="sr" data-title="Електрична импеданса" data-language-autonym="Српски / srpski" data-language-local-name="serbisk" 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/Elektri%C4%8Dna_impedansa" title="Električna impedansa – serbokroatisk" lang="sh" hreflang="sh" data-title="Električna impedansa" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbokroatisk" 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/Impedanssi" title="Impedanssi – finsk" lang="fi" hreflang="fi" data-title="Impedanssi" data-language-autonym="Suomi" data-language-local-name="finsk" class="interlanguage-link-target"><span>Suomi</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%A9%E0%AF%86%E0%AE%A4%E0%AE%BF%E0%AE%B0%E0%AF%8D%E0%AE%AA%E0%AF%8D%E0%AE%AA%E0%AF%81" title="மின்னெதிர்ப்பு – tamil" lang="ta" hreflang="ta" data-title="மின்னெதிர்ப்பு" data-language-autonym="தமிழ்" data-language-local-name="tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%AD%E0%B8%B4%E0%B8%A1%E0%B8%9E%E0%B8%B5%E0%B9%81%E0%B8%94%E0%B8%99%E0%B8%8B%E0%B9%8C" title="อิมพีแดนซ์ – thai" lang="th" hreflang="th" data-title="อิมพีแดนซ์" data-language-autonym="ไทย" data-language-local-name="thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/%C3%96z_empedans" title="Öz empedans – tyrkisk" lang="tr" hreflang="tr" data-title="Öz empedans" data-language-autonym="Türkçe" data-language-local-name="tyrkisk" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%95%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%B8%D1%87%D0%BD%D0%B8%D0%B9_%D1%96%D0%BC%D0%BF%D0%B5%D0%B4%D0%B0%D0%BD%D1%81" title="Електричний імпеданс – ukrainsk" lang="uk" hreflang="uk" data-title="Електричний імпеданс" data-language-autonym="Українська" data-language-local-name="ukrainsk" 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%A8%D8%B1%D9%82%DB%8C_%D9%85%D8%B3%D8%AF%D9%88%D8%AF%DB%8C%D8%AA" title="برقی مسدودیت – urdu" lang="ur" hreflang="ur" data-title="برقی مسدودیت" 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/Tr%E1%BB%9F_kh%C3%A1ng" title="Trở kháng – vietnamesisk" lang="vi" hreflang="vi" data-title="Trở kháng" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamesisk" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E9%98%BB%E6%8A%97" title="阻抗 – wu" lang="wuu" hreflang="wuu" data-title="阻抗" 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%9E%D7%A4%D7%A2%D7%93%D7%90%D7%A0%D7%A5" title="אימפעדאנץ – jiddisk" lang="yi" hreflang="yi" data-title="אימפעדאנץ" data-language-autonym="ייִדיש" data-language-local-name="jiddisk" 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%E9%98%BB%E6%8A%97" title="電阻抗 – kantonesisk" lang="yue" hreflang="yue" data-title="電阻抗" data-language-autonym="粵語" data-language-local-name="kantonesisk" 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/%E9%98%BB%E6%8A%97" title="阻抗 – kinesisk" lang="zh" hreflang="zh" data-title="阻抗" data-language-autonym="中文" data-language-local-name="kinesisk" 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/Q179043#sitelinks-wikipedia" title="Rediger lenker til artikkelen på andre språk" class="wbc-editpage">Rediger lenker</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="Navnerom"> <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/Impedans" title="Vis innholdssiden [c]" accesskey="c"><span>Artikkel</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Diskusjon:Impedans" rel="discussion" title="Diskusjon om innholdssiden [t]" accesskey="t"><span>Diskusjon</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="Bytt språkvariant" > <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">norsk bokmål</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="Visninger"> <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/Impedans"><span>Les</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Impedans&veaction=edit" title="Rediger siden [v]" accesskey="v"><span>Rediger</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Impedans&action=edit" title="Rediger kildekoden for denne siden [e]" accesskey="e"><span>Rediger kilde</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Impedans&action=history" title="Tidligere sideversjoner av denne siden [h]" accesskey="h"><span>Vis historikk</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Sideverktøy"> <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="Verktøy" > <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">Verktøy</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">Verktøy</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">flytt til sidefeltet</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">skjul</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Flere alternativer" > <div class="vector-menu-heading"> Handlinger </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/Impedans"><span>Les</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Impedans&veaction=edit" title="Rediger siden [v]" accesskey="v"><span>Rediger</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Impedans&action=edit" title="Rediger kildekoden for denne siden [e]" accesskey="e"><span>Rediger kilde</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Impedans&action=history"><span>Vis historikk</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Generelt </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Spesial:Lenker_hit/Impedans" title="Liste over alle wikisider som lenker hit [j]" accesskey="j"><span>Lenker hit</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Spesial:Relaterte_endringer/Impedans" rel="nofollow" title="Siste endringer i sider som blir lenket fra denne siden [k]" accesskey="k"><span>Relaterte endringer</span></a></li><li id="t-upload" class="mw-list-item"><a href="//commons.wikimedia.org/wiki/Special:UploadWizard?uselang=no" title="Last opp filer [u]" accesskey="u"><span>Last opp fil</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Impedans&oldid=24393641" title="Permanent lenke til denne versjonen av siden"><span>Permanent lenke</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Impedans&action=info" title="Mer informasjon om denne siden"><span>Sideinformasjon</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Spesial:Siteringshjelp&page=Impedans&id=24393641&wpFormIdentifier=titleform" title="Informasjon om hvordan denne siden kan siteres"><span>Siter denne siden</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Spesial:UrlShortener&url=https%3A%2F%2Fno.wikipedia.org%2Fwiki%2FImpedans"><span>Hent forkortet URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Spesial:QrCode&url=https%3A%2F%2Fno.wikipedia.org%2Fwiki%2FImpedans"><span>Last ned QR-kode</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"> Skriv ut / eksporter </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=Spesial:DownloadAsPdf&page=Impedans&action=show-download-screen"><span>Last ned som PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Impedans&printable=yes" title="Utskriftsvennlig versjon av denne siden [p]" accesskey="p"><span>Utskriftsvennlig versjon</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"> På andre prosjekter </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/Category:Electrical_impedance" 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/Q179043" title="Lenke til koblet dataregisterelement [g]" accesskey="g"><span>Wikidata-element</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="Sideverktøy"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Utseende"> <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">Utseende</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">flytt til sidefeltet</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">skjul</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">Fra Wikipedia, den frie encyklopedi</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="nb" dir="ltr"><style data-mw-deduplicate="TemplateStyles:r24553676">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}html.client-js body.skin-minerva .mw-parser-output .mbox-text-span{margin-left:23px!important}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}</style><table class="plainlinks metadata ambox ambox-content ambox-Unsourced" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/Fil:Question_book-new.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span"><b>Kildeløs</b>: Denne artikkelen mangler <a href="/wiki/Wikipedia:Bruk_av_kilder" title="Wikipedia:Bruk av kilder">kildehenvisninger</a>, og opplysningene i den kan dermed være vanskelige å <a href="/wiki/Wikipedia:Verifiserbarhet" title="Wikipedia:Verifiserbarhet">verifisere</a>. Kildeløst materiale kan bli <a href="/wiki/Wikipedia:Verifiserbarhet#Bevisbyrden" title="Wikipedia:Verifiserbarhet">fjernet</a>. Helt uten kilder. <span class="date-container"><i>(<span class="date">10. okt. 2015</span>)</i></span></div></td></tr></tbody></table> <p><b>Impedans</b>, også kalt <b>vekselstrømsmotstand</b>, er forholdet mellom vekselspenning over og vekselstrøm gjennom en <a href="/wiki/Topol" class="mw-disambig" title="Topol">topol</a> ved en gitt frekvens. Impedansens størrelse er (matematisk) <a href="/wiki/Komplekst_tall" title="Komplekst tall">kompleks</a>. </p><p>Begrepet impedans er en utvidelse av begrepet <a href="/wiki/Motstand_(resistans)" class="mw-redirect" title="Motstand (resistans)">resistans</a>, og trengs når betraktningen utvides til å inkludere <a href="/wiki/Reaktans" title="Reaktans">reaktanser</a> i tillegg til resistanser, det vil si når likestrømsbetraktninger utvides til vekselstrømsbetraktninger. Reaktanser, og derfor også impedanser, har frekvensavhengig motstand for strømledning. </p><p>Impedansen erstatter resistansen i formelen <b>R = U/I,</b> og <b>U</b> og <b>I</b> er nå vekselspenning og -strøm. Impedansen får bokstaven <b>Z</b> som symbol i stedet for <b>R</b>, og måles også i <b><a href="/wiki/Ohm" title="Ohm">Ohm</a>,</b> eller <b><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 mathvariant="normal">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/24b0d5ca6f381068d756f6337c08e0af9d1eeb6f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \Omega }" /></span></b>. </p><p><b>Z = u/i</b>, der små bokstaver gjelder vekselstørrelser. </p> <ul><li>En <b>impedans</b> er satt sammen som en seriekopling av to komponenter, en <b>reaktans</b> og en <b>resistans</b>.</li> <li>En <b>reaktans</b> kan være enten en <a href="/wiki/Kapasitans" title="Kapasitans">kapasitans</a> eller en <a href="/wiki/Induktans" title="Induktans">induktans</a>, som uttrykk for virkningene av henholdsvis en <a href="/wiki/Kondensator_(elektrisk)" title="Kondensator (elektrisk)">kondensator</a> eller en <a href="/wiki/Spole_(induktans)" title="Spole (induktans)">spole</a>.</li></ul> <p>For hver frekvens finnes alltid <i>én</i> reaktansverdi og <i>én</i> resistansverdi for topolen, og vektorsummen deres utgjør impedansen ved denne frekvensen. Dette gjelder for alle tenkelige (linjære) nettverk mellom polene, uten begrensning av antall resistanser og reaktanser som den består av. Reaktansens fortegn bestemmer typen; en negativ reaktans er kapasitiv og en positiv reaktans er induktiv. Ved frekvensendring er det særlig reaktansen <b>X</b> som endrer sin verdi, verdien av <b>R</b> er i forhold langt mer konstant. </p> <figure typeof="mw:File/Thumb"><a href="/wiki/Fil:Complex_Impedance.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Complex_Impedance.svg/200px-Complex_Impedance.svg.png" decoding="async" width="200" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Complex_Impedance.svg/300px-Complex_Impedance.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Complex_Impedance.svg/400px-Complex_Impedance.svg.png 2x" data-file-width="200" data-file-height="200" /></a><figcaption>Vektorfremstilling av resistans <b>R</b>, reaktans <b>X</b> (her: induktans) og resulterende impedans <b>Z</b>. Her ses impedansens verdi som lengden <b>|Z|</b>, samt dens fasevinkel <b>θ</b>. Aksene kalles den reelle (<b>Re</b>, horisontal) og den imaginære aksen (<b>Im</b>, vertikal).</figcaption></figure> <p><b>Impedansen</b>, seriekoplingen av resistansen og reaktansen blir: </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 \mathbb {Z} =R+jX}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mo>=</mo> <mi>R</mi> <mo>+</mo> <mi>j</mi> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {Z} =R+jX}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8683eaecb8d85c557b111e71e63ab5afa7e522c7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.191ex; height:2.509ex;" alt="{\displaystyle \mathbb {Z} =R+jX}" /></span></dd></dl> <p>hvor </p> <ul><li><i><b>Z</b></i> er impedansen</li> <li><i><b>X</b></i> er reaktansen</li> <li><i><b>R</b></i> er resistansen</li></ul> <p>alle målt i <b>Ohm</b> [<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 mathvariant="normal">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/24b0d5ca6f381068d756f6337c08e0af9d1eeb6f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \Omega }" /></span>]. </p> <ul><li><b>j</b> er den imaginære enheten fra komplekse tall i matematikken.</li></ul> <p>Siden resistanser og reaktanser er <a href="/wiki/Ortogonalitet" title="Ortogonalitet">ortogonale</a> til hverandre i tid (derfor "<b>j</b>", se senere i artikkelen), kan ikke Ohmverdiene deres bare adderes. Impedansen er vektorsummen. </p><p>Resistansen står for energitapet i topolen. De reaktive komponentene, reaktansene, opptar og avgir elektrisk energi i løpet av signalets periode, men de avgir aldri energi i form av varme. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Reaktanser_for_komponentene_kapasitet_og_induktivitet">Reaktanser for komponentene kapasitet og induktivitet</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Impedans&veaction=edit&section=1" title="Rediger avsnitt: Reaktanser for komponentene kapasitet og induktivitet" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Impedans&action=edit&section=1" title="Rediger kildekoden til seksjonen Reaktanser for komponentene kapasitet og induktivitet"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>For en gitt, fast verdi av komponenten <b>kondensator</b> eller <b>spole</b> blir den tilhørende reaktansen frekvensavhengig. Sammenhengene er som følger, hvor <b>X</b> er størrelsen av reaktansen. </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_{C}={1 \over {j\cdot 2\cdot \pi \cdot f\cdot C}}={1 \over {j\cdot \omega \cdot C}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mo>⋅</mo> <mn>2</mn> <mo>⋅</mo> <mi>π</mi> <mo>⋅</mo> <mi>f</mi> <mo>⋅</mo> <mi>C</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mo>⋅</mo> <mi>ω</mi> <mo>⋅</mo> <mi>C</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X_{C}={1 \over {j\cdot 2\cdot \pi \cdot f\cdot C}}={1 \over {j\cdot \omega \cdot C}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4aa83174bdf2c501e48d8cca8b6edce41c246734" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:32.017ex; height:5.676ex;" alt="{\displaystyle X_{C}={1 \over {j\cdot 2\cdot \pi \cdot f\cdot C}}={1 \over {j\cdot \omega \cdot C}}}" /></span> for en <b>kondensator</b>,</dd> <dd>som helst uttrykkes som <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X_{C}={-j \over {2\cdot \pi \cdot f\cdot C}}={-j \over {\omega \cdot C}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo>−</mo> <mi>j</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mo>⋅</mo> <mi>π</mi> <mo>⋅</mo> <mi>f</mi> <mo>⋅</mo> <mi>C</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo>−</mo> <mi>j</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> <mo>⋅</mo> <mi>C</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X_{C}={-j \over {2\cdot \pi \cdot f\cdot C}}={-j \over {\omega \cdot C}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53820a7b0adea85b0a02fabb73649f517a7ea8fe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:26.743ex; height:5.843ex;" alt="{\displaystyle X_{C}={-j \over {2\cdot \pi \cdot f\cdot C}}={-j \over {\omega \cdot C}}}" /></span> fordi nevneren da er reell.</dd> <dd>Tallverdien blir <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |X_{C}|={1 \over {2\cdot \pi \cdot f\cdot C}}={1 \over {\omega \cdot C}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mo>⋅</mo> <mi>π</mi> <mo>⋅</mo> <mi>f</mi> <mo>⋅</mo> <mi>C</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> <mo>⋅</mo> <mi>C</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |X_{C}|={1 \over {2\cdot \pi \cdot f\cdot C}}={1 \over {\omega \cdot C}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/02fb30d3b5580eb5798f085a6ca6365a4a85152e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:28.036ex; height:5.676ex;" alt="{\displaystyle |X_{C}|={1 \over {2\cdot \pi \cdot f\cdot C}}={1 \over {\omega \cdot C}}}" /></span></dd></dl> <p>og for en <b>spole</b>: </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_{L}={j\cdot 2\cdot \pi \cdot f\cdot L}={j\cdot \omega \cdot L}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mo>⋅</mo> <mn>2</mn> <mo>⋅</mo> <mi>π</mi> <mo>⋅</mo> <mi>f</mi> <mo>⋅</mo> <mi>L</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mo>⋅</mo> <mi>ω</mi> <mo>⋅</mo> <mi>L</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X_{L}={j\cdot 2\cdot \pi \cdot f\cdot L}={j\cdot \omega \cdot L}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/06dcc0be00667a04e24ab3e9301b550f18e1e1b7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:29.848ex; height:2.509ex;" alt="{\displaystyle X_{L}={j\cdot 2\cdot \pi \cdot f\cdot L}={j\cdot \omega \cdot L}}" /></span></dd> <dd>Tallverdien blir <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_{L}|={2\cdot \pi \cdot f\cdot L}={\omega \cdot L}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mo>⋅</mo> <mi>π</mi> <mo>⋅</mo> <mi>f</mi> <mo>⋅</mo> <mi>L</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> <mo>⋅</mo> <mi>L</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |X_{L}|={2\cdot \pi \cdot f\cdot L}={\omega \cdot L}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/29d4d25b7c5a458b7ded2d2632598689dc0d7c3e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:25.867ex; height:2.843ex;" alt="{\displaystyle |X_{L}|={2\cdot \pi \cdot f\cdot L}={\omega \cdot L}}" /></span></dd></dl> <p>hvor </p> <dl><dd><ul><li>C er kapasitansen i <a href="/wiki/Farad" title="Farad">Farad</a></li> <li>L er induktiviteten i <a href="/wiki/Henry_(enhet)" title="Henry (enhet)">Henry</a></li> <li>f er frekvensen i <a href="/wiki/Hz" class="mw-redirect" title="Hz">Hz</a> eller [perioder/sek]</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 \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> er vinkelfrekvensen i [radianer/sek]</li> <li>1 <a href="/wiki/Radian" title="Radian">radian</a> = 360 grader/<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 \ 2\pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mn>2</mn> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ 2\pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/685e78ce3c69cf9cc2e1330f60f80e5beb6029c4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.075ex; height:2.176ex;" alt="{\displaystyle \ 2\pi }" /></span></li> <li><b>j</b> plasserer <b>X</b> på den imaginære aksen, og her ses hvorfor kapasitansen <b>X<sub>C</sub></b> alltid er negativ.</li></ul></dd></dl> <p>Tallverdien for reaktansen til en spole er proporsjonal med frekvensen, mens tallverdien for kondensatorens reaktans er omvendt proporsjonal med frekvensen. </p><p>Komponenter er ikke perfekte; kondensatorer og (særlig) spoler er i praksis beheftet med noe <b>energitap,</b> som gjerne er frekvensavhengig. Det føyes en serieresistans til komponentens symbol for å beskrive dette. </p> <div class="mw-heading mw-heading2"><h2 id="Inverse_verdier,_ledningsevner"><span id="Inverse_verdier.2C_ledningsevner"></span>Inverse verdier, ledningsevner</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Impedans&veaction=edit&section=2" title="Rediger avsnitt: Inverse verdier, ledningsevner" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Impedans&action=edit&section=2" title="Rediger kildekoden til seksjonen Inverse verdier, ledningsevner"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>For parallellkopling blir matematikken mye enklere ved bruk av de inverse verdiene av resistansen og reaktansen i formlene. De inverse størrelsene kalles </p> <dl><dd><i>Suseptans</i>, <b>B = 1/X</b> som den inverse av reaktans <b>X</b>. Måles i <a href="/wiki/Siemens_(enhet)" title="Siemens (enhet)">Siemens</a> [<b>S</b>] eller <b>Mho</b></dd> <dd><i>Admittans</i>, <b>Y =1/Z</b> som den inverse av impedans <b>Z</b>. Måles i Siemens [<b>S</b>] eller <b>Mho</b></dd></dl> <p>En positiv suseptans er kapasitiv og en negativ suseptans er induktiv (!). </p><p>Admittansen, parallellkoplingen av konduktansen <b>G = 1/R</b> og suseptansen <b>B=1/X</b> blir <b>Y=G+jB</b> </p><p>hvor </p> <dl><dd><b>Y</b> er admittansen</dd> <dd><b>B</b> er suseptansen</dd> <dd><b>G</b> er konduktansen</dd></dl> <p>alle målt i Siemens (<b>S</b>), eller <b>Mho.</b> </p><p>Se ellers <a href="/wiki/Motstand_(resistans)" class="mw-redirect" title="Motstand (resistans)">motstand</a> for videre formler. </p> <div class="mw-heading mw-heading2"><h2 id="Topoler_med_resistanser_og_reaktanser">Topoler med resistanser og reaktanser</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Impedans&veaction=edit&section=3" title="Rediger avsnitt: Topoler med resistanser og reaktanser" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Impedans&action=edit&section=3" title="Rediger kildekoden til seksjonen Topoler med resistanser og reaktanser"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Det er ved frekvenser som frembringer de samme absoluttverdier for reaktans og resistans (som ved lav- og høypassfiltre, se <a href="/wiki/Pol_(elektronikk)" title="Pol (elektronikk)">pol</a>), eller like absoluttverdier for induktivitet og kapasitet (som ved resonans), at grense- eller resonansfrekvenser for den tiltenkte funksjonen finnes. I det videre gjelder altså <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ |X_{C}|=R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>=</mo> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ |X_{C}|=R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bdde8bbfea1ea896acf1f2a241c33513ddf8534e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.142ex; height:2.843ex;" alt="{\displaystyle \ |X_{C}|=R}" /></span> (pol) eller<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_{L}|=R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>=</mo> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ |X_{L}|=R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a52c716cdf0461b1d648cee06cf66c830738dbd1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.013ex; height:2.843ex;" alt="{\displaystyle \ |X_{L}|=R}" /></span> (pol) eller<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ |X_{C}|=|X_{L}|}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ |X_{C}|=|X_{L}|}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b12285e9ee75182113034106e3c9fe1aea9fc905" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.948ex; height:2.843ex;" alt="{\displaystyle \ |X_{C}|=|X_{L}|}" /></span>(resonans, som har en dobbelt pol). Lave og høye frekvenser i forhold til den frekvensen som oppfyller likheten kommenteres også nedenfor. </p><p><b>R og C i serie</b> </p> <dl><dd>Lav f: Z går mot X<sub>C</sub>, går mot uendelig</dd> <dd>Grense: <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|={\sqrt {2}}\cdot R={\sqrt {2}}\cdot |X_{C}|}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <mo>⋅</mo> <mi>R</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ |Z|={\sqrt {2}}\cdot R={\sqrt {2}}\cdot |X_{C}|}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fbfbaedcd7a9705d671357f8902653f0419847b0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:25.77ex; height:3.176ex;" alt="{\displaystyle \ |Z|={\sqrt {2}}\cdot R={\sqrt {2}}\cdot |X_{C}|}" /></span></dd> <dd>Høy f: Z går mot R</dd></dl> <p><b>R og C i parallell</b> </p> <dl><dd>Lav f: Z går mot R</dd> <dd>Grense: <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|={R \over {\sqrt {2}}}={|X_{C}| \over {\sqrt {2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ |Z|={R \over {\sqrt {2}}}={|X_{C}| \over {\sqrt {2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b1ceab9eaa38d6637a6c54f502d9c9fa5fa1742" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:19.221ex; height:6.676ex;" alt="{\displaystyle \ |Z|={R \over {\sqrt {2}}}={|X_{C}| \over {\sqrt {2}}}}" /></span></dd> <dd>Høy f: Z går mot X<sub>C</sub>, som går mot null</dd></dl> <p><b>R og L i serie</b> </p> <dl><dd>Lav f: Z går mot R</dd> <dd>Grense: <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|={\sqrt {2}}\cdot R={\sqrt {2}}\cdot |X_{C}|}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <mo>⋅</mo> <mi>R</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ |Z|={\sqrt {2}}\cdot R={\sqrt {2}}\cdot |X_{C}|}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fbfbaedcd7a9705d671357f8902653f0419847b0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:25.77ex; height:3.176ex;" alt="{\displaystyle \ |Z|={\sqrt {2}}\cdot R={\sqrt {2}}\cdot |X_{C}|}" /></span></dd> <dd>Høy f: Z går mot X<sub>L</sub>, som går mot uendelig</dd></dl> <p><b>R og L i parallell</b> </p> <dl><dd>Lav f: Z går mot X<sub>L</sub>, går mot null</dd> <dd>Grense: <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|={R \over {\sqrt {2}}}={|X_{C}| \over {\sqrt {2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ |Z|={R \over {\sqrt {2}}}={|X_{C}| \over {\sqrt {2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b1ceab9eaa38d6637a6c54f502d9c9fa5fa1742" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:19.221ex; height:6.676ex;" alt="{\displaystyle \ |Z|={R \over {\sqrt {2}}}={|X_{C}| \over {\sqrt {2}}}}" /></span></dd> <dd>Høy f: Z går mot R</dd></dl> <p><b>C og L i serie</b> </p> <dl><dd>Lav f: C dominerer, |Z| høy, går mot uendelig</dd> <dd>Z går mot X<sub>L</sub>+X<sub>C</sub>, som går mot null siden Xc er negativ (serieresonans)</dd> <dd>Høy f: L dominerer, |Z| høy, går mot uendelig</dd></dl> <p><b>C og L i parallell</b> </p> <dl><dd>Lav f: L dominerer, |Z| lav, går mot null</dd> <dd>Z går mot X<sub>L</sub>*X<sub>C</sub>/(X<sub>L</sub>+X<sub>C</sub>) som går mot uendelig (Xc er negativ, nevneren går mot null, parallellresonans)</dd> <dd>Høy f: C dominerer, |Z| lav, går mot null</dd></dl> <p>Ved <b>resonans</b> er begge reaktansene like store, altså er </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 \ {1 \over \omega C}={\omega L}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>ω</mi> <mi>C</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> <mi>L</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ {1 \over \omega C}={\omega L}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5b83d5aba69ac755fcc881f2dd0c61a9fc8b0054" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:10.756ex; height:5.343ex;" alt="{\displaystyle \ {1 \over \omega C}={\omega L}}" /></span> og fra dette finner vi</dd> <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 \ \omega ^{2}={1 \over {LC}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msup> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> <mi>C</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \omega ^{2}={1 \over {LC}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86af488b35361a937ec20f512ed8e0e4b4bb60d8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:10.364ex; height:5.343ex;" alt="{\displaystyle \ \omega ^{2}={1 \over {LC}}}" /></span> og</dd> <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 {2\pi f}={\omega }={1 \over {\sqrt {LC}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mi>π</mi> <mi>f</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>L</mi> <mi>C</mi> </msqrt> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {2\pi f}={\omega }={1 \over {\sqrt {LC}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1517762a7f4b76bf7b3774975fb818ddb92df74c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:17.537ex; height:6.176ex;" alt="{\displaystyle {2\pi f}={\omega }={1 \over {\sqrt {LC}}}}" /></span> og</dd> <dd>resonansfrekvensen blir<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={1 \over {2\pi {\sqrt {LC}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>f</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>L</mi> <mi>C</mi> </msqrt> </mrow> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ f={1 \over {2\pi {\sqrt {LC}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1a4406b05d00619f1c7cd9277158d34bbb779c92" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:13.573ex; height:6.176ex;" alt="{\displaystyle \ f={1 \over {2\pi {\sqrt {LC}}}}}" /></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Analogier">Analogier</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Impedans&veaction=edit&section=4" title="Rediger avsnitt: Analogier" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Impedans&action=edit&section=4" title="Rediger kildekoden til seksjonen Analogier"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Det er ofte lettere å få begrep om kompliserte forhold hvis vi bruker analogier til mer dagligdagse ting som vi alt har en brukbar forestilling om. Her assosieres den elektriske spenningen med kraft og strømmen med hastighet. Analogien her er god fordi matematisk behandling av begge systemene frembringer de samme løsningene på differensialligningene. Energibetraktninger er <i>ikke</i> gyldige i denne anlogien. </p> <ul><li><b>Kapasitans</b> kan assosieres med en <b>spiralfjær</b>. Kondensatoren lades = fjæra trekkes ut (positiv spenning) eller stuves sammen (negativ spenning). En høy kapasitet tilsvarer en slapp fjær. Når fjæra går tilbake gis energien tilbake; bevegelsen frem og tilbake koster ikke energi.</li> <li><b>Induktans</b> kan betraktes som en <b>masse,</b> eksempelvis målt i <b>kg</b>. Massen tilføres energi ved flytting høyere opp i rommet. En høy induktivitet tilsvarer en stor masse. Det er ikke energiforbruk ved å flytte massen opp og så ned igjen; når massen senkes gis energien tilbake.</li> <li><b>Resistans</b> tilsvarer friksjon. Det er bare ved friksjon at omgivelsene tilføres varme, noe som koster energi.</li> <li><b>Resonansfrekvensen</b> ved induktans og kapasitans tilsvarer resonansfrekvensen som ses ved at massen henges i fjæra (som på den andre siden er fast til en referanse, eksempelvis et tak eller en bjelke) og så eksitere massen med en dult i retning langs fjæra. Det er ved svingningene som oppstår at kraft og hastighet skifter periodisk på, ved resonansfrekvensen. Frekvensen øker for mindre masser og stivere fjærer, altså for mindre induktiviteter og mindre kapasiteter.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Matematisk_grunnlag">Matematisk grunnlag</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Impedans&veaction=edit&section=5" title="Rediger avsnitt: Matematisk grunnlag" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Impedans&action=edit&section=5" title="Rediger kildekoden til seksjonen Matematisk grunnlag"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><b>Kapasitansen</b> koplet til en spenningskilde fører størst strøm når spenningen stiger hurtigst. Uttrykt matematisk: Strømmen er proporsjonal til den deriverte av spenningen, du/dt.</li> <li><b>Induktansen</b> koplet til en strømkilde oppviser størst spenning når strømmen økes hurtigst. Tilsvarende er spenningen proporsjonal til den deriverte av strømmen, dI/dt.</li></ul> <p>Med formler: </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}={C\cdot {dU \over dt}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>I</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>U</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {I}={C\cdot {dU \over dt}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a5f6cf29259f151bfab49bed0153b5d6de4995b0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:11.55ex; height:5.509ex;" alt="{\displaystyle {I}={C\cdot {dU \over dt}}}" /></span> for kapasitet <br /></dd> <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 {U}={L\cdot {dI \over dt}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>U</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>L</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> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {U}={L\cdot {dI \over dt}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2aca37db1c8b3b856131c63d649b738889973821" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:11.367ex; height:5.509ex;" alt="{\displaystyle {U}={L\cdot {dI \over dt}}}" /></span> for induktivitet</dd> <dd></dd></dl> <p><b>Regneeksempel:</b> Vi bruker en motstand på 150 Ohm koplet i serie med en kondensator på 1.2 µF og en spole på 3.3 mH. Impedansen blir generelt: </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=}150-{j \over {\omega C}}+{j\omega L}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mi>Z</mi> <mo>=</mo> </mrow> <mn>150</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>j</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> <mi>C</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mi>ω</mi> <mi>L</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ {Z=}150-{j \over {\omega C}}+{j\omega L}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5e4d73cacb629a7c6886da1c064190304cc2337f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:21.917ex; height:5.509ex;" alt="{\displaystyle \ {Z=}150-{j \over {\omega C}}+{j\omega L}}" /></span></dd></dl> <dl><dd><dl><dd><ul><li><dl><dd>Ved <b>2kHz</b> er <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"> <mtext> </mtext> <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/abf2c1eb8ec34fbb75667b7bf5345c987c05ea33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.026ex; height:1.676ex;" alt="{\displaystyle \ \omega }" /></span> ca. 12566 rad/sek og</dd></dl></li></ul></dd></dl></dd></dl> <dl><dd><dl><dd><ul><li><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=150-j66.3+j41.5[\Omega ]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>Z</mi> <mo>=</mo> <mn>150</mn> <mo>−</mo> <mi>j</mi> <mn>66.3</mn> <mo>+</mo> <mi>j</mi> <mn>41.5</mn> <mo stretchy="false">[</mo> <mi mathvariant="normal">Ω</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ Z=150-j66.3+j41.5[\Omega ]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fe4c0f1c4a0aa6d3e0395808528cffce0a15912a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:27.684ex; height:2.843ex;" alt="{\displaystyle \ Z=150-j66.3+j41.5[\Omega ]}" /></span></dd> <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=150-j24.8[\Omega ]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>Z</mi> <mo>=</mo> <mn>150</mn> <mo>−</mo> <mi>j</mi> <mn>24.8</mn> <mo stretchy="false">[</mo> <mi mathvariant="normal">Ω</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ Z=150-j24.8[\Omega ]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8531bf1cf097006a5354b08b887fc52e9143a0c2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.751ex; height:2.843ex;" alt="{\displaystyle \ Z=150-j24.8[\Omega ]}" /></span></dd></dl></li></ul></dd></dl></dd></dl> <dl><dd><dl><dd><ul><li><dl><dd>Impedansen domineres av resistansen og er ellers kapasitiv</dd></dl></li></ul></dd></dl></dd></dl> <dl><dd><dl><dd><ul><li><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 }={{\tan ^{-1}}\left({X \over R}\right)}={\tan ^{-1}-0.1653}=-9.39\mathrm {\ grader} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mi>ϕ</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>tan</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>X</mi> <mi>R</mi> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>tan</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>−</mo> <mn>0.1653</mn> </mrow> <mo>=</mo> <mo>−</mo> <mn>9.39</mn> <mrow class="MJX-TeXAtom-ORD"> <mtext> </mtext> <mi mathvariant="normal">g</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">r</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ {\phi }={{\tan ^{-1}}\left({X \over R}\right)}={\tan ^{-1}-0.1653}=-9.39\mathrm {\ grader} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6b9daf550d197950aab1d2bff753baa95f3450f3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:50.921ex; height:6.176ex;" alt="{\displaystyle \ {\phi }={{\tan ^{-1}}\left({X \over R}\right)}={\tan ^{-1}-0.1653}=-9.39\mathrm {\ grader} }" /></span></dd></dl></li></ul></dd></dl></dd></dl> <dl><dd><dl><dd><ul><li><dl><dd>Impedansens størrelse blir:</dd> <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|={\sqrt {R^{2}+X^{2}}}={\sqrt {22500+615}}=\mathrm {\ ca.\ } 152[\Omega ]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>22500</mn> <mo>+</mo> <mn>615</mn> </msqrt> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext> </mtext> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">a</mi> <mo>.</mo> <mtext> </mtext> </mrow> <mn>152</mn> <mo stretchy="false">[</mo> <mi mathvariant="normal">Ω</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ |Z|={\sqrt {R^{2}+X^{2}}}={\sqrt {22500+615}}=\mathrm {\ ca.\ } 152[\Omega ]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c8676b030beadfb1a54270096db3f2dba16dc8cc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:48.809ex; height:3.509ex;" alt="{\displaystyle \ |Z|={\sqrt {R^{2}+X^{2}}}={\sqrt {22500+615}}=\mathrm {\ ca.\ } 152[\Omega ]}" /></span></dd></dl></li></ul></dd></dl></dd></dl> <dl><dd><dl><dd><ul><li><dl><dd>Ved <b>20kHz</b> er <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"> <mtext> </mtext> <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/abf2c1eb8ec34fbb75667b7bf5345c987c05ea33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.026ex; height:1.676ex;" alt="{\displaystyle \ \omega }" /></span> ca. 125663 rad/sek og</dd></dl></li></ul></dd></dl></dd></dl> <dl><dd><dl><dd><ul><li><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=150-j6.63+j415[\Omega ]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>Z</mi> <mo>=</mo> <mn>150</mn> <mo>−</mo> <mi>j</mi> <mn>6.63</mn> <mo>+</mo> <mi>j</mi> <mn>415</mn> <mo stretchy="false">[</mo> <mi mathvariant="normal">Ω</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ Z=150-j6.63+j415[\Omega ]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/85206f9b9d41bbf95a880fdafe2d98b171819b1d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:27.037ex; height:2.843ex;" alt="{\displaystyle \ Z=150-j6.63+j415[\Omega ]}" /></span></dd> <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=150+j408[\Omega ]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>Z</mi> <mo>=</mo> <mn>150</mn> <mo>+</mo> <mi>j</mi> <mn>408</mn> <mo stretchy="false">[</mo> <mi mathvariant="normal">Ω</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ Z=150+j408[\Omega ]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1a3d2284e68e8d24161e1ac4294a9d78084e7415" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.104ex; height:2.843ex;" alt="{\displaystyle \ Z=150+j408[\Omega ]}" /></span></dd></dl></li></ul></dd></dl></dd></dl> <dl><dd><dl><dd><ul><li><dl><dd>Impedansen domineres av induktiviteten og er derfor induktiv</dd></dl></li></ul></dd></dl></dd></dl> <dl><dd><dl><dd><ul><li><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 }={{\tan ^{-1}}\left({X \over R}\right)}={\tan ^{-1}2.72}=69.8\mathrm {\ grader} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mi>ϕ</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>tan</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>X</mi> <mi>R</mi> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>tan</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>⁡</mo> <mn>2.72</mn> </mrow> <mo>=</mo> <mn>69.8</mn> <mrow class="MJX-TeXAtom-ORD"> <mtext> </mtext> <mi mathvariant="normal">g</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">r</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ {\phi }={{\tan ^{-1}}\left({X \over R}\right)}={\tan ^{-1}2.72}=69.8\mathrm {\ grader} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/69e1f3832ea8e1db0c1432369bcf8f1d2b51336f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:44.98ex; height:6.176ex;" alt="{\displaystyle \ {\phi }={{\tan ^{-1}}\left({X \over R}\right)}={\tan ^{-1}2.72}=69.8\mathrm {\ grader} }" /></span></dd></dl></li></ul></dd></dl></dd></dl> <dl><dd><dl><dd><ul><li><dl><dd>Impedansens størrelse blir:</dd> <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|={\sqrt {R^{2}+X^{2}}}={\sqrt {22500+166464}}=\mathrm {\ ca.\ } 435[\Omega ]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>22500</mn> <mo>+</mo> <mn>166464</mn> </msqrt> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext> </mtext> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">a</mi> <mo>.</mo> <mtext> </mtext> </mrow> <mn>435</mn> <mo stretchy="false">[</mo> <mi mathvariant="normal">Ω</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ |Z|={\sqrt {R^{2}+X^{2}}}={\sqrt {22500+166464}}=\mathrm {\ ca.\ } 435[\Omega ]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/95b7afd0810249b7343fc87e96a7ab19c8a561b2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:52.296ex; height:3.509ex;" alt="{\displaystyle \ |Z|={\sqrt {R^{2}+X^{2}}}={\sqrt {22500+166464}}=\mathrm {\ ca.\ } 435[\Omega ]}" /></span></dd></dl></li></ul></dd></dl></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Beskrivelse_med_kompleks_matematikk">Beskrivelse med kompleks matematikk</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Impedans&veaction=edit&section=6" title="Rediger avsnitt: Beskrivelse med kompleks matematikk" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Impedans&action=edit&section=6" title="Rediger kildekoden til seksjonen Beskrivelse med kompleks matematikk"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Impedanser kan beskrives ved hjelp av vektorer, men det er nokså tungvint. </p><p>Impedansbeskrivelser og kompleks matematikk har det til felles at begge bruker to størrelser som er ortogonale til hverandre, altså alltid står 90 grader på hverandre. Av den grunn passer denne grenen av matematikken ypperlig som verktøy for beskrivelse av og operasjoner med, impedanser. Begreper som imaginær og reell kommer fra matematikken som vi benytter, men det er ingenting som er imaginært med fysikken som vi betrakter. </p><p>Ved å definere reaktansen som imaginær, kan hele regelverket fra den komplekse matematikken brukes for å beskrive eller behandle kompliserte impedanser. </p><p>En impedans beskrives som </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 \mathbb {Z} =R+jX}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mo>=</mo> <mi>R</mi> <mo>+</mo> <mi>j</mi> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {Z} =R+jX}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8683eaecb8d85c557b111e71e63ab5afa7e522c7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.191ex; height:2.509ex;" alt="{\displaystyle \mathbb {Z} =R+jX}" /></span></dd></dl> <p>Impedansens tallverdi blir da: </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|={\sqrt {R^{2}+X^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |Z|={\sqrt {R^{2}+X^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/983a9501f84e0cf54844e3846d813335afa2d217" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.106ex; height:3.509ex;" alt="{\displaystyle |Z|={\sqrt {R^{2}+X^{2}}}}" /></span></dd></dl> <p>Fasevinkelen mellom R og X er </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 ={\tan ^{-1}\left({X \over R}\right)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϕ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>tan</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>X</mi> <mi>R</mi> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi ={\tan ^{-1}\left({X \over R}\right)}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bac4f84a72505b935c88ae8f39094171060bfa3a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:16.414ex; height:6.176ex;" alt="{\displaystyle \phi ={\tan ^{-1}\left({X \over R}\right)}}" /></span></dd></dl> <p>Beskrivelse av Z kan også gjøres med formelen </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=|Z|(\cos \phi +j\sin \phi )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>Z</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo stretchy="false">(</mo> <mi>cos</mi> <mo>⁡</mo> <mi>ϕ</mi> <mo>+</mo> <mi>j</mi> <mi>sin</mi> <mo>⁡</mo> <mi>ϕ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ Z=|Z|(\cos \phi +j\sin \phi )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/050a1a8b0ed58b64120ff108f127064c12e85011" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:23.84ex; height:2.843ex;" alt="{\displaystyle \ Z=|Z|(\cos \phi +j\sin \phi )}" /></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Beregning_for_parallellkopling_av_reaktans_og_resistans">Beregning for parallellkopling av reaktans og resistans</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Impedans&veaction=edit&section=7" title="Rediger avsnitt: Beregning for parallellkopling av reaktans og resistans" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Impedans&action=edit&section=7" title="Rediger kildekoden til seksjonen Beregning for parallellkopling av reaktans og resistans"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Først finnes admittansen ved addisjon: </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 \ Y_{p}={1 \over R}+{1 \over {jX}}={{jX} \over {jXR}}+{R \over {jXR}}={{R+jX} \over {jXR}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>R</mi> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mi>X</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mi>X</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mi>X</mi> <mi>R</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mi>X</mi> <mi>R</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> <mo>+</mo> <mi>j</mi> <mi>X</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mi>X</mi> <mi>R</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ Y_{p}={1 \over R}+{1 \over {jX}}={{jX} \over {jXR}}+{R \over {jXR}}={{R+jX} \over {jXR}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a075b0befc493362f1e6f076937821f318878e25" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:43.796ex; height:5.843ex;" alt="{\displaystyle \ Y_{p}={1 \over R}+{1 \over {jX}}={{jX} \over {jXR}}+{R \over {jXR}}={{R+jX} \over {jXR}}}" /></span></dd></dl> <p>Impedansen er den inverse av admittansen: </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_{p}={{jXR} \over {R+jX}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mi>X</mi> <mi>R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> <mo>+</mo> <mi>j</mi> <mi>X</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z_{p}={{jXR} \over {R+jX}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/27efc4b60337c3ef2e5960f0d575a8418b66e34d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:14.124ex; height:5.843ex;" alt="{\displaystyle Z_{p}={{jXR} \over {R+jX}}}" /></span></dd></dl> <p>Nå ganges både teller og nevner med den kompleks konjugerte<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-jX)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mo stretchy="false">(</mo> <mi>R</mi> <mo>−</mo> <mi>j</mi> <mi>X</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ (R-jX)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/191d3845761fe0635065c363205b239aba60432d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.932ex; height:2.843ex;" alt="{\displaystyle \ (R-jX)}" /></span>. </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_{p}={{jXR\cdot (R-jX)} \over {(R+jX)\cdot (R-jX)}}={{jXR^{2}-j^{2}X^{2}R} \over {R^{2}-j^{2}X^{2}}}={{jXR^{2}+X^{2}R} \over {R^{2}+X^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mi>X</mi> <mi>R</mi> <mo>⋅</mo> <mo stretchy="false">(</mo> <mi>R</mi> <mo>−</mo> <mi>j</mi> <mi>X</mi> <mo stretchy="false">)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mi>R</mi> <mo>+</mo> <mi>j</mi> <mi>X</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mo stretchy="false">(</mo> <mi>R</mi> <mo>−</mo> <mi>j</mi> <mi>X</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mi>X</mi> <msup> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>j</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>j</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mi>X</mi> <msup> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z_{p}={{jXR\cdot (R-jX)} \over {(R+jX)\cdot (R-jX)}}={{jXR^{2}-j^{2}X^{2}R} \over {R^{2}-j^{2}X^{2}}}={{jXR^{2}+X^{2}R} \over {R^{2}+X^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d97125c8c60be11d1474e67a595ae2e94bbd21e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:63.669ex; height:6.509ex;" alt="{\displaystyle Z_{p}={{jXR\cdot (R-jX)} \over {(R+jX)\cdot (R-jX)}}={{jXR^{2}-j^{2}X^{2}R} \over {R^{2}-j^{2}X^{2}}}={{jXR^{2}+X^{2}R} \over {R^{2}+X^{2}}}}" /></span></dd></dl> <p>Grunnen til denne multiplikasjonen ses over; nevneren er blitt reell. </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_{p}={{(X+jR)\cdot RX} \over {R^{2}+X^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mi>X</mi> <mo>+</mo> <mi>j</mi> <mi>R</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>R</mi> <mi>X</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z_{p}={{(X+jR)\cdot RX} \over {R^{2}+X^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fb60cb7bdb77bd0c6a1070cca5ed4b7551c53535" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:21.356ex; height:6.176ex;" alt="{\displaystyle Z_{p}={{(X+jR)\cdot RX} \over {R^{2}+X^{2}}}}" /></span></dd></dl> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r24994932">.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:r24994942">.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;color:black}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd;color:black}.mw-parser-output .navbox-list-with-group{text-align:left;border-left-width:2px}.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}.mw-parser-output .navbox-title{background-color:#ccf;color:black}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf;color:black}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff;color:black}.mw-parser-output .navbox-even{background-color:#f7f7f7;color:black}.mw-parser-output .navbox-odd{background-color:transparent;color:black}.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}</style></div><div role="navigation" class="navbox" aria-labelledby="Oppslagsverk/autoritetsdata" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th id="Oppslagsverk/autoritetsdata" scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Hjelp:Autoritetsdata" title="Hjelp:Autoritetsdata">Oppslagsverk/autoritetsdata</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0em 0.25em"><a rel="nofollow" class="external text" href="https://snl.no/impedans_-_fysikk">Store norske leksikon</a> <b>·</b> <a rel="nofollow" class="external text" href="https://denstoredanske.lex.dk/impedans">Store Danske Encyklopædi</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.britannica.com/science/electrical-impedance">Encyclopædia Britannica</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.universalis.fr/encyclopedie/impedance-physique/">Encyclopædia Universalis</a> <b>·</b> <a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4128475-6">GND</a> <b>·</b> <a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/sh85064610">LCCN</a> <b>·</b> <a rel="nofollow" class="external text" href="https://id.ndl.go.jp/auth/ndlna/00564146">NDL</a></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Hentet fra «<a dir="ltr" href="https://no.wikipedia.org/w/index.php?title=Impedans&oldid=24393641">https://no.wikipedia.org/w/index.php?title=Impedans&oldid=24393641</a>»</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Kategori:Kategorier" title="Kategori:Kategorier">Kategorier</a>: <ul><li><a href="/wiki/Kategori:Elektrisitet" title="Kategori:Elektrisitet">Elektrisitet</a></li><li><a href="/wiki/Kategori:Fysiske_st%C3%B8rrelser" title="Kategori:Fysiske størrelser">Fysiske størrelser</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Skjulte kategorier: <ul><li><a href="/wiki/Kategori:Artikler_uten_kilder" title="Kategori:Artikler uten kilder">Artikler uten kilder</a></li><li><a href="/wiki/Kategori:Artikler_med_autoritetsdatalenker_fra_Wikidata" title="Kategori:Artikler med autoritetsdatalenker fra Wikidata">Artikler med autoritetsdatalenker fra 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"> Denne siden ble sist redigert 13. apr. 2024 kl. 11:56.</li> <li id="footer-info-copyright">Innholdet er tilgjengelig under <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.no">Creative Commons-lisensen Navngivelse-DelPåSammeVilkår</a>, men ytterligere betingelser kan gjelde. Se <a class="external text" href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Terms_of_Use">bruksvilkårene</a> for detaljer.</li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">Personvern</a></li> <li id="footer-places-about"><a href="/wiki/Wikipedia:Om">Om Wikipedia</a></li> <li id="footer-places-disclaimers"><a href="/wiki/Wikipedia:Generelle_forbehold">Forbehold</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">Atferdsnorm</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">Utviklere</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/no.wikipedia.org">Statistikk</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">Erklæring om informasjonskapsler</a></li> <li id="footer-places-mobileview"><a href="//no.m.wikipedia.org/w/index.php?title=Impedans&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">Mobilvisning</a></li> </ul> <ul id="footer-icons" class="noprint"> <li id="footer-copyrightico"><a href="https://wikimediafoundation.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><picture><source media="(min-width: 500px)" srcset="/static/images/footer/wikimedia-button.svg" width="84" height="29"><img src="/static/images/footer/wikimedia.svg" width="25" height="25" alt="Wikimedia Foundation" lang="en" loading="lazy"></picture></a></li> <li id="footer-poweredbyico"><a href="https://www.mediawiki.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><picture><source media="(min-width: 500px)" srcset="/w/resources/assets/poweredby_mediawiki.svg" width="88" height="31"><img src="/w/resources/assets/mediawiki_compact.svg" alt="Powered by MediaWiki" lang="en" width="25" height="25" loading="lazy"></picture></a></li> </ul> </footer> </div> </div> </div> <div class="vector-header-container vector-sticky-header-container"> <div id="vector-sticky-header" class="vector-sticky-header"> <div class="vector-sticky-header-start"> <div class="vector-sticky-header-icon-start vector-button-flush-left vector-button-flush-right" aria-hidden="true"> <button class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-sticky-header-search-toggle" tabindex="-1" data-event-name="ui.vector-sticky-search-form.icon"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Søk</span> </button> </div> <div role="search" class="vector-search-box-vue vector-search-box-show-thumbnail vector-search-box"> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail"> <form action="/w/index.php" id="vector-sticky-search-form" class="cdx-search-input cdx-search-input--has-end-button"> <div class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Søk i Wikipedia"> <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Spesial:Søk"> </div> <button class="cdx-button cdx-search-input__end-button">Søk</button> </form> </div> </div> </div> <div class="vector-sticky-header-context-bar"> <nav aria-label="Innhold" class="vector-toc-landmark"> <div id="vector-sticky-header-toc" class="vector-dropdown mw-portlet mw-portlet-sticky-header-toc vector-sticky-header-toc vector-button-flush-left" > <input type="checkbox" id="vector-sticky-header-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-sticky-header-toc" class="vector-dropdown-checkbox " aria-label="Vis/skjul innholdsfortegnelsen" > <label id="vector-sticky-header-toc-label" for="vector-sticky-header-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Vis/skjul innholdsfortegnelsen</span> </label> <div class="vector-dropdown-content"> <div id="vector-sticky-header-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div class="vector-sticky-header-context-bar-primary" aria-hidden="true" ><span class="mw-page-title-main">Impedans</span></div> </div> </div> <div class="vector-sticky-header-end" aria-hidden="true"> <div class="vector-sticky-header-icons"> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-talk-sticky-header" tabindex="-1" data-event-name="talk-sticky-header"><span class="vector-icon mw-ui-icon-speechBubbles mw-ui-icon-wikimedia-speechBubbles"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-subject-sticky-header" tabindex="-1" data-event-name="subject-sticky-header"><span class="vector-icon mw-ui-icon-article mw-ui-icon-wikimedia-article"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-history-sticky-header" tabindex="-1" data-event-name="history-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-history mw-ui-icon-wikimedia-wikimedia-history"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only mw-watchlink" id="ca-watchstar-sticky-header" tabindex="-1" data-event-name="watch-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-star mw-ui-icon-wikimedia-wikimedia-star"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-ve-edit-sticky-header" tabindex="-1" data-event-name="ve-edit-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-edit mw-ui-icon-wikimedia-wikimedia-edit"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-edit-sticky-header" tabindex="-1" data-event-name="wikitext-edit-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-wikiText mw-ui-icon-wikimedia-wikimedia-wikiText"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-viewsource-sticky-header" tabindex="-1" data-event-name="ve-edit-protected-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-editLock mw-ui-icon-wikimedia-wikimedia-editLock"></span> <span></span> </a> </div> <div class="vector-sticky-header-buttons"> <button class="cdx-button cdx-button--weight-quiet mw-interlanguage-selector" id="p-lang-btn-sticky-header" tabindex="-1" data-event-name="ui.dropdown-p-lang-btn-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-language mw-ui-icon-wikimedia-wikimedia-language"></span> <span>60 språk</span> </button> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive" id="ca-addsection-sticky-header" tabindex="-1" data-event-name="addsection-sticky-header"><span class="vector-icon mw-ui-icon-speechBubbleAdd-progressive mw-ui-icon-wikimedia-speechBubbleAdd-progressive"></span> <span>Nytt emne</span> </a> </div> <div class="vector-sticky-header-icon-end"> <div class="vector-user-links"> </div> </div> </div> </div> </div> <div class="mw-portlet mw-portlet-dock-bottom emptyPortlet" id="p-dock-bottom"> <ul> </ul> </div> <script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.codfw.main-79f89b9df-l44gs","wgBackendResponseTime":164,"wgPageParseReport":{"limitreport":{"cputime":"0.352","walltime":"0.486","ppvisitednodes":{"value":1088,"limit":1000000},"postexpandincludesize":{"value":9068,"limit":2097152},"templateargumentsize":{"value":1147,"limit":2097152},"expansiondepth":{"value":8,"limit":100},"expensivefunctioncount":{"value":5,"limit":500},"unstrip-depth":{"value":0,"limit":20},"unstrip-size":{"value":7759,"limit":5000000},"entityaccesscount":{"value":6,"limit":400},"timingprofile":["100.00% 345.694 1 -total"," 61.50% 212.603 1 Mal:Autoritetsdata"," 37.99% 131.342 1 Mal:Kildeløs"," 27.84% 96.232 1 Mal:Navboks"," 26.72% 92.355 1 Mal:Navbox"," 23.61% 81.618 1 Mal:Amboks"]},"scribunto":{"limitreport-timeusage":{"value":"0.245","limit":"10.000"},"limitreport-memusage":{"value":4672900,"limit":52428800}},"cachereport":{"origin":"mw-web.codfw.main-59b6f7c6f4-gjjqs","timestamp":"20250227163012","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"Impedans","url":"https:\/\/no.wikipedia.org\/wiki\/Impedans","sameAs":"http:\/\/www.wikidata.org\/entity\/Q179043","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q179043","author":{"@type":"Organization","name":"Bidragsytere til Wikimedia-prosjektene"},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2004-12-08T19:53:48Z","dateModified":"2024-04-13T10:56:11Z","image":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/c\/c4\/Complex_Impedance.svg","headline":"Forholdet mellom vekselspenning og vekselstr\u00f8m ved en gitt frekvens."}</script> </body> </html>

CINXE.COM

Impedans – Wikipedia