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id="toc-Classification_of_sources" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Classification_of_sources"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Classification of sources</span> </div> </a> <button aria-controls="toc-Classification_of_sources-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Classification of sources subsection</span> </button> <ul id="toc-Classification_of_sources-sublist" class="vector-toc-list"> <li id="toc-Independent" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Independent"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Independent</span> </div> </a> <ul id="toc-Independent-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Dependent" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Dependent"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Dependent</span> </div> </a> <ul id="toc-Dependent-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Applying_electrical_laws" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Applying_electrical_laws"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Applying electrical laws</span> </div> </a> <ul id="toc-Applying_electrical_laws-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Design_methods" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Design_methods"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Design methods</span> </div> </a> <ul id="toc-Design_methods-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Network_simulation_software" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Network_simulation_software"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Network simulation software</span> </div> </a> <button aria-controls="toc-Network_simulation_software-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Network simulation software subsection</span> </button> <ul id="toc-Network_simulation_software-sublist" class="vector-toc-list"> <li id="toc-Linearization_around_operating_point" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Linearization_around_operating_point"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Linearization around operating point</span> </div> </a> <ul id="toc-Linearization_around_operating_point-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Piecewise-linear_approximation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Piecewise-linear_approximation"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Piecewise-linear approximation</span> </div> </a> <ul id="toc-Piecewise-linear_approximation-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>See also</span> </div> </a> <button aria-controls="toc-See_also-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle See also subsection</span> </button> <ul id="toc-See_also-sublist" class="vector-toc-list"> <li id="toc-Representation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Representation"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Representation</span> </div> </a> <ul id="toc-Representation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Design_and_analysis_methodologies" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Design_and_analysis_methodologies"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.2</span> <span>Design and analysis methodologies</span> </div> </a> <ul id="toc-Design_and_analysis_methodologies-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Measurement" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Measurement"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.3</span> <span>Measurement</span> </div> </a> <ul id="toc-Measurement-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Analogies" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Analogies"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.4</span> <span>Analogies</span> </div> </a> <ul id="toc-Analogies-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Specific_topologies" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Specific_topologies"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.5</span> <span>Specific topologies</span> </div> </a> <ul id="toc-Specific_topologies-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Electrical network</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 75 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-75" 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">75 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Elektriese_kragnetwerk" title="Elektriese kragnetwerk – Afrikaans" lang="af" hreflang="af" data-title="Elektriese kragnetwerk" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%8A%A4%E1%88%8C%E1%8A%AD%E1%89%B5%E1%88%AA%E1%8A%AD_%E1%8B%91%E1%8B%B0%E1%89%B5" title="ኤሌክትሪክ ዑደት – Amharic" lang="am" hreflang="am" data-title="ኤሌክትሪክ ዑደት" data-language-autonym="አማርኛ" data-language-local-name="Amharic" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AF%D8%A7%D8%B1%D8%A9_%D9%83%D9%87%D8%B1%D8%A8%D8%A7%D8%A6%D9%8A%D8%A9" title="دارة كهربائية – Arabic" lang="ar" hreflang="ar" data-title="دارة كهربائية" data-language-autonym="العربية" data-language-local-name="Arabic" 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/Circuitu" title="Circuitu – Asturian" lang="ast" hreflang="ast" data-title="Circuitu" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%A4%E0%A6%A1%E0%A6%BC%E0%A6%BF%E0%A7%8E_%E0%A6%AC%E0%A6%B0%E0%A7%8D%E0%A6%A4%E0%A6%A8%E0%A7%80" title="তড়িৎ বর্তনী – Bangla" lang="bn" hreflang="bn" data-title="তড়িৎ বর্তনী" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%AD%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D1%8B%D1%87%D0%BD%D1%8B_%D0%BB%D0%B0%D0%BD%D1%86%D1%83%D0%B3" title="Электрычны ланцуг – Belarusian" lang="be" hreflang="be" data-title="Электрычны ланцуг" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%95%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B0_%D0%B2%D0%B5%D1%80%D0%B8%D0%B3%D0%B0" title="Електрическа верига – Bulgarian" lang="bg" hreflang="bg" data-title="Електрическа верига" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Elektri%C4%8Dna_mre%C5%BEa" title="Električna mreža – Bosnian" lang="bs" hreflang="bs" data-title="Električna mreža" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Circuit_el%C3%A8ctric" title="Circuit elèctric – Catalan" lang="ca" hreflang="ca" data-title="Circuit elèctric" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%AD%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%BE_%D0%B2%C4%83%D1%87%C4%83%D1%80%D0%B0" title="Электро вăчăра – Chuvash" lang="cv" hreflang="cv" data-title="Электро вăчăра" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Elektrick%C3%BD_obvod" title="Elektrický obvod – Czech" lang="cs" hreflang="cs" data-title="Elektrický obvod" data-language-autonym="Čeština" data-language-local-name="Czech" 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/Netzwerk_(Elektrotechnik)" title="Netzwerk (Elektrotechnik) – German" lang="de" hreflang="de" data-title="Netzwerk (Elektrotechnik)" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Elektriahel" title="Elektriahel – Estonian" lang="et" hreflang="et" data-title="Elektriahel" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BB%CE%B5%CE%BA%CF%84%CF%81%CE%B9%CE%BA%CF%8C_%CE%BA%CF%8D%CE%BA%CE%BB%CF%89%CE%BC%CE%B1" title="Ηλεκτρικό κύκλωμα – Greek" lang="el" hreflang="el" data-title="Ηλεκτρικό κύκλωμα" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Circuito" title="Circuito – Spanish" lang="es" hreflang="es" data-title="Circuito" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Elektra_cirkvito" title="Elektra cirkvito – Esperanto" lang="eo" hreflang="eo" data-title="Elektra cirkvito" 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/Zirkuitu_elektriko" title="Zirkuitu elektriko – Basque" lang="eu" hreflang="eu" data-title="Zirkuitu elektriko" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%D8%AF%D8%A7%D8%B1_%D8%A7%D9%84%DA%A9%D8%AA%D8%B1%DB%8C%DA%A9%DB%8C" title="مدار الکتریکی – Persian" lang="fa" hreflang="fa" data-title="مدار الکتریکی" data-language-autonym="فارسی" data-language-local-name="Persian" 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/Circuit_%C3%A9lectrique" title="Circuit électrique – French" lang="fr" hreflang="fr" data-title="Circuit électrique" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Ciorcad_leictreach" title="Ciorcad leictreach – Irish" lang="ga" hreflang="ga" data-title="Ciorcad leictreach" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Circu%C3%ADto_el%C3%A9ctrico" title="Circuíto eléctrico – Galician" lang="gl" hreflang="gl" data-title="Circuíto eléctrico" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%A0%84%EA%B8%B0_%ED%9A%8C%EB%A1%9C" title="전기 회로 – Korean" lang="ko" hreflang="ko" data-title="전기 회로" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B7%D5%AC%D5%A5%D5%AF%D5%BF%D6%80%D5%A1%D5%AF%D5%A1%D5%B6_%D5%B7%D5%B2%D5%A9%D5%A1" title="Էլեկտրական շղթա – Armenian" lang="hy" hreflang="hy" data-title="Էլեկտրական շղթա" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B5%E0%A4%BF%E0%A4%A6%E0%A5%8D%E0%A4%AF%E0%A5%81%E0%A4%A4_%E0%A4%AA%E0%A4%B0%E0%A4%BF%E0%A4%AA%E0%A4%A5" title="विद्युत परिपथ – Hindi" lang="hi" hreflang="hi" data-title="विद्युत परिपथ" 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%8Dne_mre%C5%BEe" title="Električne mreže – Croatian" lang="hr" hreflang="hr" data-title="Električne mreže" data-language-autonym="Hrvatski" data-language-local-name="Croatian" 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/Rangkaian_listrik" title="Rangkaian listrik – Indonesian" lang="id" hreflang="id" data-title="Rangkaian listrik" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Circuito_elettrico" title="Circuito elettrico – Italian" lang="it" hreflang="it" data-title="Circuito elettrico" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%A2%D7%92%D7%9C_%D7%97%D7%A9%D7%9E%D7%9C%D7%99" title="מעגל חשמלי – Hebrew" lang="he" hreflang="he" data-title="מעגל חשמלי" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%B5%E0%B2%BF%E0%B2%A6%E0%B3%8D%E0%B2%AF%E0%B3%81%E0%B2%A4%E0%B3%8D_%E0%B2%9C%E0%B2%BE%E0%B2%B2" title="ವಿದ್ಯುತ್ ಜಾಲ – Kannada" lang="kn" hreflang="kn" data-title="ವಿದ್ಯುತ್ ಜಾಲ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Sikui_elektrik" title="Sikui elektrik – Haitian Creole" lang="ht" hreflang="ht" data-title="Sikui elektrik" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Sirkwi_ent%C3%A9gr%C3%A9" title="Sirkwi entégré – Guianan Creole" lang="gcr" hreflang="gcr" data-title="Sirkwi entégré" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Circuitus_electricus" title="Circuitus electricus – Latin" lang="la" hreflang="la" data-title="Circuitus electricus" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Elektrisk%C4%81_%C4%B7%C4%93de" title="Elektriskā ķēde – Latvian" lang="lv" hreflang="lv" data-title="Elektriskā ķēde" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Elektrin%C4%97_grandin%C4%97" title="Elektrinė grandinė – Lithuanian" lang="lt" hreflang="lt" data-title="Elektrinė grandinė" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" 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/%C3%81ramk%C3%B6r" title="Áramkör – Hungarian" lang="hu" hreflang="hu" data-title="Áramkör" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A1%D1%82%D1%80%D1%83%D1%98%D0%BD%D0%BE_%D0%BA%D0%BE%D0%BB%D0%BE" title="Струјно коло – Macedonian" lang="mk" hreflang="mk" data-title="Струјно коло" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%B5%E0%B5%88%E0%B4%A6%E0%B5%8D%E0%B4%AF%E0%B5%81%E0%B4%A4_%E0%B4%AA%E0%B4%B0%E0%B4%BF%E0%B4%AA%E0%B4%A5%E0%B4%82" title="വൈദ്യുത പരിപഥം – Malayalam" lang="ml" hreflang="ml" data-title="വൈദ്യുത പരിപഥം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Litar_elektrik" title="Litar elektrik – Malay" lang="ms" hreflang="ms" data-title="Litar elektrik" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-min mw-list-item"><a href="https://min.wikipedia.org/wiki/Sirkuit_listrik" title="Sirkuit listrik – Minangkabau" lang="min" hreflang="min" data-title="Sirkuit listrik" data-language-autonym="Minangkabau" data-language-local-name="Minangkabau" class="interlanguage-link-target"><span>Minangkabau</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A6%D0%B0%D1%85%D0%B8%D0%BB%D0%B3%D0%B0%D0%B0%D0%BD_%D1%85%D1%8D%D0%BB%D1%85%D1%8D%D1%8D" title="Цахилгаан хэлхээ – Mongolian" lang="mn" hreflang="mn" data-title="Цахилгаан хэлхээ" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Elektrisch_netwerk" title="Elektrisch netwerk – Dutch" lang="nl" hreflang="nl" data-title="Elektrisch netwerk" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%B5%E0%A4%BF%E0%A4%A6%E0%A5%8D%E0%A4%AF%E0%A5%81%E0%A4%A4_%E0%A4%AA%E0%A4%B0%E0%A4%BF%E0%A4%AA%E0%A4%A5" title="विद्युत परिपथ – Nepali" lang="ne" hreflang="ne" data-title="विद्युत परिपथ" data-language-autonym="नेपाली" data-language-local-name="Nepali" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E9%9B%BB%E6%B0%97%E5%9B%9E%E8%B7%AF" title="電気回路 – Japanese" lang="ja" hreflang="ja" data-title="電気回路" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Elektrisk_krets" title="Elektrisk krets – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Elektrisk krets" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Elektrisk_krins" title="Elektrisk krins – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Elektrisk krins" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Circuit_electric" title="Circuit electric – Occitan" lang="oc" hreflang="oc" data-title="Circuit electric" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Elektr_zanjiri" title="Elektr zanjiri – Uzbek" lang="uz" hreflang="uz" data-title="Elektr zanjiri" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Obw%C3%B3d_elektryczny" title="Obwód elektryczny – Polish" lang="pl" hreflang="pl" data-title="Obwód elektryczny" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Circuito_el%C3%A9trico" title="Circuito elétrico – Portuguese" lang="pt" hreflang="pt" data-title="Circuito elétrico" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Circuit_electric" title="Circuit electric – Romanian" lang="ro" hreflang="ro" data-title="Circuit electric" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Pinchikilla_muyu" title="Pinchikilla muyu – Quechua" lang="qu" hreflang="qu" data-title="Pinchikilla muyu" data-language-autonym="Runa Simi" data-language-local-name="Quechua" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%95%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D1%96%D1%87%D0%BD%D1%8B%D0%B9_%D0%BE%D0%B1%D0%B2%D0%BE%D0%B4" title="Електрічный обвод – Rusyn" lang="rue" hreflang="rue" data-title="Електрічный обвод" data-language-autonym="Русиньскый" data-language-local-name="Rusyn" class="interlanguage-link-target"><span>Русиньскый</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%AD%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B0%D1%8F_%D1%86%D0%B5%D0%BF%D1%8C" title="Электрическая цепь – Russian" lang="ru" hreflang="ru" data-title="Электрическая цепь" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Qarku_elektrik" title="Qarku elektrik – Albanian" lang="sq" hreflang="sq" data-title="Qarku elektrik" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Electrical_circuit" title="Electrical circuit – Simple English" lang="en-simple" hreflang="en-simple" data-title="Electrical circuit" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Elektrick%C3%BD_obvod" title="Elektrický obvod – Slovak" lang="sk" hreflang="sk" data-title="Elektrický obvod" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Elektri%C4%8Dni_krog" title="Električni krog – Slovenian" lang="sl" hreflang="sl" data-title="Električni krog" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%B3%D9%88%D9%88%DA%95%DB%8C_%DA%A9%D8%A7%D8%B1%DB%95%D8%A8%D8%A7" title="سووڕی کارەبا – Central Kurdish" lang="ckb" hreflang="ckb" data-title="سووڕی کارەبا" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</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%BA%D0%BE%D0%BB%D0%B0" title="Електрична кола – Serbian" lang="sr" hreflang="sr" data-title="Електрична кола" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Elektri%C4%8Dno_kolo" title="Električno kolo – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Električno kolo" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Virtapiiri" title="Virtapiiri – Finnish" lang="fi" hreflang="fi" data-title="Virtapiiri" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Elektrisk_krets" title="Elektrisk krets – Swedish" lang="sv" hreflang="sv" data-title="Elektrisk krets" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Network_na_elektrikal" title="Network na elektrikal – Tagalog" lang="tl" hreflang="tl" data-title="Network na elektrikal" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AE%E0%AE%BF%E0%AE%A9%E0%AF%8D%E0%AE%9A%E0%AF%81%E0%AE%B1%E0%AF%8D%E0%AE%B1%E0%AF%81" title="மின்சுற்று – Tamil" lang="ta" hreflang="ta" data-title="மின்சுற்று" 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%B9%80%E0%B8%84%E0%B8%A3%E0%B8%B7%E0%B8%AD%E0%B8%82%E0%B9%88%E0%B8%B2%E0%B8%A2%E0%B9%84%E0%B8%9F%E0%B8%9F%E0%B9%89%E0%B8%B2" title="เครือข่ายไฟฟ้า – Thai" lang="th" hreflang="th" data-title="เครือข่ายไฟฟ้า" 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/Elektrik_devresi" title="Elektrik devresi – Turkish" lang="tr" hreflang="tr" data-title="Elektrik devresi" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tk mw-list-item"><a href="https://tk.wikipedia.org/wiki/Elektrik_Sepi" title="Elektrik Sepi – Turkmen" lang="tk" hreflang="tk" data-title="Elektrik Sepi" data-language-autonym="Türkmençe" data-language-local-name="Turkmen" class="interlanguage-link-target"><span>Türkmençe</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%B5_%D0%BA%D0%BE%D0%BB%D0%BE" title="Електричне коло – Ukrainian" lang="uk" hreflang="uk" data-title="Електричне коло" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%A8%D8%B1%D9%82%DB%8C_%D8%AF%D9%88%D8%B1%D8%A7%D9%86" title="برقی دوران – Urdu" lang="ur" hreflang="ur" data-title="برقی دوران" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-ug mw-list-item"><a href="https://ug.wikipedia.org/wiki/%D8%AA%D9%88%D9%83_%D9%8A%D9%88%D9%84%D9%89" title="توك يولى – Uyghur" lang="ug" hreflang="ug" data-title="توك يولى" data-language-autonym="ئۇيغۇرچە / Uyghurche" data-language-local-name="Uyghur" class="interlanguage-link-target"><span>ئۇيغۇرچە / Uyghurche</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/M%E1%BA%A1ch_%C4%91i%E1%BB%87n" title="Mạch điện – Vietnamese" lang="vi" hreflang="vi" data-title="Mạch điện" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wo mw-list-item"><a href="https://wo.wikipedia.org/wiki/Ndombo_gu_mb%C3%ABj" title="Ndombo gu mbëj – Wolof" lang="wo" hreflang="wo" data-title="Ndombo gu mbëj" data-language-autonym="Wolof" data-language-local-name="Wolof" class="interlanguage-link-target"><span>Wolof</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E7%94%B5%E8%B7%AF" title="电路 – Wu" lang="wuu" hreflang="wuu" data-title="电路" 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-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E9%9B%BB%E8%B7%AF" title="電路 – Cantonese" lang="yue" hreflang="yue" data-title="電路" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%94%B5%E8%B7%AF" title="电路 – Chinese" lang="zh" hreflang="zh" data-title="电路" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q132629#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespaces"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Electrical_network" title="View the content 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var(--color-base)"><a href="/wiki/Electrostatics" title="Electrostatics">Electrostatics</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Charge_density" title="Charge density">Charge density</a></li> <li><a href="/wiki/Electrical_conductor" title="Electrical conductor">Conductor</a></li> <li><a href="/wiki/Coulomb%27s_law" title="Coulomb's law">Coulomb law</a></li> <li><a href="/wiki/Electret" title="Electret">Electret</a></li> <li><a href="/wiki/Electric_charge" title="Electric charge">Electric charge</a></li> <li><a href="/wiki/Electric_dipole_moment" title="Electric dipole moment">Electric dipole</a></li> <li><a href="/wiki/Electric_field" title="Electric field">Electric field</a></li> <li><a href="/wiki/Electric_flux" title="Electric flux">Electric flux</a></li> <li><a href="/wiki/Electric_potential" title="Electric potential">Electric potential</a></li> <li><a href="/wiki/Electrostatic_discharge" title="Electrostatic discharge">Electrostatic discharge</a></li> <li><a href="/wiki/Electrostatic_induction" title="Electrostatic induction">Electrostatic induction</a></li> <li><a href="/wiki/Gauss%27s_law" title="Gauss's law">Gauss law</a></li> <li><a href="/wiki/Insulator_(electricity)" title="Insulator (electricity)">Insulator</a></li> <li><a href="/wiki/Permittivity" title="Permittivity">Permittivity</a></li> <li><a href="/wiki/Polarization_density" title="Polarization density">Polarization</a></li> <li><a href="/wiki/Electric_potential_energy" title="Electric potential energy">Potential energy</a></li> <li><a href="/wiki/Static_electricity" title="Static electricity">Static electricity</a></li> <li><a href="/wiki/Triboelectric_effect" title="Triboelectric effect">Triboelectricity</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Magnetostatics" title="Magnetostatics">Magnetostatics</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Amp%C3%A8re%27s_circuital_law" title="Ampère's circuital law">Ampère law</a></li> <li><a href="/wiki/Biot%E2%80%93Savart_law" title="Biot–Savart law">Biot–Savart law</a></li> <li><a href="/wiki/Gauss%27s_law_for_magnetism" title="Gauss's law for magnetism">Gauss magnetic law</a></li> <li><a href="/wiki/Magnetic_moment" title="Magnetic moment">Magnetic dipole</a></li> <li><a href="/wiki/Magnetic_field" title="Magnetic field">Magnetic field</a></li> <li><a href="/wiki/Magnetic_flux" title="Magnetic flux">Magnetic flux</a></li> <li><a href="/wiki/Magnetic_scalar_potential" title="Magnetic scalar potential">Magnetic scalar potential</a></li> <li><a href="/wiki/Magnetic_vector_potential" title="Magnetic vector potential">Magnetic vector potential</a></li> <li><a href="/wiki/Magnetization" title="Magnetization">Magnetization</a></li> <li><a href="/wiki/Permeability_(electromagnetism)" title="Permeability (electromagnetism)">Permeability</a></li> <li><a href="/wiki/Right-hand_rule#Electromagnetism" title="Right-hand rule">Right-hand rule</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Classical_electromagnetism" title="Classical electromagnetism">Electrodynamics</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Bremsstrahlung" title="Bremsstrahlung">Bremsstrahlung</a></li> <li><a href="/wiki/Cyclotron_radiation" title="Cyclotron radiation">Cyclotron radiation</a></li> <li><a href="/wiki/Displacement_current" title="Displacement current">Displacement current</a></li> <li><a href="/wiki/Eddy_current" title="Eddy current">Eddy current</a></li> <li><a href="/wiki/Electromagnetic_field" title="Electromagnetic field">Electromagnetic field</a></li> <li><a href="/wiki/Electromagnetic_induction" title="Electromagnetic induction">Electromagnetic induction</a></li> <li><a href="/wiki/Electromagnetic_pulse" title="Electromagnetic pulse">Electromagnetic pulse</a></li> <li><a href="/wiki/Electromagnetic_radiation" title="Electromagnetic radiation">Electromagnetic radiation</a></li> <li><a href="/wiki/Faraday%27s_law_of_induction" title="Faraday's law of induction">Faraday law</a></li> <li><a href="/wiki/Jefimenko%27s_equations" title="Jefimenko's equations">Jefimenko equations</a></li> <li><a href="/wiki/Larmor_formula" title="Larmor formula">Larmor formula</a></li> <li><a href="/wiki/Lenz%27s_law" title="Lenz's law">Lenz law</a></li> <li><a href="/wiki/Li%C3%A9nard%E2%80%93Wiechert_potential" title="Liénard–Wiechert potential">Liénard–Wiechert potential</a></li> <li><a href="/wiki/London_equations" title="London equations">London equations</a></li> <li><a href="/wiki/Lorentz_force" title="Lorentz force">Lorentz force</a></li> <li><a href="/wiki/Maxwell%27s_equations" title="Maxwell's equations">Maxwell equations</a></li> <li><a href="/wiki/Maxwell_stress_tensor" title="Maxwell stress tensor">Maxwell tensor</a></li> <li><a href="/wiki/Poynting_vector" title="Poynting vector">Poynting vector</a></li> <li><a href="/wiki/Synchrotron_radiation" title="Synchrotron radiation">Synchrotron radiation</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a class="mw-selflink selflink">Electrical network</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Alternating_current" title="Alternating current">Alternating current</a></li> <li><a href="/wiki/Capacitance" title="Capacitance">Capacitance</a></li> <li><a href="/wiki/Current_density" title="Current density">Current density</a></li> <li><a href="/wiki/Direct_current" title="Direct current">Direct current</a></li> <li><a href="/wiki/Electric_current" title="Electric current">Electric current</a></li> <li><a href="/wiki/Electric_power" title="Electric power">Electric power</a></li> <li><a href="/wiki/Electrolysis" title="Electrolysis">Electrolysis</a></li> <li><a href="/wiki/Electromotive_force" title="Electromotive force">Electromotive force</a></li> <li><a href="/wiki/Electrical_impedance" title="Electrical impedance">Impedance</a></li> <li><a href="/wiki/Inductance" title="Inductance">Inductance</a></li> <li><a href="/wiki/Joule_heating" title="Joule heating">Joule heating</a></li> <li><a href="/wiki/Kirchhoff%27s_circuit_laws" title="Kirchhoff's circuit laws">Kirchhoff laws</a></li> <li><a href="/wiki/Network_analysis_(electrical_circuits)" title="Network analysis (electrical circuits)">Network analysis</a></li> <li><a href="/wiki/Ohm%27s_law" title="Ohm's law">Ohm law</a></li> <li><a href="/wiki/Series_and_parallel_circuits#Parallel_circuits" title="Series and parallel circuits">Parallel circuit</a></li> <li><a href="/wiki/Electrical_resistance_and_conductance" title="Electrical resistance and conductance">Resistance</a></li> <li><a href="/wiki/Resonator#Electromagnetics" title="Resonator">Resonant cavities</a></li> <li><a href="/wiki/Series_and_parallel_circuits#Series_circuits" title="Series and parallel circuits">Series circuit</a></li> <li><a href="/wiki/Voltage" title="Voltage">Voltage</a></li> <li><a href="/wiki/Watt" title="Watt">Watt</a></li> <li><a href="/wiki/Waveguide_(radio_frequency)" title="Waveguide (radio frequency)">Waveguides</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Magnetic_circuit" title="Magnetic circuit">Magnetic circuit</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/AC_motor" title="AC motor">AC motor</a></li> <li><a href="/wiki/DC_motor" title="DC motor">DC motor</a></li> <li><a href="/wiki/Electric_machine" title="Electric machine">Electric machine</a></li> <li><a href="/wiki/Electric_motor" title="Electric motor">Electric motor</a></li> <li><a href="/wiki/Gyrator%E2%80%93capacitor_model" title="Gyrator–capacitor model">Gyrator–capacitor</a></li> <li><a href="/wiki/Induction_motor" title="Induction motor">Induction motor</a></li> <li><a href="/wiki/Linear_motor" title="Linear motor">Linear motor</a></li> <li><a href="/wiki/Magnetomotive_force" title="Magnetomotive force">Magnetomotive force</a></li> <li><a href="/wiki/Permeance" title="Permeance">Permeance</a></li> <li><a href="/wiki/Magnetic_complex_reluctance" title="Magnetic complex reluctance">Reluctance (complex)</a></li> <li><a href="/wiki/Magnetic_reluctance" title="Magnetic reluctance">Reluctance (real)</a></li> <li><a href="/wiki/Rotor_(electric)" title="Rotor (electric)">Rotor</a></li> <li><a href="/wiki/Stator" title="Stator">Stator</a></li> <li><a href="/wiki/Transformer" title="Transformer">Transformer</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Covariant_formulation_of_classical_electromagnetism" title="Covariant formulation of classical electromagnetism">Covariant formulation</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Electromagnetic_tensor" title="Electromagnetic tensor">Electromagnetic tensor</a></li> <li><a href="/wiki/Classical_electromagnetism_and_special_relativity" title="Classical electromagnetism and special relativity">Electromagnetism and special relativity</a></li> <li><a href="/wiki/Four-current" title="Four-current">Four-current</a></li> <li><a href="/wiki/Electromagnetic_four-potential" title="Electromagnetic four-potential">Four-potential</a></li> <li><a href="/wiki/Mathematical_descriptions_of_the_electromagnetic_field" title="Mathematical descriptions of the electromagnetic field">Mathematical descriptions</a></li> <li><a href="/wiki/Maxwell%27s_equations_in_curved_spacetime" title="Maxwell's equations in curved spacetime">Maxwell equations in curved spacetime</a></li> <li><a href="/wiki/Relativistic_electromagnetism" title="Relativistic electromagnetism">Relativistic electromagnetism</a></li> <li><a href="/wiki/Electromagnetic_stress%E2%80%93energy_tensor" title="Electromagnetic stress–energy tensor">Stress–energy tensor</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)">Scientists</div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Andr%C3%A9-Marie_Amp%C3%A8re" title="André-Marie Ampère">Ampère</a></li> <li><a href="/wiki/Jean-Baptiste_Biot" title="Jean-Baptiste Biot">Biot</a></li> <li><a href="/wiki/Charles-Augustin_de_Coulomb" title="Charles-Augustin de Coulomb">Coulomb</a></li> <li><a href="/wiki/Humphry_Davy" title="Humphry Davy">Davy</a></li> <li><a href="/wiki/Albert_Einstein" title="Albert Einstein">Einstein</a></li> <li><a href="/wiki/Michael_Faraday" title="Michael Faraday">Faraday</a></li> <li><a href="/wiki/Hippolyte_Fizeau" title="Hippolyte Fizeau">Fizeau</a></li> <li><a href="/wiki/Carl_Friedrich_Gauss" title="Carl Friedrich Gauss">Gauss</a></li> <li><a href="/wiki/Oliver_Heaviside" title="Oliver Heaviside">Heaviside</a></li> <li><a href="/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz">Helmholtz</a></li> <li><a href="/wiki/Joseph_Henry" title="Joseph Henry">Henry</a></li> <li><a href="/wiki/Heinrich_Hertz" title="Heinrich Hertz">Hertz</a></li> <li><a href="/wiki/John_Hopkinson" title="John Hopkinson">Hopkinson</a></li> <li><a href="/wiki/Oleg_D._Jefimenko" title="Oleg D. Jefimenko">Jefimenko</a></li> <li><a href="/wiki/James_Prescott_Joule" title="James Prescott Joule">Joule</a></li> <li><a href="/wiki/Lord_Kelvin" title="Lord Kelvin">Kelvin</a></li> <li><a href="/wiki/Gustav_Kirchhoff" title="Gustav Kirchhoff">Kirchhoff</a></li> <li><a href="/wiki/Joseph_Larmor" title="Joseph Larmor">Larmor</a></li> <li><a href="/wiki/Emil_Lenz" title="Emil Lenz">Lenz</a></li> <li><a href="/wiki/Alfred-Marie_Li%C3%A9nard" title="Alfred-Marie Liénard">Liénard</a></li> <li><a href="/wiki/Hendrik_Lorentz" title="Hendrik Lorentz">Lorentz</a></li> <li><a href="/wiki/James_Clerk_Maxwell" title="James Clerk Maxwell">Maxwell</a></li> <li><a href="/wiki/Franz_Ernst_Neumann" title="Franz Ernst Neumann">Neumann</a></li> <li><a href="/wiki/Georg_Ohm" title="Georg Ohm">Ohm</a></li> <li><a href="/wiki/Hans_Christian_%C3%98rsted" title="Hans Christian Ørsted">Ørsted</a></li> <li><a href="/wiki/Sim%C3%A9on_Denis_Poisson" title="Siméon Denis Poisson">Poisson</a></li> <li><a href="/wiki/John_Henry_Poynting" title="John Henry Poynting">Poynting</a></li> <li><a href="/wiki/William_Ritchie_(physicist)" title="William Ritchie (physicist)">Ritchie</a></li> <li><a href="/wiki/F%C3%A9lix_Savart" title="Félix Savart">Savart</a></li> <li><a href="/wiki/George_Singer" title="George Singer">Singer</a></li> <li><a href="/wiki/Charles_Proteus_Steinmetz" title="Charles Proteus Steinmetz">Steinmetz</a></li> <li><a href="/wiki/Nikola_Tesla" title="Nikola Tesla">Tesla</a></li> <li><a href="/wiki/J._J._Thomson" title="J. J. Thomson">Thomson</a></li> <li><a href="/wiki/Alessandro_Volta" title="Alessandro Volta">Volta</a></li> <li><a href="/wiki/Wilhelm_Eduard_Weber" title="Wilhelm Eduard Weber">Weber</a></li> <li><a href="/wiki/Emil_Wiechert" title="Emil Wiechert">Wiechert</a></li></ul></div></div></td> </tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Electromagnetism" title="Template:Electromagnetism"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Electromagnetism" title="Template talk:Electromagnetism"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Electromagnetism" title="Special:EditPage/Template:Electromagnetism"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Ohm%27s_Law_with_Voltage_source_TeX.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Ohm%27s_Law_with_Voltage_source_TeX.svg/220px-Ohm%27s_Law_with_Voltage_source_TeX.svg.png" decoding="async" width="220" height="144" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Ohm%27s_Law_with_Voltage_source_TeX.svg/330px-Ohm%27s_Law_with_Voltage_source_TeX.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Ohm%27s_Law_with_Voltage_source_TeX.svg/440px-Ohm%27s_Law_with_Voltage_source_TeX.svg.png 2x" data-file-width="302" data-file-height="198" /></a><figcaption>A simple electric circuit made up of a voltage source and a resistor. Here, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v=iR}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo>=</mo> <mi>i</mi> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v=iR}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92bd885f8bee2fdeee70bcfcbb4d129da9346dbd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.793ex; height:2.176ex;" alt="{\displaystyle v=iR}"></span>, according to <a href="/wiki/Ohm%27s_law" title="Ohm's law">Ohm's law</a>.</figcaption></figure> <p>An <b>electrical network</b> is an interconnection of <a href="/wiki/Electronic_component" title="Electronic component">electrical components</a> (e.g., <a href="/wiki/Battery_(electricity)" class="mw-redirect" title="Battery (electricity)">batteries</a>, <a href="/wiki/Resistor" title="Resistor">resistors</a>, <a href="/wiki/Inductor" title="Inductor">inductors</a>, <a href="/wiki/Capacitor" title="Capacitor">capacitors</a>, <a href="/wiki/Switch" title="Switch">switches</a>, <a href="/wiki/Transistor" title="Transistor">transistors</a>) or a model of such an interconnection, consisting of <a href="/wiki/Electrical_element" title="Electrical element">electrical elements</a> (e.g., <a href="/wiki/Voltage_source" title="Voltage source">voltage sources</a>, <a href="/wiki/Current_source" title="Current source">current sources</a>, <a href="/wiki/Electrical_resistance_and_conductance" title="Electrical resistance and conductance">resistances</a>, <a href="/wiki/Inductance" title="Inductance">inductances</a>, <a href="/wiki/Capacitance" title="Capacitance">capacitances</a>). An <b>electrical circuit</b> is a network consisting of a closed loop, giving a return path for the current. Thus all circuits are networks, but not all networks are circuits (although networks without a closed loop are often imprecisely referred to as "circuits"). <a href="/wiki/Linear_circuit" title="Linear circuit">Linear</a> electrical networks, a special type consisting only of sources (voltage or current), linear lumped elements (resistors, capacitors, inductors), and linear distributed elements (transmission lines), have the property that signals are <a href="/wiki/Superposition_principle" title="Superposition principle">linearly superimposable</a>. They are thus more easily analyzed, using powerful <a href="/wiki/Frequency_domain" title="Frequency domain">frequency domain</a> methods such as <a href="/wiki/Laplace_transform" title="Laplace transform">Laplace transforms</a>, to determine <a href="/wiki/Direct_current" title="Direct current">DC response</a>, <a href="/wiki/Alternating_current" title="Alternating current">AC response</a>, and <a href="/wiki/Transient_response" title="Transient response">transient response</a>. </p><p>A <b>resistive network</b> is a network containing only resistors and ideal current and voltage sources. <a href="/wiki/Network_analysis_(electrical_circuits)" title="Network analysis (electrical circuits)">Analysis</a> of resistive networks is less complicated than analysis of networks containing capacitors and inductors. If the sources are constant (<a href="/wiki/Direct_current" title="Direct current">DC</a>) sources, the result is a DC network. The effective resistance and current distribution properties of arbitrary resistor networks can be modeled in terms of their graph measures and geometrical properties.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>A network that contains <a href="/wiki/Active_component" class="mw-redirect" title="Active component">active</a> <a href="/wiki/Electronics" title="Electronics">electronic</a> components is known as an <i><a href="/wiki/Electronic_circuit" title="Electronic circuit">electronic circuit</a></i>. Such networks are generally nonlinear and require more complex design and analysis tools. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Classification">Classification</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_network&action=edit&section=1" title="Edit section: Classification"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="By_passivity">By passivity</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_network&action=edit&section=2" title="Edit section: By passivity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>An active network contains at least one <a href="/wiki/Voltage_source" title="Voltage source">voltage source</a> or <a href="/wiki/Current_source" title="Current source">current source</a> that can supply energy to the network indefinitely. A <a href="/wiki/Passivity_(engineering)" title="Passivity (engineering)">passive</a> network does not contain an active source. </p><p>An active network contains one or more sources of <a href="/wiki/Electromotive_force" title="Electromotive force">electromotive force</a>. Practical examples of such sources include a <a href="/wiki/Electric_battery" title="Electric battery">battery</a> or a <a href="/wiki/Electric_generator" title="Electric generator">generator</a>. Active elements can inject power to the circuit, provide power gain, and control the current flow within the circuit. </p><p>Passive networks do not contain any sources of electromotive force. They consist of passive elements like resistors and capacitors. </p> <div class="mw-heading mw-heading3"><h3 id="By_linearity">By linearity</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_network&action=edit&section=3" title="Edit section: By linearity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A network is linear if its signals obey the principle of <a href="/wiki/Superposition_theorem" class="mw-redirect" title="Superposition theorem">superposition</a>; otherwise it is non-linear. Passive networks are generally taken to be linear, but there are exceptions. For instance, an <a href="/wiki/Inductor" title="Inductor">inductor</a> with an iron core can be driven into <a href="/wiki/Saturation_(magnetic)" title="Saturation (magnetic)">saturation</a> if driven with a large enough current. In this region, the behaviour of the inductor is very non-linear. </p> <div class="mw-heading mw-heading3"><h3 id="By_lumpiness">By lumpiness</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_network&action=edit&section=4" title="Edit section: By lumpiness"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Discrete passive components (resistors, capacitors and inductors) are called <i>lumped elements</i> because all of their, respectively, resistance, capacitance and inductance is assumed to be located ("lumped") at one place. This design philosophy is called the <a href="/wiki/Lumped-element_model" title="Lumped-element model">lumped-element model</a> and networks so designed are called <i>lumped-element circuits</i>. This is the conventional approach to circuit design. At high enough frequencies, or for long enough circuits (such as <a href="/wiki/Electric_power_transmission" title="Electric power transmission">power transmission lines</a>), the lumped assumption no longer holds because there is a significant fraction of a <a href="/wiki/Wavelength" title="Wavelength">wavelength</a> across the component dimensions. A new design model is needed for such cases called the <a href="/wiki/Distributed-element_model" title="Distributed-element model">distributed-element model</a>. Networks designed to this model are called <i><a href="/wiki/Distributed-element_circuit" title="Distributed-element circuit">distributed-element circuits</a></i>. </p><p>A distributed-element circuit that includes some lumped components is called a <i>semi-lumped</i> design. An example of a semi-lumped circuit is the <a href="/wiki/Combline_filter" class="mw-redirect" title="Combline filter">combline filter</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Classification_of_sources">Classification of sources</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_network&action=edit&section=5" title="Edit section: Classification of sources"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Sources can be classified as independent sources and dependent sources. </p> <div class="mw-heading mw-heading3"><h3 id="Independent">Independent</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_network&action=edit&section=6" title="Edit section: Independent"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>An ideal independent source maintains the same voltage or current regardless of the other elements present in the circuit. Its value is either constant (DC) or sinusoidal (AC). The strength of voltage or current is not changed by any variation in the connected network. </p> <div class="mw-heading mw-heading3"><h3 id="Dependent">Dependent</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_network&action=edit&section=7" title="Edit section: Dependent"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Dependent_source" title="Dependent source">Dependent sources</a> depend upon a particular element of the circuit for delivering the power or voltage or current depending upon the type of source it is. </p> <div class="mw-heading mw-heading2"><h2 id="Applying_electrical_laws">Applying electrical laws</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_network&action=edit&section=8" title="Edit section: Applying electrical laws"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A number of electrical laws apply to all linear resistive networks. These include: </p> <ul><li><a href="/wiki/Kirchhoff%27s_current_law" class="mw-redirect" title="Kirchhoff's current law">Kirchhoff's current law</a>: The sum of all currents entering a node is equal to the sum of all currents leaving the node.</li></ul> <ul><li><a href="/wiki/Kirchhoff%27s_voltage_law" class="mw-redirect" title="Kirchhoff's voltage law">Kirchhoff's voltage law</a>: The directed sum of the electrical potential differences around a loop must be zero.</li></ul> <ul><li><a href="/wiki/Ohm%27s_law" title="Ohm's law">Ohm's law</a>: The voltage across a resistor is equal to the product of the resistance and the current flowing through it.</li></ul> <ul><li><a href="/wiki/Norton%27s_theorem" title="Norton's theorem">Norton's theorem</a>: Any network of voltage or current sources and resistors is electrically equivalent to an ideal current source in parallel with a single resistor.</li></ul> <ul><li><a href="/wiki/Th%C3%A9venin%27s_theorem" title="Thévenin's theorem">Thévenin's theorem</a>: Any network of voltage or current sources and resistors is electrically equivalent to a single voltage source in series with a single resistor.</li></ul> <ul><li><a href="/wiki/Superposition_theorem" class="mw-redirect" title="Superposition theorem">Superposition theorem</a>: In a linear network with several independent sources, the response in a particular branch when all the sources are acting simultaneously is equal to the linear sum of individual responses calculated by taking one independent source at a time.</li></ul> <p>Applying these laws results in a set of simultaneous equations that can be solved either algebraically or numerically. The laws can generally be extended to networks containing <a href="/wiki/Electrical_reactance" title="Electrical reactance">reactances</a>. They cannot be used in networks that contain nonlinear or time-varying components. </p> <div class="mw-heading mw-heading2"><h2 id="Design_methods">Design methods</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_network&action=edit&section=9" title="Edit section: Design methods"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table style="float:right; clear:right; margin-left:5px; margin-top:5px; border:3px solid #98c4e4; padding:2px;" cellspacing="0"> <tbody><tr> <th colspan="2" style="align:center; font-size:larger;">Linear <a href="/wiki/Network_analysis_(electrical_circuits)" title="Network analysis (electrical circuits)">network analysis</a> </th></tr> <tr style="border-bottom:2px solid #c4d3df; border-top:2px solid #98c4e4; border-left:2px solid #98c4e4; border-right:2px solid #98c4e4;"> <th colspan="2" style="border-top:2px solid #98c4e4; border-bottom:2px solid #c4d3df; border-left:2px solid #98c4e4; border-right:2px solid #98c4e4;"><a href="/wiki/Electrical_element" title="Electrical element">Elements</a> </th></tr> <tr> <td colspan="2" style="border-bottom:2px solid #98c4e4; border-left:2px solid #98c4e4; border-right:2px solid #98c4e4;"> <p><span typeof="mw:File"><a href="/wiki/Electrical_resistance" title="Resistance"><img alt="Resistance" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Resistor_button.svg/40px-Resistor_button.svg.png" decoding="async" width="40" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Resistor_button.svg/60px-Resistor_button.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Resistor_button.svg/80px-Resistor_button.svg.png 2x" data-file-width="146" data-file-height="133" /></a></span><span typeof="mw:File"><a href="/wiki/Capacitance" title="Capacitance"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/91/Capacitor_button.svg/40px-Capacitor_button.svg.png" decoding="async" width="40" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/91/Capacitor_button.svg/60px-Capacitor_button.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/91/Capacitor_button.svg/80px-Capacitor_button.svg.png 2x" data-file-width="146" data-file-height="133" /></a></span><span typeof="mw:File"><a href="/wiki/Inductance" title="Inductance"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Inductor_button.svg/40px-Inductor_button.svg.png" decoding="async" width="40" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Inductor_button.svg/60px-Inductor_button.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Inductor_button.svg/80px-Inductor_button.svg.png 2x" data-file-width="146" data-file-height="133" /></a></span><span typeof="mw:File"><a href="/wiki/Electrical_reactance" title="Reactance"><img alt="Reactance" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5d/Reactance_button.svg/40px-Reactance_button.svg.png" decoding="async" width="40" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5d/Reactance_button.svg/60px-Reactance_button.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5d/Reactance_button.svg/80px-Reactance_button.svg.png 2x" data-file-width="146" data-file-height="133" /></a></span><span typeof="mw:File"><a href="/wiki/Electrical_impedance" title="Impedance"><img alt="Impedance" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/11/Impedance_button.svg/40px-Impedance_button.svg.png" decoding="async" width="40" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/11/Impedance_button.svg/60px-Impedance_button.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/11/Impedance_button.svg/80px-Impedance_button.svg.png 2x" data-file-width="146" data-file-height="133" /></a></span><span typeof="mw:File"><a href="/wiki/Voltage_source" title="Voltage source"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Voltage_button.svg/40px-Voltage_button.svg.png" decoding="async" width="40" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Voltage_button.svg/60px-Voltage_button.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Voltage_button.svg/80px-Voltage_button.svg.png 2x" data-file-width="146" data-file-height="133" /></a></span><br /> <span typeof="mw:File"><a href="/wiki/Electrical_conductance" title="Conductance"><img alt="Conductance" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9c/Conductance_button.svg/40px-Conductance_button.svg.png" decoding="async" width="40" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9c/Conductance_button.svg/60px-Conductance_button.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9c/Conductance_button.svg/80px-Conductance_button.svg.png 2x" data-file-width="146" data-file-height="133" /></a></span><span typeof="mw:File"><a href="/wiki/Elastance" title="Elastance"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/43/Elastance_button.svg/40px-Elastance_button.svg.png" decoding="async" width="40" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/43/Elastance_button.svg/60px-Elastance_button.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/43/Elastance_button.svg/80px-Elastance_button.svg.png 2x" data-file-width="146" data-file-height="133" /></a></span><span typeof="mw:File"><a href="/wiki/File:Blank_button.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/98/Blank_button.svg/40px-Blank_button.svg.png" decoding="async" width="40" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/98/Blank_button.svg/60px-Blank_button.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/98/Blank_button.svg/80px-Blank_button.svg.png 2x" data-file-width="146" data-file-height="133" /></a></span><span typeof="mw:File"><a href="/wiki/Susceptance" title="Susceptance"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/38/Susceptance_button.svg/40px-Susceptance_button.svg.png" decoding="async" width="40" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/38/Susceptance_button.svg/60px-Susceptance_button.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/38/Susceptance_button.svg/80px-Susceptance_button.svg.png 2x" data-file-width="146" data-file-height="133" /></a></span><span typeof="mw:File"><a href="/wiki/Admittance" title="Admittance"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Admittance_button.svg/40px-Admittance_button.svg.png" decoding="async" width="40" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Admittance_button.svg/60px-Admittance_button.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Admittance_button.svg/80px-Admittance_button.svg.png 2x" data-file-width="146" data-file-height="133" /></a></span><span typeof="mw:File"><a href="/wiki/Current_source" title="Current source"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Current_button.svg/40px-Current_button.svg.png" decoding="async" width="40" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Current_button.svg/60px-Current_button.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Current_button.svg/80px-Current_button.svg.png 2x" data-file-width="146" data-file-height="133" /></a></span> </p> </td></tr> <tr> <th colspan="2" style="border-bottom:2px solid #c4d3df; border-left:2px solid #98c4e4; border-right:2px solid #98c4e4;"><a href="/wiki/Electrical_component" class="mw-redirect" title="Electrical component">Components</a> </th></tr> <tr> <td colspan="2" style="border-bottom:2px solid #98c4e4; border-left:2px solid #98c4e4; border-right:2px solid #98c4e4;"> <p><span typeof="mw:File"><a href="/wiki/Resistor" title="Resistor"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Resistor_button.svg/40px-Resistor_button.svg.png" decoding="async" width="40" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Resistor_button.svg/60px-Resistor_button.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Resistor_button.svg/80px-Resistor_button.svg.png 2x" data-file-width="146" data-file-height="133" /></a></span> <span typeof="mw:File"><a href="/wiki/Capacitor" title="Capacitor"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/91/Capacitor_button.svg/40px-Capacitor_button.svg.png" decoding="async" width="40" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/91/Capacitor_button.svg/60px-Capacitor_button.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/91/Capacitor_button.svg/80px-Capacitor_button.svg.png 2x" data-file-width="146" data-file-height="133" /></a></span> <span typeof="mw:File"><a href="/wiki/Inductor" title="Inductor"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Inductor_button.svg/40px-Inductor_button.svg.png" decoding="async" width="40" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Inductor_button.svg/60px-Inductor_button.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Inductor_button.svg/80px-Inductor_button.svg.png 2x" data-file-width="146" data-file-height="133" /></a></span> <span typeof="mw:File"><a href="/wiki/Ohm%27s_law" title="Ohm's law"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8e/Ohm%27s_law_button.svg/40px-Ohm%27s_law_button.svg.png" decoding="async" width="40" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8e/Ohm%27s_law_button.svg/60px-Ohm%27s_law_button.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8e/Ohm%27s_law_button.svg/80px-Ohm%27s_law_button.svg.png 2x" data-file-width="146" data-file-height="133" /></a></span> </p> </td></tr> <tr> <th colspan="2" style="border-bottom:2px solid #c4d3df; border-left:2px solid #98c4e4; border-right:2px solid #98c4e4;"><a href="/wiki/Series_and_parallel_circuits" title="Series and parallel circuits">Series and parallel circuits</a> </th></tr> <tr> <td colspan="2" style="border-bottom:2px solid #98c4e4; border-left:2px solid #98c4e4; border-right:2px solid #98c4e4;"> <p><span typeof="mw:File"><a href="/wiki/Resistors_in_series" title="Resistors in series"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Series_resistor_button.svg/40px-Series_resistor_button.svg.png" decoding="async" width="40" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Series_resistor_button.svg/60px-Series_resistor_button.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Series_resistor_button.svg/80px-Series_resistor_button.svg.png 2x" data-file-width="146" data-file-height="133" /></a></span><span typeof="mw:File"><a href="/wiki/Resistors_in_parallel" title="Resistors in parallel"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Parallel_resistor_button.svg/40px-Parallel_resistor_button.svg.png" decoding="async" width="40" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Parallel_resistor_button.svg/60px-Parallel_resistor_button.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/51/Parallel_resistor_button.svg/80px-Parallel_resistor_button.svg.png 2x" data-file-width="146" data-file-height="133" /></a></span><span typeof="mw:File"><a href="/wiki/Capacitors_in_series" title="Capacitors in series"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2b/Series_capacitor_button.svg/40px-Series_capacitor_button.svg.png" decoding="async" width="40" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2b/Series_capacitor_button.svg/60px-Series_capacitor_button.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2b/Series_capacitor_button.svg/80px-Series_capacitor_button.svg.png 2x" data-file-width="146" data-file-height="133" /></a></span><span typeof="mw:File"><a href="/wiki/Capacitors_in_parallel" title="Capacitors in parallel"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/86/Parallel_capacitor_button.svg/40px-Parallel_capacitor_button.svg.png" decoding="async" width="40" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/86/Parallel_capacitor_button.svg/60px-Parallel_capacitor_button.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/86/Parallel_capacitor_button.svg/80px-Parallel_capacitor_button.svg.png 2x" data-file-width="146" data-file-height="133" /></a></span><span typeof="mw:File"><a href="/wiki/Inductors_in_series" title="Inductors in series"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Series_inductor_button.svg/40px-Series_inductor_button.svg.png" decoding="async" width="40" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Series_inductor_button.svg/60px-Series_inductor_button.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Series_inductor_button.svg/80px-Series_inductor_button.svg.png 2x" data-file-width="146" data-file-height="133" /></a></span><span typeof="mw:File"><a href="/wiki/Inductors_in_parallel" title="Inductors in parallel"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3f/Parallel_inductor_button.svg/40px-Parallel_inductor_button.svg.png" decoding="async" width="40" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3f/Parallel_inductor_button.svg/60px-Parallel_inductor_button.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3f/Parallel_inductor_button.svg/80px-Parallel_inductor_button.svg.png 2x" data-file-width="146" data-file-height="133" /></a></span> </p> </td></tr> <tr> <th colspan="2" style="border-bottom:2px solid #c4d3df; border-left:2px solid #98c4e4; border-right:2px solid #98c4e4;"><a href="/wiki/Equivalent_impedance_transforms" title="Equivalent impedance transforms">Impedance transforms</a> </th></tr> <tr> <td colspan="2" style="border-bottom:2px solid #98c4e4; border-left:2px solid #98c4e4; border-right:2px solid #98c4e4;"> <p><span typeof="mw:File"><a href="/wiki/Y-%CE%94_transform#Equations_for_the_transformation_from_Y_to_Δ" title="Y-Δ transform"><img alt="Y-Δ transform" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/39/Y-delta_button.svg/40px-Y-delta_button.svg.png" decoding="async" width="40" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/39/Y-delta_button.svg/60px-Y-delta_button.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/39/Y-delta_button.svg/80px-Y-delta_button.svg.png 2x" data-file-width="146" data-file-height="133" /></a></span> <span typeof="mw:File"><a href="/wiki/Y-%CE%94_transform#Equations_for_the_transformation_from_Δ_to_Y" title="Δ-Y transform"><img alt="Δ-Y transform" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Delta-Y_button.svg/40px-Delta-Y_button.svg.png" decoding="async" width="40" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Delta-Y_button.svg/60px-Delta-Y_button.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Delta-Y_button.svg/80px-Delta-Y_button.svg.png 2x" data-file-width="146" data-file-height="133" /></a></span> <span typeof="mw:File"><a href="/wiki/Network_analysis_(electrical_circuits)#General_form_of_network_node_elimination" title="star-polygon transforms"><img alt="star-polygon transforms" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/13/Star-polygon_button.svg/40px-Star-polygon_button.svg.png" decoding="async" width="40" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/13/Star-polygon_button.svg/60px-Star-polygon_button.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/13/Star-polygon_button.svg/80px-Star-polygon_button.svg.png 2x" data-file-width="146" data-file-height="133" /></a></span> <span typeof="mw:File"><a href="/wiki/Dual_impedance" title="Dual impedance"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/89/Dual_button.svg/40px-Dual_button.svg.png" decoding="async" width="40" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/89/Dual_button.svg/60px-Dual_button.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/89/Dual_button.svg/80px-Dual_button.svg.png 2x" data-file-width="146" data-file-height="133" /></a></span> </p> </td></tr> <tr> <th style="border-bottom:2px solid #c4d3df; border-left:2px solid #98c4e4; border-right:2px solid #98c4e4;">Generator theorems </th> <th style="border-bottom:2px solid #c4d3df; border-right:2px solid #98c4e4;"><a class="mw-selflink selflink">Network</a> theorems </th></tr> <tr> <td style="width:120px; border-bottom:2px solid #98c4e4; border-left:2px solid #98c4e4; border-right:2px solid #98c4e4;"> <p><span typeof="mw:File"><a href="/wiki/Th%C3%A9venin%27s_theorem" title="Thévenin's theorem"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/02/Thevenin_button.svg/40px-Thevenin_button.svg.png" decoding="async" width="40" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/02/Thevenin_button.svg/60px-Thevenin_button.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/02/Thevenin_button.svg/80px-Thevenin_button.svg.png 2x" data-file-width="146" data-file-height="133" /></a></span><span typeof="mw:File"><a href="/wiki/Norton%27s_theorem" title="Norton's theorem"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Norton_button.svg/40px-Norton_button.svg.png" decoding="async" width="40" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Norton_button.svg/60px-Norton_button.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Norton_button.svg/80px-Norton_button.svg.png 2x" data-file-width="146" data-file-height="133" /></a></span><span typeof="mw:File"><a href="/wiki/Millman%27s_theorem" title="Millman's theorem"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/44/Millman_button.svg/40px-Millman_button.svg.png" decoding="async" width="40" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/44/Millman_button.svg/60px-Millman_button.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/44/Millman_button.svg/80px-Millman_button.svg.png 2x" data-file-width="146" data-file-height="133" /></a></span> </p> </td> <td style="border-bottom:2px solid #98c4e4; border-right:2px solid #98c4e4;"> <p><span typeof="mw:File"><a href="/wiki/Kirchoff%27s_current_law" title="Kirchoff's current law"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/KCL_button.svg/40px-KCL_button.svg.png" decoding="async" width="40" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/KCL_button.svg/60px-KCL_button.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/KCL_button.svg/80px-KCL_button.svg.png 2x" data-file-width="146" data-file-height="133" /></a></span><span typeof="mw:File"><a href="/wiki/Kirchoff%27s_voltage_law" title="Kirchoff's voltage law"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1d/KVL_button.svg/40px-KVL_button.svg.png" decoding="async" width="40" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1d/KVL_button.svg/60px-KVL_button.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1d/KVL_button.svg/80px-KVL_button.svg.png 2x" data-file-width="146" data-file-height="133" /></a></span><span typeof="mw:File"><a href="/wiki/Tellegen%27s_theorem" title="Tellegen's theorem"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/36/Tellegen_button.svg/40px-Tellegen_button.svg.png" decoding="async" width="40" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/36/Tellegen_button.svg/60px-Tellegen_button.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/36/Tellegen_button.svg/80px-Tellegen_button.svg.png 2x" data-file-width="146" data-file-height="133" /></a></span> </p> </td></tr> <tr> <th colspan="2" style="border-bottom:2px solid #c4d3df; border-left:2px solid #98c4e4; border-right:2px solid #98c4e4;">Network analysis methods </th></tr> <tr> <td colspan="2" style="border-bottom:2px solid #98c4e4; border-left:2px solid #98c4e4; border-right:2px solid #98c4e4;"> <p><span typeof="mw:File"><a href="/wiki/Nodal_analysis" title="Nodal analysis"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/KCL_button.svg/40px-KCL_button.svg.png" decoding="async" width="40" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/KCL_button.svg/60px-KCL_button.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/KCL_button.svg/80px-KCL_button.svg.png 2x" data-file-width="146" data-file-height="133" /></a></span> <span typeof="mw:File"><a href="/wiki/Mesh_analysis" title="Mesh analysis"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1d/KVL_button.svg/40px-KVL_button.svg.png" decoding="async" width="40" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1d/KVL_button.svg/60px-KVL_button.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1d/KVL_button.svg/80px-KVL_button.svg.png 2x" data-file-width="146" data-file-height="133" /></a></span> <span typeof="mw:File"><a href="/wiki/Superposition_theorem" title="Superposition theorem"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Superposition_button.svg/40px-Superposition_button.svg.png" decoding="async" width="40" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Superposition_button.svg/60px-Superposition_button.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Superposition_button.svg/80px-Superposition_button.svg.png 2x" data-file-width="146" data-file-height="133" /></a></span> </p> </td></tr> <tr> <th colspan="2" style="border-bottom:2px solid #c4d3df; border-left:2px solid #98c4e4; border-right:2px solid #98c4e4;"><a href="/wiki/Two-port_network" title="Two-port network">Two-port parameters</a> </th></tr> <tr> <td colspan="2" style="border-bottom:2px solid #98c4e4; border-left:2px solid #98c4e4; border-right:2px solid #98c4e4;"> <p><span typeof="mw:File"><a href="/wiki/Impedance_parameters" title="z-parameters"><img alt="z-parameters" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/26/Z-parameter_button.svg/40px-Z-parameter_button.svg.png" decoding="async" width="40" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/26/Z-parameter_button.svg/60px-Z-parameter_button.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/26/Z-parameter_button.svg/80px-Z-parameter_button.svg.png 2x" data-file-width="146" data-file-height="133" /></a></span><span typeof="mw:File"><a href="/wiki/Admittance_parameters" title="y-parameters"><img alt="y-parameters" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Y-parameter_button.svg/40px-Y-parameter_button.svg.png" decoding="async" width="40" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Y-parameter_button.svg/60px-Y-parameter_button.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Y-parameter_button.svg/80px-Y-parameter_button.svg.png 2x" data-file-width="146" data-file-height="133" /></a></span><span typeof="mw:File"><a href="/wiki/Hybrid_parameters" title="h-parameters"><img alt="h-parameters" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ac/H-parameter_button.svg/40px-H-parameter_button.svg.png" decoding="async" width="40" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ac/H-parameter_button.svg/60px-H-parameter_button.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ac/H-parameter_button.svg/80px-H-parameter_button.svg.png 2x" data-file-width="146" data-file-height="133" /></a></span><span typeof="mw:File"><a href="/wiki/Inverse_hybrid_parameters" title="g-parameters"><img alt="g-parameters" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/G-parameter_button.svg/40px-G-parameter_button.svg.png" decoding="async" width="40" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/G-parameter_button.svg/60px-G-parameter_button.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ae/G-parameter_button.svg/80px-G-parameter_button.svg.png 2x" data-file-width="146" data-file-height="133" /></a></span><span typeof="mw:File"><a href="/wiki/ABCD-parameters" title="ABCD-parameters"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/94/Abcd-parameter_button.svg/40px-Abcd-parameter_button.svg.png" decoding="async" width="40" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/94/Abcd-parameter_button.svg/60px-Abcd-parameter_button.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/94/Abcd-parameter_button.svg/80px-Abcd-parameter_button.svg.png 2x" data-file-width="146" data-file-height="133" /></a></span><span typeof="mw:File"><a href="/wiki/Scattering_parameters" title="S-parameters"><img alt="S-parameters" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/06/S-parameter_button.svg/40px-S-parameter_button.svg.png" decoding="async" width="40" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/06/S-parameter_button.svg/60px-S-parameter_button.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/06/S-parameter_button.svg/80px-S-parameter_button.svg.png 2x" data-file-width="146" data-file-height="133" /></a></span> </p> </td></tr> <tr> <td> </td> <td style="text-align:right;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist"><ul><li class="nv-view"><a href="/wiki/Template:Network_analysis_navigation" title="Template:Network analysis navigation"><span title="View this template">view</span></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Network_analysis_navigation" title="Template talk:Network analysis navigation"><span title="Discuss this template">talk</span></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Network_analysis_navigation" title="Special:EditPage/Template:Network analysis navigation"><span title="Edit this template">edit</span></a></li></ul></div> </td></tr></tbody></table> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Network_analysis_(electrical_circuits)" title="Network analysis (electrical circuits)">Network analysis (electrical circuits)</a></div> <p>To design any electrical circuit, either <a href="/wiki/Analogue_electronics" title="Analogue electronics">analog</a> or <a href="/wiki/Digital_circuit" class="mw-redirect" title="Digital circuit">digital</a>, <a href="/wiki/Electrical_engineering" title="Electrical engineering">electrical engineers</a> need to be able to predict the voltages and currents at all places within the circuit. Simple <a href="/wiki/Linear_circuit" title="Linear circuit">linear circuits</a> can be analyzed by hand using <a href="/wiki/Complex_number" title="Complex number">complex number theory</a>. In more complex cases the circuit may be analyzed with specialized <a href="/wiki/Computer_program" title="Computer program">computer programs</a> or estimation techniques such as the piecewise-linear model. </p><p>Circuit simulation software, such as <a href="/wiki/HSPICE" class="mw-redirect" title="HSPICE">HSPICE</a> (an analog circuit simulator),<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> and languages such as <a href="/wiki/VHDL-AMS" title="VHDL-AMS">VHDL-AMS</a> and <a href="/wiki/Verilog-AMS" title="Verilog-AMS">verilog-AMS</a> allow engineers to design circuits without the time, cost and risk of error involved in building circuit prototypes. </p> <div class="mw-heading mw-heading2"><h2 id="Network_simulation_software">Network simulation software</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_network&action=edit&section=10" title="Edit section: Network simulation software"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>More complex circuits can be analyzed numerically with software such as <a href="/wiki/SPICE" title="SPICE">SPICE</a> or <a href="/wiki/GNU_Circuit_Analysis_Package" title="GNU Circuit Analysis Package">GNUCAP</a>, or symbolically using software such as <a href="/wiki/SapWin" title="SapWin">SapWin</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Linearization_around_operating_point">Linearization around operating point</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_network&action=edit&section=11" title="Edit section: Linearization around operating point"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>When faced with a new circuit, the software first tries to find a <a href="/wiki/Steady_state" title="Steady state">steady state solution</a>, that is, one where all nodes conform to Kirchhoff's current law <i>and</i> the voltages across and through each element of the circuit conform to the voltage/current equations governing that element. </p><p>Once the steady state solution is found, the <i><a href="/wiki/Operating_point" title="Operating point">operating points</a></i> of each element in the circuit are known. For a small signal analysis, every non-linear element can be linearized around its operation point to obtain the small-signal estimate of the voltages and currents. This is an application of Ohm's Law. The resulting linear circuit matrix can be solved with <a href="/wiki/Gaussian_elimination" title="Gaussian elimination">Gaussian elimination</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Piecewise-linear_approximation">Piecewise-linear approximation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_network&action=edit&section=12" title="Edit section: Piecewise-linear approximation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Software such as the <a href="/wiki/PLECS" title="PLECS">PLECS</a> interface to <a href="/wiki/Simulink" title="Simulink">Simulink</a> uses <a href="/wiki/Piecewise_linear_function" title="Piecewise linear function">piecewise-linear</a> approximation of the equations governing the elements of a circuit. The circuit is treated as a completely linear network of <a href="/wiki/Diode_modelling#Mathematically_idealized_diode" title="Diode modelling">ideal diodes</a>. Every time a diode switches from on to off or vice versa, the configuration of the linear network changes. Adding more detail to the approximation of equations increases the accuracy of the simulation, but also increases its running time. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_network&action=edit&section=13" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 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</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1235681985"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237033735"><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/40px-Wiktionary-logo-en-v2.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/60px-Wiktionary-logo-en-v2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/80px-Wiktionary-logo-en-v2.svg.png 2x" data-file-width="512" data-file-height="512" /></span></span></div> <div class="side-box-text plainlist">Look up <i><b><a href="https://en.wiktionary.org/wiki/electrical_circuit" class="extiw" title="wiktionary:electrical circuit">electrical circuit</a></b></i> in Wiktionary, the free dictionary.</div></div> </div> <ul><li><a href="/wiki/Digital_circuit" class="mw-redirect" title="Digital circuit">Digital circuit</a></li> <li><a href="/wiki/Ground_(electricity)" title="Ground (electricity)">Ground (electricity)</a></li> <li><a href="/wiki/Electrical_impedance" title="Electrical impedance">Impedance</a></li> <li><a href="/wiki/External_electric_load" class="mw-redirect" title="External electric load">Load</a></li> <li><a href="/wiki/Memristor" title="Memristor">Memristor</a></li> <li><a href="/wiki/Open-circuit_voltage" title="Open-circuit voltage">Open-circuit voltage</a></li> <li><a href="/wiki/Short_circuit" title="Short circuit">Short circuit</a></li> <li><a href="/wiki/Voltage_drop" title="Voltage drop">Voltage drop</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Representation">Representation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_network&action=edit&section=14" title="Edit section: Representation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Circuit_diagram" title="Circuit diagram">Circuit diagram</a></li> <li><a href="/wiki/Schematic" title="Schematic">Schematic</a></li> <li><a href="/wiki/Netlist" title="Netlist">Netlist</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Design_and_analysis_methodologies">Design and analysis methodologies</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_network&action=edit&section=15" title="Edit section: Design and analysis methodologies"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Network_analysis_(electrical_circuits)" title="Network analysis (electrical circuits)">Network analysis (electrical circuits)</a></li> <li><a href="/wiki/Mathematical_methods_in_electronics" title="Mathematical methods in electronics">Mathematical methods in electronics</a></li> <li><a href="/wiki/Superposition_theorem" class="mw-redirect" title="Superposition theorem">Superposition theorem</a></li> <li><a href="/wiki/Topology_(electronics)" class="mw-redirect" title="Topology (electronics)">Topology (electronics)</a></li> <li><a href="/wiki/Mesh_analysis" title="Mesh analysis">Mesh analysis</a></li> <li><a href="/wiki/Prototype_filter" title="Prototype filter">Prototype filter</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Measurement">Measurement</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_network&action=edit&section=16" title="Edit section: Measurement"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Network_analyzer_(electrical)" title="Network analyzer (electrical)">Network analyzer (electrical)</a></li> <li><a href="/wiki/Network_analyzer_(AC_power)" title="Network analyzer (AC power)">Network analyzer (AC power)</a></li> <li><a href="/wiki/Continuity_test" title="Continuity test">Continuity test</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Analogies">Analogies</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_network&action=edit&section=17" title="Edit section: Analogies"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Hydraulic_analogy" title="Hydraulic analogy">Hydraulic analogy</a></li> <li><a href="/wiki/Mechanical%E2%80%93electrical_analogies" title="Mechanical–electrical analogies">Mechanical–electrical analogies</a></li> <li><a href="/wiki/Impedance_analogy" title="Impedance analogy">Impedance analogy</a> (Maxwell analogy)</li> <li><a href="/wiki/Mobility_analogy" title="Mobility analogy">Mobility analogy</a> (Firestone analogy)</li> <li><a href="/wiki/Through_and_across_analogy" class="mw-redirect" title="Through and across analogy">Through and across analogy</a> (Trent analogy)</li></ul> <div class="mw-heading mw-heading3"><h3 id="Specific_topologies">Specific topologies</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_network&action=edit&section=18" title="Edit section: Specific topologies"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Bridge_circuit" title="Bridge circuit">Bridge circuit</a></li> <li><a href="/wiki/LC_circuit" title="LC circuit">LC circuit</a></li> <li><a href="/wiki/RC_circuit" title="RC circuit">RC circuit</a></li> <li><a href="/wiki/RL_circuit" title="RL circuit">RL circuit</a></li> <li><a href="/wiki/RLC_circuit" title="RLC circuit">RLC circuit</a></li> <li><a href="/wiki/Potential_divider" class="mw-redirect" title="Potential divider">Potential divider</a></li> <li><a href="/wiki/Series_and_parallel_circuits" title="Series and parallel circuits">Series and parallel circuits</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_network&action=edit&section=19" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output 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.id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFKumarVidhyadhirajaKulkarni2017" class="citation journal cs1">Kumar, Ankush; Vidhyadhiraja, N. S.; Kulkarni, G. U . (2017). "Current distribution in conducting nanowire networks". <i>Journal of Applied Physics</i>. <b>122</b> (4): 045101. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2017JAP...122d5101K">2017JAP...122d5101K</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.4985792">10.1063/1.4985792</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Applied+Physics&rft.atitle=Current+distribution+in+conducting+nanowire+networks&rft.volume=122&rft.issue=4&rft.pages=045101&rft.date=2017&rft_id=info%3Adoi%2F10.1063%2F1.4985792&rft_id=info%3Abibcode%2F2017JAP...122d5101K&rft.aulast=Kumar&rft.aufirst=Ankush&rft.au=Vidhyadhiraja%2C+N.+S.&rft.au=Kulkarni%2C+G.+U+.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AElectrical+network" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.stanford.edu/class/ee133/spice/HSpice.pdf">"HSPICE"</a> <span class="cs1-format">(PDF)</span>. <i>HSpice</i>. Stanford University, Electrical Engineering Department. 1999.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=HSpice&rft.atitle=HSPICE&rft.date=1999&rft_id=https%3A%2F%2Fweb.stanford.edu%2Fclass%2Fee133%2Fspice%2FHSpice.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AElectrical+network" class="Z3988"></span></span> </li> </ol></div></div> <style data-mw-deduplicate="TemplateStyles:r1130092004">.mw-parser-output .portal-bar{font-size:88%;font-weight:bold;display:flex;justify-content:center;align-items:baseline}.mw-parser-output .portal-bar-bordered{padding:0 2em;background-color:#fdfdfd;border:1px solid #a2a9b1;clear:both;margin:1em auto 0}.mw-parser-output .portal-bar-related{font-size:100%;justify-content:flex-start}.mw-parser-output .portal-bar-unbordered{padding:0 1.7em;margin-left:0}.mw-parser-output .portal-bar-header{margin:0 1em 0 0.5em;flex:0 0 auto;min-height:24px}.mw-parser-output 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