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class="vector-toc-list"> <li id="toc-Electrostatics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Electrostatics"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Electrostatics</span> </div> </a> <ul id="toc-Electrostatics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Electrodynamics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Electrodynamics"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Electrodynamics</span> </div> </a> <ul id="toc-Electrodynamics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Circuit_theory" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Circuit_theory"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Circuit theory</span> </div> </a> <ul id="toc-Circuit_theory-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Volt" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Volt"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Volt</span> </div> </a> <ul id="toc-Volt-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Hydraulic_analogy" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Hydraulic_analogy"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Hydraulic analogy</span> </div> </a> <ul id="toc-Hydraulic_analogy-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Applications" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Applications"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Applications</span> </div> </a> <button aria-controls="toc-Applications-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Applications subsection</span> </button> <ul id="toc-Applications-sublist" class="vector-toc-list"> <li id="toc-Addition_of_voltages" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Addition_of_voltages"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Addition of voltages</span> </div> </a> <ul id="toc-Addition_of_voltages-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Measuring_instruments" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Measuring_instruments"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Measuring instruments</span> </div> </a> <ul id="toc-Measuring_instruments-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Typical_voltages" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Typical_voltages"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Typical voltages</span> </div> </a> <ul id="toc-Typical_voltages-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Galvani_potential_vs._electrochemical_potential" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Galvani_potential_vs._electrochemical_potential"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Galvani potential vs. electrochemical potential</span> </div> </a> <ul id="toc-Galvani_potential_vs._electrochemical_potential-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-History" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#History"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>History</span> </div> </a> <ul id="toc-History-sublist" class="vector-toc-list"> </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">9</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </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">10</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Footnotes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Footnotes"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>Footnotes</span> </div> </a> <ul id="toc-Footnotes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">12</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <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">Voltage</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 99 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-99" 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">99 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_spanning" title="Elektriese spanning – Afrikaans" lang="af" hreflang="af" data-title="Elektriese spanning" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AC%D9%87%D8%AF_%D9%83%D9%87%D8%B1%D8%A8%D8%A7%D8%A6%D9%8A" title="جهد كهربائي – Arabic" lang="ar" hreflang="ar" data-title="جهد كهربائي" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/G%C9%99rginlik_(elektrik)" title="Gərginlik (elektrik) – Azerbaijani" lang="az" hreflang="az" data-title="Gərginlik (elektrik)" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D9%88%D9%88%D9%84%D8%AA%D8%A7%DA%98" title="وولتاژ – South Azerbaijani" lang="azb" hreflang="azb" data-title="وولتاژ" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AC%E0%A6%BF%E0%A6%AD%E0%A6%AC" title="বিভব – Bangla" lang="bn" hreflang="bn" data-title="বিভব" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Ti%C4%81n-ap" title="Tiān-ap – Minnan" lang="nan" hreflang="nan" data-title="Tiān-ap" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-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%D0%B0%D0%B5_%D0%BD%D0%B0%D0%BF%D1%80%D1%83%D0%B6%D0%B0%D0%BD%D0%BD%D0%B5" title="Электрычнае напружанне – Belarusian" lang="be" hreflang="be" data-title="Электрычнае напружанне" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%9D%D0%B0%D0%BF%D1%80%D1%83%D0%B3%D0%B0" title="Напруга – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Напруга" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%95%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%BE_%D0%BD%D0%B0%D0%BF%D1%80%D0%B5%D0%B6%D0%B5%D0%BD%D0%B8%D0%B5" title="Електрическо напрежение – Bulgarian" lang="bg" hreflang="bg" data-title="Електрическо напрежение" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bar mw-list-item"><a href="https://bar.wikipedia.org/wiki/Elektrische_Spaunnung" title="Elektrische Spaunnung – Bavarian" lang="bar" hreflang="bar" data-title="Elektrische Spaunnung" data-language-autonym="Boarisch" data-language-local-name="Bavarian" class="interlanguage-link-target"><span>Boarisch</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Elektri%C4%8Dni_napon" title="Električni napon – Bosnian" lang="bs" hreflang="bs" data-title="Električni napon" 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/Difer%C3%A8ncia_de_potencial" title="Diferència de potencial – Catalan" lang="ca" hreflang="ca" data-title="Diferència de potencial" 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_%D1%85%D0%B8%D0%B2%D1%80%D0%B5%D0%BB%C4%95%D1%85" title="Электро хиврелĕх – Chuvash" lang="cv" hreflang="cv" data-title="Электро хиврелĕх" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-ceb mw-list-item"><a href="https://ceb.wikipedia.org/wiki/Boltahe" title="Boltahe – Cebuano" lang="ceb" hreflang="ceb" data-title="Boltahe" data-language-autonym="Cebuano" data-language-local-name="Cebuano" class="interlanguage-link-target"><span>Cebuano</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Elektrick%C3%A9_nap%C4%9Bt%C3%AD" title="Elektrické napětí – Czech" lang="cs" hreflang="cs" data-title="Elektrické napětí" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Foltedd" title="Foltedd – Welsh" lang="cy" hreflang="cy" data-title="Foltedd" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Elektrisk_sp%C3%A6nding" title="Elektrisk spænding – Danish" lang="da" hreflang="da" data-title="Elektrisk spænding" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Elektrische_Spannung" title="Elektrische Spannung – German" lang="de" hreflang="de" data-title="Elektrische Spannung" 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/Pinge_(elekter)" title="Pinge (elekter) – Estonian" lang="et" hreflang="et" data-title="Pinge (elekter)" 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%94%CE%B9%CE%B1%CF%86%CE%BF%CF%81%CE%AC_%CE%B4%CF%85%CE%BD%CE%B1%CE%BC%CE%B9%CE%BA%CE%BF%CF%8D" title="Διαφορά δυναμικού – Greek" lang="el" hreflang="el" data-title="Διαφορά δυναμικού" 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/Tensi%C3%B3n_(electricidad)" title="Tensión (electricidad) – Spanish" lang="es" hreflang="es" data-title="Tensión (electricidad)" 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_tensio" title="Elektra tensio – Esperanto" lang="eo" hreflang="eo" data-title="Elektra tensio" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-ext mw-list-item"><a href="https://ext.wikipedia.org/wiki/Tensi%C3%B3n" title="Tensión – Extremaduran" lang="ext" hreflang="ext" data-title="Tensión" data-language-autonym="Estremeñu" data-language-local-name="Extremaduran" class="interlanguage-link-target"><span>Estremeñu</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Tentsio_(elektrizitatea)" title="Tentsio (elektrizitatea) – Basque" lang="eu" hreflang="eu" data-title="Tentsio (elektrizitatea)" 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%88%D9%84%D8%AA%D8%A7%DA%98" title="ولتاژ – Persian" lang="fa" hreflang="fa" data-title="ولتاژ" 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/Tension_%C3%A9lectrique" title="Tension électrique – French" lang="fr" hreflang="fr" data-title="Tension 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/Difr%C3%ADocht_poit%C3%A9insil" title="Difríocht poitéinsil – Irish" lang="ga" hreflang="ga" data-title="Difríocht poitéinsil" 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/Tensi%C3%B3n_el%C3%A9ctrica" title="Tensión eléctrica – Galician" lang="gl" hreflang="gl" data-title="Tensión eléctrica" 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%EC%95%95" title="전압 – Korean" lang="ko" hreflang="ko" data-title="전압" 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%AC%D5%A1%D6%80%D5%B8%D6%82%D5%B4" title="Էլեկտրական լարում – Armenian" lang="hy" hreflang="hy" data-title="Էլեկտրական լարում" 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%AD%E0%A4%B5%E0%A4%BE%E0%A4%82%E0%A4%A4%E0%A4%B0" title="विभवांतर – Hindi" lang="hi" hreflang="hi" data-title="विभवांतर" 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/Napon" title="Napon – Croatian" lang="hr" hreflang="hr" data-title="Napon" 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/Tegangan_listrik" title="Tegangan listrik – Indonesian" lang="id" hreflang="id" data-title="Tegangan 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-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Voltage" title="Voltage – Interlingua" lang="ia" hreflang="ia" data-title="Voltage" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-zu mw-list-item"><a href="https://zu.wikipedia.org/wiki/Ubuvuve" title="Ubuvuve – Zulu" lang="zu" hreflang="zu" data-title="Ubuvuve" data-language-autonym="IsiZulu" data-language-local-name="Zulu" class="interlanguage-link-target"><span>IsiZulu</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Rafspenna" title="Rafspenna – Icelandic" lang="is" hreflang="is" data-title="Rafspenna" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Tensione_elettrica" title="Tensione elettrica – Italian" lang="it" hreflang="it" data-title="Tensione elettrica" 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%AA%D7%97_%D7%97%D7%A9%D7%9E%D7%9C%D7%99" title="מתח חשמלי – Hebrew" lang="he" hreflang="he" data-title="מתח חשמלי" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Tegangan" title="Tegangan – Javanese" lang="jv" hreflang="jv" data-title="Tegangan" data-language-autonym="Jawa" data-language-local-name="Javanese" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%94%E1%83%9A%E1%83%94%E1%83%A5%E1%83%A2%E1%83%A0%E1%83%A3%E1%83%9A%E1%83%98_%E1%83%AB%E1%83%90%E1%83%91%E1%83%95%E1%83%90" title="ელექტრული ძაბვა – Georgian" lang="ka" hreflang="ka" data-title="ელექტრული ძაბვა" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9A%D0%B5%D1%80%D0%BD%D0%B5%D1%83" title="Кернеу – Kazakh" lang="kk" hreflang="kk" data-title="Кернеу" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Volteji" title="Volteji – Swahili" lang="sw" hreflang="sw" data-title="Volteji" data-language-autonym="Kiswahili" data-language-local-name="Swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%AD%D0%BB%D0%B5%D0%BA%D1%82%D1%80_%D1%87%D1%8B%D2%A3%D0%B0%D0%BB%D1%83%D1%83%D1%81%D1%83" title="Электр чыңалуусу – Kyrgyz" lang="ky" hreflang="ky" data-title="Электр чыңалуусу" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Tensio_electrica" title="Tensio electrica – Latin" lang="la" hreflang="la" data-title="Tensio electrica" 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/Spriegums" title="Spriegums – Latvian" lang="lv" hreflang="lv" data-title="Spriegums" 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_%C4%AFtampa" title="Elektrinė įtampa – Lithuanian" lang="lt" hreflang="lt" data-title="Elektrinė įtampa" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Tension_eletriga" title="Tension eletriga – Lombard" lang="lmo" hreflang="lmo" data-title="Tension eletriga" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Elektromos_fesz%C3%BClts%C3%A9g" title="Elektromos feszültség – Hungarian" lang="hu" hreflang="hu" data-title="Elektromos feszültség" 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%9D%D0%B0%D0%BF%D0%BE%D0%BD" title="Напон – Macedonian" lang="mk" hreflang="mk" data-title="Напон" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Herinaratra" title="Herinaratra – Malagasy" lang="mg" hreflang="mg" data-title="Herinaratra" data-language-autonym="Malagasy" data-language-local-name="Malagasy" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%B5%E0%B5%8B%E0%B5%BE%E0%B4%9F%E0%B5%8D%E0%B4%9F%E0%B4%A4" title="വോൾട്ടത – Malayalam" lang="ml" hreflang="ml" data-title="വോൾട്ടത" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%B5%E0%A4%BF%E0%A4%AD%E0%A4%B5%E0%A4%BE%E0%A4%82%E0%A4%A4%E0%A4%B0" title="विभवांतर – Marathi" lang="mr" hreflang="mr" data-title="विभवांतर" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Voltan" title="Voltan – Malay" lang="ms" hreflang="ms" data-title="Voltan" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A5%D2%AF%D1%87%D0%B4%D1%8D%D0%BB" title="Хүчдэл – Mongolian" lang="mn" hreflang="mn" data-title="Хүчдэл" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%97%E1%80%AD%E1%80%AF%E1%80%B7%E1%80%A1%E1%80%AC%E1%80%B8" title="ဗို့အား – Burmese" lang="my" hreflang="my" data-title="ဗို့အား" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmese" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Elektrische_spanning" title="Elektrische spanning – Dutch" lang="nl" hreflang="nl" data-title="Elektrische spanning" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E9%9B%BB%E5%9C%A7" title="電圧 – Japanese" lang="ja" hreflang="ja" data-title="電圧" 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-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Elektrisk_sp%C3%A4%C3%A4nang" title="Elektrisk späänang – Northern Frisian" lang="frr" hreflang="frr" data-title="Elektrisk späänang" data-language-autonym="Nordfriisk" data-language-local-name="Northern Frisian" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-no badge-Q17437798 badge-goodarticle mw-list-item" title="good article badge"><a href="https://no.wikipedia.org/wiki/Elektrisk_spenning" title="Elektrisk spenning – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Elektrisk spenning" 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_spenning" title="Elektrisk spenning – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Elektrisk spenning" 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/Tension_electrica" title="Tension electrica – Occitan" lang="oc" hreflang="oc" data-title="Tension electrica" 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_kuchlanish" title="Elektr kuchlanish – Uzbek" lang="uz" hreflang="uz" data-title="Elektr kuchlanish" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%B5%E0%A9%8B%E0%A8%B2%E0%A8%9F%E0%A9%87%E0%A8%9C" title="ਵੋਲਟੇਜ – Punjabi" lang="pa" hreflang="pa" data-title="ਵੋਲਟੇਜ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D9%88%D9%88%D9%84%D9%B9%DB%8C%D8%AC" title="وولٹیج – Western Punjabi" lang="pnb" hreflang="pnb" data-title="وولٹیج" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D9%88%D9%84%D9%BC%DB%90%D8%AC" title="ولټېج – Pashto" lang="ps" hreflang="ps" data-title="ولټېج" data-language-autonym="پښتو" data-language-local-name="Pashto" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Napi%C4%99cie_elektryczne" title="Napięcie elektryczne – Polish" lang="pl" hreflang="pl" data-title="Napięcie elektryczne" 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/Tens%C3%A3o_el%C3%A9trica" title="Tensão elétrica – Portuguese" lang="pt" hreflang="pt" data-title="Tensão elétrica" 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/Tensiune_electric%C4%83" title="Tensiune electrică – Romanian" lang="ro" hreflang="ro" data-title="Tensiune electrică" 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_mast%27ay" title="Pinchikilla mast'ay – Quechua" lang="qu" hreflang="qu" data-title="Pinchikilla mast'ay" data-language-autonym="Runa Simi" data-language-local-name="Quechua" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%AD%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%BE%D0%B5_%D0%BD%D0%B0%D0%BF%D1%80%D1%8F%D0%B6%D0%B5%D0%BD%D0%B8%D0%B5" title="Электрическое напряжение – Russian" lang="ru" hreflang="ru" data-title="Электрическое напряжение" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Voltage" title="Voltage – Scots" lang="sco" hreflang="sco" data-title="Voltage" data-language-autonym="Scots" data-language-local-name="Scots" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Tensioni_elektrik" title="Tensioni elektrik – Albanian" lang="sq" hreflang="sq" data-title="Tensioni elektrik" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B7%80%E0%B7%9D%E0%B6%BD%E0%B7%8A%E0%B6%A7%E0%B7%93%E0%B6%BA%E0%B6%AD%E0%B7%8F%E0%B7%80" title="වෝල්ටීයතාව – Sinhala" lang="si" hreflang="si" data-title="වෝල්ටීයතාව" data-language-autonym="සිංහල" data-language-local-name="Sinhala" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Voltage" title="Voltage – Simple English" lang="en-simple" hreflang="en-simple" data-title="Voltage" 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%A9_nap%C3%A4tie" title="Elektrické napätie – Slovak" lang="sk" hreflang="sk" data-title="Elektrické napätie" 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%8Dna_napetost" title="Električna napetost – Slovenian" lang="sl" hreflang="sl" data-title="Električna napetost" 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/%DA%A4%DB%86%DA%B5%D8%AA%DB%8C%DB%95" title="ڤۆڵتیە – Central Kurdish" lang="ckb" hreflang="ckb" data-title="ڤۆڵتیە" 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%B8_%D0%BD%D0%B0%D0%BF%D0%BE%D0%BD" title="Електрични напон – Serbian" lang="sr" hreflang="sr" data-title="Електрични напон" 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%8Dni_napon" title="Električni napon – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Električni napon" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Voltase" title="Voltase – Sundanese" lang="su" hreflang="su" data-title="Voltase" data-language-autonym="Sunda" data-language-local-name="Sundanese" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/J%C3%A4nnite" title="Jännite – Finnish" lang="fi" hreflang="fi" data-title="Jännite" 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_sp%C3%A4nning" title="Elektrisk spänning – Swedish" lang="sv" hreflang="sv" data-title="Elektrisk spänning" 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/Boltahe" title="Boltahe – Tagalog" lang="tl" hreflang="tl" data-title="Boltahe" 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%A9%E0%AE%B4%E0%AF%81%E0%AE%A4%E0%AF%8D%E0%AE%A4%E0%AE%AE%E0%AF%8D" title="மின்னழுத்தம் – Tamil" lang="ta" hreflang="ta" data-title="மின்னழுத்தம்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%AD%D0%BB%D0%B5%D0%BA%D1%82%D1%80_%D0%BA%D3%A9%D1%87%D3%99%D0%BD%D0%B5%D1%88%D0%B5" title="Электр көчәнеше – Tatar" lang="tt" hreflang="tt" data-title="Электр көчәнеше" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatar" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%B5%E0%B1%8B%E0%B0%B2%E0%B1%8D%E0%B0%9F%E0%B1%87%E0%B0%9C%E0%B1%8D" title="వోల్టేజ్ – Telugu" lang="te" hreflang="te" data-title="వోల్టేజ్" data-language-autonym="తెలుగు" data-language-local-name="Telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%81%E0%B8%A3%E0%B8%87%E0%B8%94%E0%B8%B1%E0%B8%99%E0%B9%84%E0%B8%9F%E0%B8%9F%E0%B9%89%E0%B8%B2" title="แรงดันไฟฟ้า – Thai" lang="th" hreflang="th" data-title="แรงดันไฟฟ้า" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li 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<div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Difference in electric potential between two points in space</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">For other uses, see <a href="/wiki/Voltage_(disambiguation)" class="mw-disambig" title="Voltage (disambiguation)">Voltage (disambiguation)</a>.</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">"Potential difference" redirects here. For other uses, see <a href="/wiki/Potential" title="Potential">Potential</a>.</div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-More_citations_needed plainlinks metadata ambox ambox-content ambox-Refimprove" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This article <b>needs additional citations for <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verification</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Voltage" title="Special:EditPage/Voltage">improve this article</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and removed.<br /><small><span class="plainlinks"><i>Find sources:</i> <a rel="nofollow" class="external text" href="https://www.google.com/search?as_eq=wikipedia&q=%22Voltage%22">"Voltage"</a> – <a rel="nofollow" class="external text" href="https://www.google.com/search?tbm=nws&q=%22Voltage%22+-wikipedia&tbs=ar:1">news</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?&q=%22Voltage%22&tbs=bkt:s&tbm=bks">newspapers</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?tbs=bks:1&q=%22Voltage%22+-wikipedia">books</a> <b>·</b> <a rel="nofollow" class="external text" href="https://scholar.google.com/scholar?q=%22Voltage%22">scholar</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.jstor.org/action/doBasicSearch?Query=%22Voltage%22&acc=on&wc=on">JSTOR</a></span></small></span> <span class="date-container"><i>(<span class="date">February 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.infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox"><tbody><tr><th colspan="2" class="infobox-above">Voltage</th></tr><tr><td colspan="2" class="infobox-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:AA_AAA_AAAA_A23_battery_comparison-1.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/AA_AAA_AAAA_A23_battery_comparison-1.jpg/220px-AA_AAA_AAAA_A23_battery_comparison-1.jpg" decoding="async" width="220" height="198" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/AA_AAA_AAAA_A23_battery_comparison-1.jpg/330px-AA_AAA_AAAA_A23_battery_comparison-1.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d6/AA_AAA_AAAA_A23_battery_comparison-1.jpg/440px-AA_AAA_AAAA_A23_battery_comparison-1.jpg 2x" data-file-width="510" data-file-height="458" /></a></span><div class="infobox-caption"><a href="/wiki/Battery_(electricity)" class="mw-redirect" title="Battery (electricity)">Batteries</a> are sources of voltage in many <a href="/wiki/Electrical_network" title="Electrical network">electric circuits</a>.</div></td></tr><tr><th scope="row" class="infobox-label"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;">Common symbols</div></th><td class="infobox-data"><span class="texhtml"><i>V</i></span> , <span class="texhtml">∆<i>V</i></span> , <span class="texhtml"><i>U</i></span> , <span class="texhtml">∆<i>U</i></span></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/SI_unit" class="mw-redirect" title="SI unit">SI unit</a></th><td class="infobox-data"><a href="/wiki/Volt" title="Volt">volt</a></td></tr><tr><th scope="row" class="infobox-label">In <a href="/wiki/SI_base_unit" title="SI base unit"><span class="wrap">SI base units</span></a></th><td class="infobox-data">kg⋅m<sup>2</sup>⋅s<sup>−3</sup>⋅A<sup>−1</sup></td></tr><tr><th scope="row" class="infobox-label"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;">Derivations from<br />other quantities</div></th><td class="infobox-data">Voltage = <a href="/wiki/Energy" title="Energy">Energy</a> / <a href="/wiki/Electric_charge" title="Electric charge">charge</a></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Dimensional_analysis#Formulation" title="Dimensional analysis">Dimension</a></th><td class="infobox-data"><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 {\mathsf {M}}{\mathsf {L}}^{2}{\mathsf {T}}^{-3}{\mathsf {I}}^{-1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">M</mi> </mrow> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">L</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">T</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>3</mn> </mrow> </msup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">I</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathsf {M}}{\mathsf 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srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0d/VFPt_Solenoid_correct2.svg/285px-VFPt_Solenoid_correct2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0d/VFPt_Solenoid_correct2.svg/380px-VFPt_Solenoid_correct2.svg.png 2x" data-file-width="490" data-file-height="200" /></a></span></td></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Electricity" title="Electricity">Electricity</a></li> <li><a href="/wiki/Magnetism" title="Magnetism">Magnetism</a></li> <li><a href="/wiki/Optics" title="Optics">Optics</a></li> <li><a href="/wiki/History_of_electromagnetic_theory" title="History of electromagnetic theory">History</a></li> <li><a href="/wiki/Computational_electromagnetics" title="Computational electromagnetics">Computational</a></li> <li><a href="/wiki/List_of_textbooks_in_electromagnetism" title="List of textbooks in electromagnetism">Textbooks</a></li> <li><a href="/wiki/List_of_electrical_phenomena" title="List of electrical phenomena">Phenomena</a></li></ul></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/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 href="/wiki/Electrical_network" title="Electrical network">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 class="mw-selflink selflink">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> <p><b>Voltage</b>, also known as <b>(electrical) potential difference</b>, <b>electric pressure</b>, or <b>electric tension</b> is the difference in <a href="/wiki/Electric_potential" title="Electric potential">electric potential</a> between two points.<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><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> In a <a href="/wiki/Electrostatics" title="Electrostatics">static</a> <a href="/wiki/Electric_field" title="Electric field">electric field</a>, it corresponds to the <a href="/wiki/Work_(electrical)" class="mw-redirect" title="Work (electrical)">work</a> needed per unit of charge to move a positive <a href="/wiki/Test_particle#Electrostatics" title="Test particle">test charge</a> from the first point to the second point. In the <a href="/wiki/SI_unit" class="mw-redirect" title="SI unit">International System of Units</a> (SI), the <a href="/wiki/SI_derived_unit" title="SI derived unit">derived unit</a> for voltage is the <i><a href="/wiki/Volt" title="Volt">volt</a> (V)</i>. <sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>The voltage between points can be caused by the build-up of <a href="/wiki/Electric_charge" title="Electric charge">electric charge</a> (e.g., a <a href="/wiki/Capacitor" title="Capacitor">capacitor</a>), and from an <a href="/wiki/Electromotive_force" title="Electromotive force">electromotive force</a> (e.g., <a href="/wiki/Electromagnetic_induction" title="Electromagnetic induction">electromagnetic induction</a> in a <a href="/wiki/Electric_generator" title="Electric generator">generator</a>).<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> On a macroscopic scale, a potential difference can be caused by electrochemical processes (e.g., cells and batteries), the pressure-induced <a href="/wiki/Piezoelectric_effect" class="mw-redirect" title="Piezoelectric effect">piezoelectric effect</a>, and the <a href="/wiki/Thermoelectric_effect" title="Thermoelectric effect">thermoelectric effect</a>. Since it is the difference in electric potential, it is a physical <a href="/wiki/Scalar_(physics)" title="Scalar (physics)">scalar</a> <a href="/wiki/Quantity" title="Quantity">quantity</a>.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p>A <a href="/wiki/Voltmeter" title="Voltmeter">voltmeter</a> can be used to measure the voltage between two points in a system.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> Often a common reference potential such as the <a href="/wiki/Ground_(electricity)" title="Ground (electricity)">ground</a> of the system is used as one of the points. In this case, voltage is often mentioned at a point without completely mentioning the other measurement point. A voltage can be associated with either a source of energy or the loss, dissipation, or storage of energy. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Definition">Definition</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Voltage&action=edit&section=1" title="Edit section: Definition"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The SI unit of work per unit charge is the <a href="/wiki/Joule" title="Joule">joule</a> per <a href="/wiki/Coulomb" title="Coulomb">coulomb</a>, where 1 volt = 1 joule (of work) per 1 coulomb of charge.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (March 2024)">citation needed</span></a></i>]</sup> The old SI definition for <i>volt</i> used <a href="/wiki/Electric_power" title="Electric power">power</a> and <a href="/wiki/Electric_current" title="Electric current">current</a>; starting in 1990, the <a href="/wiki/Quantum_Hall_effect" title="Quantum Hall effect">quantum Hall</a> and <a href="/wiki/Josephson_effect" title="Josephson effect">Josephson effect</a> were used,<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> and in 2019 <a href="/wiki/Physical_constant" title="Physical constant">physical constants</a> were given defined values for the definition of all SI units. </p><p>Voltage is denoted symbolically by <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aa0ec3d68205fb7f4452de096cb34a50f661111e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.723ex; height:2.176ex;" alt="{\displaystyle \Delta V}"></span>, simplified <i>V</i>,<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> especially in <a href="/wiki/English_language" title="English language">English</a>-speaking countries. Internationally, the symbol <i>U</i> is standardized.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> It is used, for instance, in the context of <a href="/wiki/Ohm%27s_law" title="Ohm's law">Ohm's</a> or <a href="/wiki/Kirchhoff%27s_circuit_laws" title="Kirchhoff's circuit laws">Kirchhoff's circuit laws</a>. </p><p>The <a href="/wiki/Electrochemical_potential" title="Electrochemical potential">electrochemical potential</a> is the voltage that can be directly measured with a voltmeter.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> The <a href="/wiki/Galvani_potential" title="Galvani potential">Galvani potential</a> that exists in structures with junctions of dissimilar materials is also work per charge but cannot be measured with a voltmeter in the external circuit (see <a href="#Galvani_potential_vs._electrochemical_potential">§ Galvani potential vs. electrochemical potential</a>). </p><p>Voltage is defined so that negatively charged objects are pulled towards higher voltages, while positively charged objects are pulled towards lower voltages.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> Therefore, the <a href="/wiki/Conventional_current" class="mw-redirect" title="Conventional current">conventional current</a> in a wire or <a href="/wiki/Resistor" title="Resistor">resistor</a> always flows from higher voltage to lower voltage. </p><p>Historically, voltage has been referred to using terms like "tension" and "pressure". Even today, the term "tension" is still used, for example within the phrase "<a href="/wiki/High_voltage" title="High voltage">high tension</a>" (HT) which is commonly used in thermionic valve (<a href="/wiki/Vacuum_tube" title="Vacuum tube">vacuum tube</a>) based and automotive electronics. </p> <div class="mw-heading mw-heading3"><h3 id="Electrostatics">Electrostatics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Voltage&action=edit&section=2" title="Edit section: Electrostatics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Opfindelsernes_bog3_fig282.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/52/Opfindelsernes_bog3_fig282.png/220px-Opfindelsernes_bog3_fig282.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/52/Opfindelsernes_bog3_fig282.png/330px-Opfindelsernes_bog3_fig282.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/52/Opfindelsernes_bog3_fig282.png/440px-Opfindelsernes_bog3_fig282.png 2x" data-file-width="1500" data-file-height="1500" /></a><figcaption>The electric field around the rod exerts a force on the charged pith ball, in an <a href="/wiki/Electroscope" title="Electroscope">electroscope</a></figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Electrostatic_definition_of_voltage.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/25/Electrostatic_definition_of_voltage.svg/220px-Electrostatic_definition_of_voltage.svg.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/25/Electrostatic_definition_of_voltage.svg/330px-Electrostatic_definition_of_voltage.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/25/Electrostatic_definition_of_voltage.svg/440px-Electrostatic_definition_of_voltage.svg.png 2x" data-file-width="560" data-file-height="560" /></a><figcaption>In a static field, the work is independent of the path</figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Electric_potential#Electrostatics" title="Electric potential">Electric potential § Electrostatics</a></div> <p>In <a href="/wiki/Electrostatics" title="Electrostatics">electrostatics</a>, the voltage increase from point <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 \mathbf {r} _{A}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {r} _{A}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/616d51d23b445f2129e504894af3ff6a45fff33c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.567ex; height:2.009ex;" alt="{\displaystyle \mathbf {r} _{A}}"></span> to some point <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 \mathbf {r} _{B}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {r} _{B}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0c7cdc2442eb6d55026b46a3146059c19d747438" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.582ex; height:2.009ex;" alt="{\displaystyle \mathbf {r} _{B}}"></span> is given by the change in <a href="/wiki/Electric_potential#Electrostatics" title="Electric potential">electrostatic potential</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d67b50b7ba03a56fea637093cf80e12807852d19" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\textstyle V}"></span> from <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 \mathbf {r} _{A}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {r} _{A}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/616d51d23b445f2129e504894af3ff6a45fff33c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.567ex; height:2.009ex;" alt="{\displaystyle \mathbf {r} _{A}}"></span> to <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 \mathbf {r} _{B}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {r} _{B}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0c7cdc2442eb6d55026b46a3146059c19d747438" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.582ex; height:2.009ex;" alt="{\displaystyle \mathbf {r} _{B}}"></span>. By definition,<sup id="cite_ref-:1_17-0" class="reference"><a href="#cite_note-:1-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 78">: 78 </span></sup> this is: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}\Delta V_{AB}&=V(\mathbf {r} _{B})-V(\mathbf {r} _{A})\\&=-\int _{\mathbf {r} _{0}}^{\mathbf {r} _{B}}\mathbf {E} \cdot \mathrm {d} {\boldsymbol {\ell }}-\left(-\int _{\mathbf {r} _{0}}^{\mathbf {r} _{A}}\mathbf {E} \cdot \mathrm {d} {\boldsymbol {\ell }}\right)\\&=-\int _{\mathbf {r} _{A}}^{\mathbf {r} _{B}}\mathbf {E} \cdot \mathrm {d} {\boldsymbol {\ell }}\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi mathvariant="normal">Δ</mi> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> <mi>B</mi> </mrow> </msub> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>V</mi> <mo stretchy="false">(</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>−</mo> <mi>V</mi> <mo stretchy="false">(</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mo>−</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">ℓ</mi> </mrow> <mo>−</mo> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">ℓ</mi> </mrow> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mo>−</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">ℓ</mi> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}\Delta V_{AB}&=V(\mathbf {r} _{B})-V(\mathbf {r} _{A})\\&=-\int _{\mathbf {r} _{0}}^{\mathbf {r} _{B}}\mathbf {E} \cdot \mathrm {d} {\boldsymbol {\ell }}-\left(-\int _{\mathbf {r} _{0}}^{\mathbf {r} _{A}}\mathbf {E} \cdot \mathrm {d} {\boldsymbol {\ell }}\right)\\&=-\int _{\mathbf {r} _{A}}^{\mathbf {r} _{B}}\mathbf {E} \cdot \mathrm {d} {\boldsymbol {\ell }}\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4c5042e740229945296a5e386e1391ff90f213a6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -7.338ex; width:42.234ex; height:15.843ex;" alt="{\displaystyle {\begin{aligned}\Delta V_{AB}&=V(\mathbf {r} _{B})-V(\mathbf {r} _{A})\\&=-\int _{\mathbf {r} _{0}}^{\mathbf {r} _{B}}\mathbf {E} \cdot \mathrm {d} {\boldsymbol {\ell }}-\left(-\int _{\mathbf {r} _{0}}^{\mathbf {r} _{A}}\mathbf {E} \cdot \mathrm {d} {\boldsymbol {\ell }}\right)\\&=-\int _{\mathbf {r} _{A}}^{\mathbf {r} _{B}}\mathbf {E} \cdot \mathrm {d} {\boldsymbol {\ell }}\end{aligned}}}"></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {E} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {E} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d7f22b39d51f780fc02859059c1757c606b9de2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.757ex; height:2.176ex;" alt="{\displaystyle \mathbf {E} }"></span> is the intensity of the electric field. </p><p>In this case, the voltage increase from point A to point B is equal to the work done per unit charge, against the electric field, to move the charge from A to B without causing any acceleration.<sup id="cite_ref-:1_17-1" class="reference"><a href="#cite_note-:1-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 90–91">: 90–91 </span></sup> Mathematically, this is expressed as the <a href="/wiki/Line_integral" title="Line integral">line integral</a> of the <a href="/wiki/Electric_field" title="Electric field">electric field</a> along that path. In electrostatics, this line integral is independent of the path taken.<sup id="cite_ref-:1_17-2" class="reference"><a href="#cite_note-:1-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 91">: 91 </span></sup> </p><p>Under this definition, any circuit where there are time-varying magnetic fields, such as <a href="/wiki/Alternating_current" title="Alternating current">AC circuits</a>, will not have a well-defined voltage between nodes in the circuit, since the electric force is not a <a href="/wiki/Conservative_force" title="Conservative force">conservative force</a> in those cases.<sup id="cite_ref-:0_18-0" class="reference"><a href="#cite_note-:0-18"><span class="cite-bracket">[</span>note 1<span class="cite-bracket">]</span></a></sup> However, at lower frequencies when the electric and magnetic fields are not rapidly changing, this can be neglected (see <a href="/wiki/Electrostatics#Electrostatic_approximation" title="Electrostatics">electrostatic approximation</a>). </p> <div class="mw-heading mw-heading3"><h3 id="Electrodynamics">Electrodynamics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Voltage&action=edit&section=3" title="Edit section: Electrodynamics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Electric_potential#Generalization_to_electrodynamics" title="Electric potential">Electric potential § Generalization to electrodynamics</a></div> <p>The electric potential can be generalized to electrodynamics, so that differences in electric potential between points are well-defined even in the presence of time-varying fields. However, unlike in electrostatics, the electric field can no longer be expressed only in terms of the electric potential.<sup id="cite_ref-:1_17-3" class="reference"><a href="#cite_note-:1-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 417">: 417 </span></sup> Furthermore, the potential is no longer uniquely determined up to a constant, and can take significantly different forms depending on the choice of <a href="/wiki/Gauge_fixing" title="Gauge fixing">gauge</a>.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>note 2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:1_17-4" class="reference"><a href="#cite_note-:1-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 419–422">: 419–422 </span></sup> </p><p>In this general case, some authors<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> use the word "voltage" to refer to the line integral of the electric field, rather than to differences in electric potential. In this case, the voltage rise along some path <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {P}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">P</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {P}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/10d6ec962de5797ba4f161c40e66dca74ae95cc6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.704ex; height:2.176ex;" alt="{\displaystyle {\mathcal {P}}}"></span> from <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 \mathbf {r} _{A}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {r} _{A}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/616d51d23b445f2129e504894af3ff6a45fff33c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.567ex; height:2.009ex;" alt="{\displaystyle \mathbf {r} _{A}}"></span> to <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 \mathbf {r} _{B}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {r} _{B}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0c7cdc2442eb6d55026b46a3146059c19d747438" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.582ex; height:2.009ex;" alt="{\displaystyle \mathbf {r} _{B}}"></span> is given by: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta V_{AB}=-\int _{\mathcal {P}}\mathbf {E} \cdot \mathrm {d} {\boldsymbol {\ell }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> <mi>B</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">P</mi> </mrow> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">ℓ</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta V_{AB}=-\int _{\mathcal {P}}\mathbf {E} \cdot \mathrm {d} {\boldsymbol {\ell }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/be9249bdeae8aabca0825cf103be3dd445a26b7f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:20.244ex; height:5.843ex;" alt="{\displaystyle \Delta V_{AB}=-\int _{\mathcal {P}}\mathbf {E} \cdot \mathrm {d} {\boldsymbol {\ell }}}"></span></dd></dl> <p>However, in this case the "voltage" between two points depends on the path taken. </p> <div class="mw-heading mw-heading3"><h3 id="Circuit_theory">Circuit theory</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Voltage&action=edit&section=4" title="Edit section: Circuit theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In <a href="/wiki/Network_analysis_(electrical_circuits)" title="Network analysis (electrical circuits)">circuit analysis</a> and <a href="/wiki/Electrical_engineering" title="Electrical engineering">electrical engineering</a>, <a href="/wiki/Lumped_element_model" class="mw-redirect" title="Lumped element model">lumped element models</a> are used to represent and analyze circuits. These elements are idealized and self-contained circuit elements used to model physical components.<sup id="cite_ref-:2_21-0" class="reference"><a href="#cite_note-:2-21"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p><p>When using a lumped element model, it is assumed that the effects of changing magnetic fields produced by the circuit are suitably contained to each element.<sup id="cite_ref-:2_21-1" class="reference"><a href="#cite_note-:2-21"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> Under these assumptions, the electric field in the region exterior to each component is conservative, and voltages between nodes in the circuit are well-defined, where<sup id="cite_ref-:2_21-2" class="reference"><a href="#cite_note-:2-21"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta V_{AB}=-\int _{\mathbf {r} _{A}}^{\mathbf {r} _{B}}\mathbf {E} \cdot \mathrm {d} {\boldsymbol {\ell }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> <mi>B</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">ℓ</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta V_{AB}=-\int _{\mathbf {r} _{A}}^{\mathbf {r} _{B}}\mathbf {E} \cdot \mathrm {d} {\boldsymbol {\ell }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6dbd80fd919c85cc9b56d223f47a7f6572805cda" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:22.167ex; height:6.176ex;" alt="{\displaystyle \Delta V_{AB}=-\int _{\mathbf {r} _{A}}^{\mathbf {r} _{B}}\mathbf {E} \cdot \mathrm {d} {\boldsymbol {\ell }}}"></span></dd></dl> <p>as long as the path of integration does not pass through the inside of any component. The above is the same formula used in electrostatics. This integral, with the path of integration being along the test leads, is what a voltmeter will actually measure.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>note 3<span class="cite-bracket">]</span></a></sup> </p><p>If uncontained magnetic fields throughout the circuit are not negligible, then their effects can be modelled by adding <a href="/wiki/Mutual_inductance" class="mw-redirect" title="Mutual inductance">mutual inductance</a> elements. In the case of a physical inductor though, the ideal lumped representation is often accurate. This is because the external fields of inductors are generally negligible, especially if the inductor has a closed <a href="/wiki/Magnetic_circuit" title="Magnetic circuit">magnetic path</a>. If external fields are negligible, we find that </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta V_{AB}=-\int _{\mathrm {exterior} }\mathbf {E} \cdot \mathrm {d} {\boldsymbol {\ell }}=L{\frac {dI}{dt}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> <mi>B</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">x</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">r</mi> </mrow> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">ℓ</mi> </mrow> <mo>=</mo> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>I</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta V_{AB}=-\int _{\mathrm {exterior} }\mathbf {E} \cdot \mathrm {d} {\boldsymbol {\ell }}=L{\frac {dI}{dt}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/402f8c0ba204fd9935d04ed909677ad8d4126b87" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:32.481ex; height:5.843ex;" alt="{\displaystyle \Delta V_{AB}=-\int _{\mathrm {exterior} }\mathbf {E} \cdot \mathrm {d} {\boldsymbol {\ell }}=L{\frac {dI}{dt}}}"></span></dd></dl> <p>is path-independent, and there is a well-defined voltage across the inductor's terminals.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> This is the reason that measurements with a voltmeter across an inductor are often reasonably independent of the placement of the test leads. </p> <div class="mw-heading mw-heading2"><h2 id="Volt">Volt</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Voltage&action=edit&section=5" title="Edit section: Volt"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Volt" title="Volt">Volt</a></div> <p>The volt (symbol: <span class="texhtml"><b>V</b></span>) is the <a href="/wiki/SI_derived_unit" title="SI derived unit">derived unit</a> for <a href="/wiki/Electric_potential" title="Electric potential">electric potential</a>, voltage, and <a href="/wiki/Electromotive_force" title="Electromotive force">electromotive force</a>.<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> The volt is named in honour of the Italian physicist <a href="/wiki/Alessandro_Volta" title="Alessandro Volta">Alessandro Volta</a> (1745–1827), who invented the <a href="/wiki/Voltaic_pile" title="Voltaic pile">voltaic pile</a>, possibly the first chemical <a href="/wiki/Battery_(electricity)" class="mw-redirect" title="Battery (electricity)">battery</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Hydraulic_analogy">Hydraulic analogy</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Voltage&action=edit&section=6" title="Edit section: Hydraulic analogy"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Hydraulic_analogy" title="Hydraulic analogy">Hydraulic analogy</a></div> <p>A simple analogy for an <a href="/wiki/Electric_circuit" class="mw-redirect" title="Electric circuit">electric circuit</a> is water flowing in a closed circuit of <a href="/wiki/Pipework" class="mw-redirect" title="Pipework">pipework</a>, driven by a mechanical <a href="/wiki/Pump" title="Pump">pump</a>.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (March 2024)">citation needed</span></a></i>]</sup> This can be called a "water circuit". The potential difference between two points corresponds to the <a href="/wiki/Fluid_pressure" class="mw-redirect" title="Fluid pressure">pressure difference</a> between two points. If the pump creates a pressure difference between two points, then water flowing from one point to the other will be able to do work, such as driving a <a href="/wiki/Turbine" title="Turbine">turbine</a>. Similarly, work can be done by an <a href="/wiki/Electric_current" title="Electric current">electric current</a> driven by the potential difference provided by a <a href="/wiki/Electric_battery" title="Electric battery">battery</a>. For example, the voltage provided by a sufficiently-charged automobile battery can "push" a large current through the windings of an automobile's <a href="/wiki/Starter_motor" class="mw-redirect" title="Starter motor">starter motor</a>. If the pump is not working, it produces no pressure difference, and the turbine will not rotate. Likewise, if the automobile's battery is very weak or "dead" (or "flat"), then it will not turn the starter motor. </p><p>The hydraulic analogy is a useful way of understanding many electrical concepts. In such a system, the work done to move water is equal to the "<a href="/wiki/Pressure" title="Pressure">pressure</a> drop" (compare p.d.) multiplied by the <a href="/wiki/Volume" title="Volume">volume</a> of water moved. Similarly, in an electrical circuit, the work done to move electrons or other charge carriers is equal to "electrical pressure difference" multiplied by the quantity of electrical charges moved. In relation to "flow", the larger the "pressure difference" between two points (potential difference or water pressure difference), the greater the flow between them (electric current or water flow). (See "<a href="/wiki/Electric_power#Definition" title="Electric power">electric power</a>".) </p> <div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Voltage&action=edit&section=7" title="Edit section: Applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:US_Navy_110315-N-0278E-002_High-voltage_electricians_from_Naval_Facilities_Engineering_Command_(NAVFAC)_Hawaii_reconfigure_electrical_circuitry_and.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/40/US_Navy_110315-N-0278E-002_High-voltage_electricians_from_Naval_Facilities_Engineering_Command_%28NAVFAC%29_Hawaii_reconfigure_electrical_circuitry_and.jpg/170px-US_Navy_110315-N-0278E-002_High-voltage_electricians_from_Naval_Facilities_Engineering_Command_%28NAVFAC%29_Hawaii_reconfigure_electrical_circuitry_and.jpg" decoding="async" width="170" height="255" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/40/US_Navy_110315-N-0278E-002_High-voltage_electricians_from_Naval_Facilities_Engineering_Command_%28NAVFAC%29_Hawaii_reconfigure_electrical_circuitry_and.jpg/255px-US_Navy_110315-N-0278E-002_High-voltage_electricians_from_Naval_Facilities_Engineering_Command_%28NAVFAC%29_Hawaii_reconfigure_electrical_circuitry_and.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/40/US_Navy_110315-N-0278E-002_High-voltage_electricians_from_Naval_Facilities_Engineering_Command_%28NAVFAC%29_Hawaii_reconfigure_electrical_circuitry_and.jpg/340px-US_Navy_110315-N-0278E-002_High-voltage_electricians_from_Naval_Facilities_Engineering_Command_%28NAVFAC%29_Hawaii_reconfigure_electrical_circuitry_and.jpg 2x" data-file-width="1200" data-file-height="1800" /></a><figcaption>Working on <a href="/wiki/High_voltage" title="High voltage">high voltage</a> power lines</figcaption></figure> <p>Specifying a voltage measurement requires explicit or implicit specification of the points across which the voltage is measured. When using a voltmeter to measure voltage, one electrical lead of the voltmeter must be connected to the first point, one to the second point. </p><p>A common use of the term "voltage" is in describing the voltage dropped across an electrical device (such as a resistor). The <a href="/wiki/Voltage_drop" title="Voltage drop">voltage drop</a> across the device can be understood as the difference between measurements at each terminal of the device with respect to a common reference point (or <a href="/wiki/Ground_(electricity)" title="Ground (electricity)">ground</a>). The voltage drop is the difference between the two readings. Two points in an electric circuit that are connected by an ideal conductor without resistance and not within a changing <a href="/wiki/Magnetic_field" title="Magnetic field">magnetic field</a> have a voltage of zero. Any two points with the same potential may be connected by a conductor and no current will flow between them. </p> <div class="mw-heading mw-heading3"><h3 id="Addition_of_voltages">Addition of voltages</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Voltage&action=edit&section=8" title="Edit section: Addition of voltages"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The voltage between <i>A</i> and <i>C</i> is the sum of the voltage between <i>A</i> and <i>B</i> and the voltage between <i>B</i> and <i>C</i>. The various voltages in a circuit can be computed using <a href="/wiki/Kirchhoff%27s_circuit_laws" title="Kirchhoff's circuit laws">Kirchhoff's circuit laws</a>. </p><p>When talking about <a href="/wiki/Alternating_current" title="Alternating current">alternating current</a> (AC) there is a difference between instantaneous voltage and average voltage. Instantaneous voltages can be added for <a href="/wiki/Direct_current" title="Direct current">direct current</a> (DC) and AC, but average voltages can be meaningfully added only when they apply to signals that all have the same frequency and phase. </p> <div class="mw-heading mw-heading2"><h2 id="Measuring_instruments">Measuring instruments</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Voltage&action=edit&section=9" title="Edit section: Measuring instruments"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:9VBatteryWithMeter.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1f/9VBatteryWithMeter.jpg/220px-9VBatteryWithMeter.jpg" decoding="async" width="220" height="183" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1f/9VBatteryWithMeter.jpg/330px-9VBatteryWithMeter.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1f/9VBatteryWithMeter.jpg/440px-9VBatteryWithMeter.jpg 2x" data-file-width="589" data-file-height="489" /></a><figcaption><a href="/wiki/Multimeter" title="Multimeter">Multimeter</a> set to measure voltage</figcaption></figure> <p>Instruments for measuring voltages include the <a href="/wiki/Voltmeter" title="Voltmeter">voltmeter</a>, the <a href="/wiki/Potentiometer_(measuring_instrument)" title="Potentiometer (measuring instrument)">potentiometer</a>, and the <a href="/wiki/Oscilloscope" title="Oscilloscope">oscilloscope</a>. <a href="/wiki/Voltmeter" title="Voltmeter">Analog voltmeters</a>, such as moving-coil instruments, work by measuring the current through a fixed resistor, which, according to <a href="/wiki/Ohm%27s_law" title="Ohm's law">Ohm's law</a>, is proportional to the voltage across the resistor. The potentiometer works by balancing the unknown voltage against a known voltage in a <a href="/wiki/Bridge_circuit" title="Bridge circuit">bridge circuit</a>. The cathode-ray oscilloscope works by amplifying the voltage and using it to deflect an <a href="/wiki/Electron" title="Electron">electron</a> beam from a straight path, so that the deflection of the beam is proportional to the voltage. </p> <div class="mw-heading mw-heading2"><h2 id="Typical_voltages">Typical voltages</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Voltage&action=edit&section=10" title="Edit section: Typical voltages"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Volt#Common_voltages" title="Volt">Volt § Common voltages</a>, <a href="/wiki/Orders_of_magnitude_(voltage)" title="Orders of magnitude (voltage)">Orders of magnitude (voltage)</a>, and <a href="/wiki/Mains_electricity#Choice_of_voltage" title="Mains electricity">Mains electricity § Choice of voltage</a></div> <p>A common voltage for <a href="/wiki/Battery_(electricity)" class="mw-redirect" title="Battery (electricity)">flashlight batteries</a> is 1.5 volts (DC). A common voltage for <a href="/wiki/Automotive_battery" title="Automotive battery">automobile batteries</a> is 12 volts (DC). </p><p>Common voltages supplied by power companies to consumers are 110 to 120 volts (AC) and 220 to 240 volts (AC). The voltage in <a href="/wiki/Electric_power_transmission" title="Electric power transmission">electric power transmission</a> lines used to distribute electricity from power stations can be several hundred times greater than consumer voltages, typically 110 to 1200 kV (AC). </p><p>The voltage used in <a href="/wiki/Overhead_line" title="Overhead line">overhead lines</a> to power railway locomotives is between 12 kV and 50 kV (AC) or between 0.75 kV and 3 kV (DC). </p> <div class="mw-heading mw-heading2"><h2 id="Galvani_potential_vs._electrochemical_potential">Galvani potential vs. electrochemical potential</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Voltage&action=edit&section=11" title="Edit section: Galvani potential vs. electrochemical potential"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Galvani_potential" title="Galvani potential">Galvani potential</a>, <a href="/wiki/Electrochemical_potential" title="Electrochemical potential">Electrochemical potential</a>, and <a href="/wiki/Fermi_level" title="Fermi level">Fermi level</a></div> <p>Inside a conductive material, the energy of an electron is affected not only by the average electric potential but also by the specific thermal and atomic environment that it is in. When a <a href="/wiki/Voltmeter" title="Voltmeter">voltmeter</a> is connected between two different types of metal, it measures not the electrostatic potential difference, but instead something else that is affected by thermodynamics.<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> The quantity measured by a voltmeter is the negative of the difference of the <a href="/wiki/Electrochemical_potential" title="Electrochemical potential">electrochemical potential</a> of electrons (<a href="/wiki/Fermi_level" title="Fermi level">Fermi level</a>) divided by the electron charge and commonly referred to as the voltage difference, while the pure unadjusted <a href="/wiki/Electrostatic_potential" class="mw-redirect" title="Electrostatic potential">electrostatic potential</a> (not measurable with a voltmeter) is sometimes called <a href="/wiki/Galvani_potential" title="Galvani potential">Galvani potential</a>. The terms "voltage" and "electric potential" are ambiguous in that, in practice, they can refer to <i>either</i> of these in different contexts. </p> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Voltage&action=edit&section=12" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The term <i>electromotive force</i> was first used by Volta in a letter to <a href="/wiki/Giovanni_Aldini" title="Giovanni Aldini">Giovanni Aldini</a> in 1798, and first appeared in a published paper in 1801 in <i><a href="/wiki/Annales_de_chimie_et_de_physique" title="Annales de chimie et de physique">Annales de chimie et de physique</a></i>.<sup id="cite_ref-Varney_28-0" class="reference"><a href="#cite_note-Varney-28"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 408">: 408 </span></sup> Volta meant by this a force that was not an <a href="/wiki/Electrostatic" class="mw-redirect" title="Electrostatic">electrostatic</a> force, specifically, an <a href="/wiki/Electrochemical" class="mw-redirect" title="Electrochemical">electrochemical</a> force.<sup id="cite_ref-Varney_28-1" class="reference"><a href="#cite_note-Varney-28"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 405">: 405 </span></sup> The term was taken up by <a href="/wiki/Michael_Faraday" title="Michael Faraday">Michael Faraday</a> in connection with <a href="/wiki/Electromagnetic_induction" title="Electromagnetic induction">electromagnetic induction</a> in the 1820s. However, a clear definition of voltage and method of measuring it had not been developed at this time.<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 554">: 554 </span></sup> Volta distinguished electromotive force (emf) from <i>tension</i> (potential difference): the observed potential difference at the terminals of an electrochemical cell when it was open circuit must exactly balance the emf of the cell so that no current flowed.<sup id="cite_ref-Varney_28-2" class="reference"><a href="#cite_note-Varney-28"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 405">: 405 </span></sup> </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 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id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Voltage&action=edit&section=14" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFCretìFontini2019" class="citation book cs1">Cretì, Anna; Fontini, Fulvio (2019-05-30). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=7IKWDwAAQBAJ&pg=PA18"><i>Economics of Electricity: Markets, Competition and Rules</i></a>. Cambridge University Press. p. 18. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-107-18565-4" title="Special:BookSources/978-1-107-18565-4"><bdi>978-1-107-18565-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Economics+of+Electricity%3A+Markets%2C+Competition+and+Rules&rft.pages=18&rft.pub=Cambridge+University+Press&rft.date=2019-05-30&rft.isbn=978-1-107-18565-4&rft.aulast=Cret%C3%AC&rft.aufirst=Anna&rft.au=Fontini%2C+Fulvio&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D7IKWDwAAQBAJ%26pg%3DPA18&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVoltage" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTregub2020" class="citation book cs1">Tregub, Stanislav (2020-08-08). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=HCxHEAAAQBAJ&pg=PA26"><i>Theory of Energy Harmony: Mechanism of Fundamental Interactions</i></a>. Stanislav Tregub. p. 26. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-5-6044739-2-4" title="Special:BookSources/978-5-6044739-2-4"><bdi>978-5-6044739-2-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Theory+of+Energy+Harmony%3A+Mechanism+of+Fundamental+Interactions&rft.pages=26&rft.pub=Stanislav+Tregub&rft.date=2020-08-08&rft.isbn=978-5-6044739-2-4&rft.aulast=Tregub&rft.aufirst=Stanislav&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DHCxHEAAAQBAJ%26pg%3DPA26&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVoltage" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDavid_B._Newell,_Eite_Tiesinga2019" class="citation report cs1">David B. Newell, Eite Tiesinga (August 2019). <a rel="nofollow" class="external text" href="https://nvlpubs.nist.gov/nistpubs/SpecialPublications/NIST.SP.330-2019.pdf">The International System of Units (SI)</a> <span class="cs1-format">(PDF)</span> (Report). National Institute of Standards and Technology. p. 31<span class="reference-accessdate">. Retrieved <span class="nowrap">2 January</span> 2024</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=report&rft.btitle=The+International+System+of+Units+%28SI%29&rft.pages=31&rft.pub=National+Institute+of+Standards+and+Technology&rft.date=2019-08&rft.au=David+B.+Newell%2C+Eite+Tiesinga&rft_id=https%3A%2F%2Fnvlpubs.nist.gov%2Fnistpubs%2FSpecialPublications%2FNIST.SP.330-2019.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVoltage" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHollowayHolloway2020" class="citation book cs1">Holloway, Michael D.; Holloway, Emma (2020-12-09). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Jx0OEAAAQBAJ&pg=PA1259"><i>Dictionary of Industrial Terminology</i></a>. John Wiley & Sons. p. 1259. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-119-36410-8" title="Special:BookSources/978-1-119-36410-8"><bdi>978-1-119-36410-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Dictionary+of+Industrial+Terminology&rft.pages=1259&rft.pub=John+Wiley+%26+Sons&rft.date=2020-12-09&rft.isbn=978-1-119-36410-8&rft.aulast=Holloway&rft.aufirst=Michael+D.&rft.au=Holloway%2C+Emma&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DJx0OEAAAQBAJ%26pg%3DPA1259&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVoltage" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAslamSharmaRahulSaluja2024" class="citation book cs1">Aslam, Dr S.; Sharma, Dr Pradosh Kumar; Rahul, Satyakam; Saluja, Dr Hitanshu (2024-01-26). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=4Wf2EAAAQBAJ&pg=PA17"><i>Integrating Electrical Systems With Intelligent Computing</i></a>. Academic Guru Publishing House. p. 17. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-81-19843-91-6" title="Special:BookSources/978-81-19843-91-6"><bdi>978-81-19843-91-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Integrating+Electrical+Systems+With+Intelligent+Computing&rft.pages=17&rft.pub=Academic+Guru+Publishing+House&rft.date=2024-01-26&rft.isbn=978-81-19843-91-6&rft.aulast=Aslam&rft.aufirst=Dr+S.&rft.au=Sharma%2C+Dr+Pradosh+Kumar&rft.au=Rahul%2C+Satyakam&rft.au=Saluja%2C+Dr+Hitanshu&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D4Wf2EAAAQBAJ%26pg%3DPA17&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVoltage" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text">Demetrius T. Paris and F. Kenneth Hurd, <i>Basic Electromagnetic Theory</i>, McGraw-Hill, New York 1969, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-07-048470-8" title="Special:BookSources/0-07-048470-8">0-07-048470-8</a>, pp. 512, 546</span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text">P. Hammond, <i>Electromagnetism for Engineers</i>, p. 135, Pergamon Press 1969 <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://www.worldcat.org/oclc/854336">854336</a>.</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFExperts2017" class="citation book cs1">Experts, Disha (2017-08-29). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=1OMyDwAAQBAJ&pg=PA64"><i>10 in One Study Package for CBSE Physics Class 12 with 5 Model Papers</i></a>. Disha Publications. p. 64. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-93-86323-72-9" title="Special:BookSources/978-93-86323-72-9"><bdi>978-93-86323-72-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=10+in+One+Study+Package+for+CBSE+Physics+Class+12+with+5+Model+Papers&rft.pages=64&rft.pub=Disha+Publications&rft.date=2017-08-29&rft.isbn=978-93-86323-72-9&rft.aulast=Experts&rft.aufirst=Disha&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D1OMyDwAAQBAJ%26pg%3DPA64&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVoltage" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFInternational" class="citation book cs1">International, Petrogav. <a rel="nofollow" class="external text" href="https://books.google.com/books?id=ZS7JDwAAQBAJ&pg=PA328"><i>Production Course for Hiring on Offshore Oil and Gas Rigs</i></a>. Petrogav International. p. 328.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Production+Course+for+Hiring+on+Offshore+Oil+and+Gas+Rigs&rft.pages=328&rft.pub=Petrogav+International&rft.aulast=International&rft.aufirst=Petrogav&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DZS7JDwAAQBAJ%26pg%3DPA328&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVoltage" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDavid_B._Newell,_Eite_Tiesinga2019" class="citation report cs1">David B. Newell, Eite Tiesinga (August 2019). <a rel="nofollow" class="external text" href="https://nvlpubs.nist.gov/nistpubs/SpecialPublications/NIST.SP.330-2019.pdf">The International System of Units (SI)</a> <span class="cs1-format">(PDF)</span> (Report). National Institute of Standards and Technology. p. 88<span class="reference-accessdate">. Retrieved <span class="nowrap">2 January</span> 2024</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=report&rft.btitle=The+International+System+of+Units+%28SI%29&rft.pages=88&rft.pub=National+Institute+of+Standards+and+Technology&rft.date=2019-08&rft.au=David+B.+Newell%2C+Eite+Tiesinga&rft_id=https%3A%2F%2Fnvlpubs.nist.gov%2Fnistpubs%2FSpecialPublications%2FNIST.SP.330-2019.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVoltage" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text">IEV: <a rel="nofollow" class="external text" href="http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=121-11-25">electric potential</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210428033941/http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=121-11-25">Archived</a> 2021-04-28 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text">IEV: <a rel="nofollow" class="external text" href="http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=121-11-27">voltage</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160203221151/http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=121-11-27">Archived</a> 2016-02-03 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFischer2009" class="citation book cs1">Fischer, Traugott (2009-03-13). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=r8Xasw5l8wQC&pg=PA434"><i>Materials Science for Engineering Students</i></a>. Academic Press. p. 434. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-08-092002-3" title="Special:BookSources/978-0-08-092002-3"><bdi>978-0-08-092002-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Materials+Science+for+Engineering+Students&rft.pages=434&rft.pub=Academic+Press&rft.date=2009-03-13&rft.isbn=978-0-08-092002-3&rft.aulast=Fischer&rft.aufirst=Traugott&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dr8Xasw5l8wQC%26pg%3DPA434&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVoltage" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPulfrey2010" class="citation book cs1">Pulfrey, David L. (2010-01-28). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=y9dYENs2SVUC&pg=PA93"><i>Understanding Modern Transistors and Diodes</i></a>. Cambridge University Press. p. 93. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-139-48467-1" title="Special:BookSources/978-1-139-48467-1"><bdi>978-1-139-48467-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Understanding+Modern+Transistors+and+Diodes&rft.pages=93&rft.pub=Cambridge+University+Press&rft.date=2010-01-28&rft.isbn=978-1-139-48467-1&rft.aulast=Pulfrey&rft.aufirst=David+L.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dy9dYENs2SVUC%26pg%3DPA93&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVoltage" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFVadari2013" class="citation book cs1">Vadari, Mani (2013). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Q85Lz70wdw8C&pg=PA41"><i>Electric System Operations: Evolving to the Modern Grid</i></a>. Artech House. p. 41. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-60807-549-2" title="Special:BookSources/978-1-60807-549-2"><bdi>978-1-60807-549-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Electric+System+Operations%3A+Evolving+to+the+Modern+Grid&rft.pages=41&rft.pub=Artech+House&rft.date=2013&rft.isbn=978-1-60807-549-2&rft.aulast=Vadari&rft.aufirst=Mani&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DQ85Lz70wdw8C%26pg%3DPA41&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVoltage" class="Z3988"></span></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFVadari2020" class="citation book cs1">Vadari, Subramanian (2020-01-31). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=c73PDwAAQBAJ&pg=PA47"><i>Electric System Operations: Evolving to the Modern Grid, Second Edition</i></a>. Artech House. p. 47. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-63081-689-6" title="Special:BookSources/978-1-63081-689-6"><bdi>978-1-63081-689-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Electric+System+Operations%3A+Evolving+to+the+Modern+Grid%2C+Second+Edition&rft.pages=47&rft.pub=Artech+House&rft.date=2020-01-31&rft.isbn=978-1-63081-689-6&rft.aulast=Vadari&rft.aufirst=Subramanian&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dc73PDwAAQBAJ%26pg%3DPA47&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVoltage" class="Z3988"></span></span> </li> <li id="cite_note-:1-17"><span class="mw-cite-backlink">^ <a href="#cite_ref-:1_17-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:1_17-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:1_17-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-:1_17-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-:1_17-4"><sup><i><b>e</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGriffiths1999" class="citation book cs1">Griffiths, David J. (1999). <i>Introduction to Electrodynamics</i> (3rd ed.). Prentice Hall. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/013805326X" title="Special:BookSources/013805326X"><bdi>013805326X</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+Electrodynamics&rft.edition=3rd&rft.pub=Prentice+Hall&rft.date=1999&rft.isbn=013805326X&rft.aulast=Griffiths&rft.aufirst=David+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVoltage" class="Z3988"></span></span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMoonSpencer2013" class="citation book cs1">Moon, Parry; Spencer, Domina Eberle (2013). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=lijEAgAAQBAJ&pg=PA126"><i>Foundations of Electrodynamics</i></a>. Dover Publications. p. 126. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-486-49703-7" title="Special:BookSources/978-0-486-49703-7"><bdi>978-0-486-49703-7</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20220319091311/https://books.google.com/books?id=lijEAgAAQBAJ&pg=PA126">Archived</a> from the original on 2022-03-19<span class="reference-accessdate">. Retrieved <span class="nowrap">2021-11-19</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Foundations+of+Electrodynamics&rft.pages=126&rft.pub=Dover+Publications&rft.date=2013&rft.isbn=978-0-486-49703-7&rft.aulast=Moon&rft.aufirst=Parry&rft.au=Spencer%2C+Domina+Eberle&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DlijEAgAAQBAJ%26pg%3DPA126&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVoltage" class="Z3988"></span></span> </li> <li id="cite_note-:2-21"><span class="mw-cite-backlink">^ <a href="#cite_ref-:2_21-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:2_21-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:2_21-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFA._Agarwal_&_J._Lang2007" class="citation web cs1">A. Agarwal & J. Lang (2007). <a rel="nofollow" class="external text" href="https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-002-circuits-and-electronics-spring-2007/video-lectures/6002_l1.pdf">"Course materials for 6.002 Circuits and Electronics"</a> <span class="cs1-format">(PDF)</span>. <i>MIT OpenCourseWare</i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160409071008/http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-002-circuits-and-electronics-spring-2007/video-lectures/6002_l1.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 9 April 2016<span class="reference-accessdate">. Retrieved <span class="nowrap">4 December</span> 2018</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=MIT+OpenCourseWare&rft.atitle=Course+materials+for+6.002+Circuits+and+Electronics&rft.date=2007&rft.au=A.+Agarwal+%26+J.+Lang&rft_id=https%3A%2F%2Focw.mit.edu%2Fcourses%2Felectrical-engineering-and-computer-science%2F6-002-circuits-and-electronics-spring-2007%2Fvideo-lectures%2F6002_l1.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVoltage" class="Z3988"></span></span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBossavit2008" class="citation journal cs1">Bossavit, Alain (January 2008). "What do voltmeters measure?". <i>COMPEL - the International Journal for Computation and Mathematics in Electrical and Electronic Engineering</i>. <b>27</b>: 9–16. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1108%2F03321640810836582">10.1108/03321640810836582</a> – via ResearchGate.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=COMPEL+-+the+International+Journal+for+Computation+and+Mathematics+in+Electrical+and+Electronic+Engineering&rft.atitle=What+do+voltmeters+measure%3F&rft.volume=27&rft.pages=9-16&rft.date=2008-01&rft_id=info%3Adoi%2F10.1108%2F03321640810836582&rft.aulast=Bossavit&rft.aufirst=Alain&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVoltage" class="Z3988"></span></span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFeynmanLeightonSands" class="citation web cs1">Feynman, Richard; Leighton, Robert B.; Sands, Matthew. <a rel="nofollow" class="external text" href="https://feynmanlectures.caltech.edu/II_22.html">"The Feynman Lectures on Physics Vol. II Ch. 22: AC Circuits"</a>. <i>Caltech</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2021-10-09</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Caltech&rft.atitle=The+Feynman+Lectures+on+Physics+Vol.+II+Ch.+22%3A+AC+Circuits&rft.aulast=Feynman&rft.aufirst=Richard&rft.au=Leighton%2C+Robert+B.&rft.au=Sands%2C+Matthew&rft_id=https%3A%2F%2Ffeynmanlectures.caltech.edu%2FII_22.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVoltage" class="Z3988"></span></span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHanssenHampson2022" class="citation book cs1">Hanssen, Steven; Hampson, Jeffery (2022-09-12). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=zG2dEAAAQBAJ&pg=PA3"><i>Electrical Trade Principles 6e</i></a>. Cengage AU. p. 3. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-17-045885-6" title="Special:BookSources/978-0-17-045885-6"><bdi>978-0-17-045885-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Electrical+Trade+Principles+6e&rft.pages=3&rft.pub=Cengage+AU&rft.date=2022-09-12&rft.isbn=978-0-17-045885-6&rft.aulast=Hanssen&rft.aufirst=Steven&rft.au=Hampson%2C+Jeffery&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DzG2dEAAAQBAJ%26pg%3DPA3&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVoltage" class="Z3988"></span></span> </li> <li id="cite_note-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-26">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCardarelli2012" class="citation book cs1">Cardarelli, Francois (2012-12-06). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=sEHtBwAAQBAJ&pg=PA340"><i>Scientific Unit Conversion: A Practical Guide to Metrication</i></a>. Springer Science & Business Media. p. 340. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4471-3394-0" title="Special:BookSources/978-1-4471-3394-0"><bdi>978-1-4471-3394-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Scientific+Unit+Conversion%3A+A+Practical+Guide+to+Metrication&rft.pages=340&rft.pub=Springer+Science+%26+Business+Media&rft.date=2012-12-06&rft.isbn=978-1-4471-3394-0&rft.aulast=Cardarelli&rft.aufirst=Francois&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DsEHtBwAAQBAJ%26pg%3DPA340&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVoltage" class="Z3988"></span></span> </li> <li id="cite_note-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-27">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBagotskii2006" class="citation book cs1">Bagotskii, Vladimir Sergeevich (2006). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=09QI-assq1cC&pg=PA22"><i>Fundamentals of electrochemistry</i></a>. John Wiley & Sons. p. 22. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-70058-6" title="Special:BookSources/978-0-471-70058-6"><bdi>978-0-471-70058-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fundamentals+of+electrochemistry&rft.pages=22&rft.pub=John+Wiley+%26+Sons&rft.date=2006&rft.isbn=978-0-471-70058-6&rft.aulast=Bagotskii&rft.aufirst=Vladimir+Sergeevich&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D09QI-assq1cC%26pg%3DPA22&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVoltage" class="Z3988"></span></span> </li> <li id="cite_note-Varney-28"><span class="mw-cite-backlink">^ <a href="#cite_ref-Varney_28-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Varney_28-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Varney_28-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text">Robert N. Varney, Leon H. Fisher, <a rel="nofollow" class="external text" href="https://aapt.scitation.org/doi/abs/10.1119/1.12115">"Electromotive force: Volta's forgotten concept"</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210416012226/https://aapt.scitation.org/doi/abs/10.1119/1.12115">Archived</a> 2021-04-16 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, <i>American Journal of Physics</i>, vol. 48, iss. 5, pp. 405–408, May 1980.</span> </li> <li id="cite_note-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-29">^</a></b></span> <span class="reference-text">C. J. Brockman, <a rel="nofollow" class="external text" href="https://pubs.acs.org/doi/abs/10.1021/ed005p549?journalCode=jceda8">"The origin of voltaic electricity: The contact vs. chemical theory before the concept of E. M. F. was developed"</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20220717034921/https://pubs.acs.org/doi/abs/10.1021/ed005p549?journalCode=jceda8">Archived</a> 2022-07-17 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, <i>Journal of Chemical Education</i>, vol. 5, no. 5, pp. 549–555, May 1928</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Footnotes">Footnotes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Voltage&action=edit&section=15" title="Edit section: Footnotes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-:0-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-:0_18-0">^</a></b></span> <span class="reference-text">This follows from the <a href="/wiki/Maxwell-Faraday_equation" class="mw-redirect" title="Maxwell-Faraday equation">Maxwell-Faraday equation</a>: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∇</mi> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2eb118e22c941e34f5537dbbdcaa3d7ba23603e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:15.495ex; height:5.509ex;" alt="{\displaystyle \nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}}"></span> If there are changing magnetic fields in some <a href="/wiki/Simply_connected_space" title="Simply connected space">simply connected</a> region, then the <a href="/wiki/Curl_(mathematics)" title="Curl (mathematics)">curl</a> of the electric field in that region is non-zero, and as a result the electric field is not conservative. For more, see <a href="/wiki/Conservative_force#Mathematical_description" title="Conservative force">Conservative force § Mathematical description</a>.</span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text">For example, in the <a href="/wiki/Lorenz_gauge_condition" title="Lorenz gauge condition">Lorenz gauge</a>, the electric potential is a <a href="/wiki/Retarded_potential" title="Retarded potential">retarded potential</a>, which propagates at the <a href="/wiki/Speed_of_light" title="Speed of light">speed of light</a>; whereas in the <a href="/wiki/Coulomb_Gauge" class="mw-redirect" title="Coulomb Gauge">Coulomb gauge</a>, the potential changes instantaneously when the source charge distribution changes.</span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text">This statement makes a few assumptions about the nature of the voltmeter (these are discussed in the cited paper). One of these assumptions is that the current drawn by the voltmeter is negligible.</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Voltage&action=edit&section=16" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output 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