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Available in 54 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-54" 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">54 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/Reaktansie" title="Reaktansie – Afrikaans" lang="af" hreflang="af" data-title="Reaktansie" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D9%81%D8%A7%D8%B9%D9%84%D8%A9_%D9%83%D9%87%D8%B1%D8%A8%D8%A7%D8%A6%D9%8A%D8%A9" title="مفاعلة كهربائية – Arabic" lang="ar" hreflang="ar" data-title="مفاعلة كهربائية" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Reactancia" title="Reactancia – Asturian" lang="ast" hreflang="ast" data-title="Reactancia" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Ti%C4%81n-kh%C3%B2ng" title="Tiān-khòng – Minnan" lang="nan" hreflang="nan" data-title="Tiān-khòng" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A0%D0%B5%D0%B0%D0%BA%D1%82%D0%B8%D0%B2%D0%BD%D0%BE_%D1%81%D1%8A%D0%BF%D1%80%D0%BE%D1%82%D0%B8%D0%B2%D0%BB%D0%B5%D0%BD%D0%B8%D0%B5" title="Реактивно съпротивление – Bulgarian" lang="bg" hreflang="bg" data-title="Реактивно съпротивление" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/React%C3%A0ncia" title="Reactància – Catalan" lang="ca" hreflang="ca" data-title="Reactància" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Reaktance" title="Reaktance – Czech" lang="cs" hreflang="cs" data-title="Reaktance" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Reaktans" title="Reaktans – Danish" lang="da" hreflang="da" data-title="Reaktans" 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/Blindwiderstand" title="Blindwiderstand – German" lang="de" hreflang="de" data-title="Blindwiderstand" 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/Reaktiivtakistus" title="Reaktiivtakistus – Estonian" lang="et" hreflang="et" data-title="Reaktiivtakistus" 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%86%CE%B5%CF%81%CE%B3%CE%B7_%CE%B1%CE%BD%CF%84%CE%AF%CF%83%CF%84%CE%B1%CF%83%CE%B7" title="Άεργη αντίσταση – Greek" lang="el" hreflang="el" data-title="Άεργη αντίσταση" 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/Reactancia" title="Reactancia – Spanish" lang="es" hreflang="es" data-title="Reactancia" 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/Reaktanco" title="Reaktanco – Esperanto" lang="eo" hreflang="eo" data-title="Reaktanco" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Erreaktantzia_elektriko" title="Erreaktantzia elektriko – Basque" lang="eu" hreflang="eu" data-title="Erreaktantzia elektriko" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B1%D8%A7%DA%A9%D8%AA%D8%A7%D9%86%D8%B3_%D8%A7%D9%84%DA%A9%D8%AA%D8%B1%DB%8C%DA%A9%DB%8C" title="راکتانس الکتریکی – Persian" lang="fa" hreflang="fa" data-title="راکتانس الکتریکی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/R%C3%A9actance_(%C3%A9lectricit%C3%A9)" title="Réactance (électricité) – French" lang="fr" hreflang="fr" data-title="Réactance (électricité)" 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/Freasaitheacht" title="Freasaitheacht – Irish" lang="ga" hreflang="ga" data-title="Freasaitheacht" 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/Reactancia" title="Reactancia – Galician" lang="gl" hreflang="gl" data-title="Reactancia" 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/%EB%B0%98%EC%9D%91%EC%A0%80%ED%95%AD" title="반응저항 – Korean" lang="ko" hreflang="ko" data-title="반응저항" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B5%E0%A5%88%E0%A4%A6%E0%A5%8D%E0%A4%AF%E0%A5%81%E0%A4%A4_%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%A4%E0%A4%BF%E0%A4%98%E0%A4%BE%E0%A4%A4" title="वैद्युत प्रतिघात – Hindi" lang="hi" hreflang="hi" data-title="वैद्युत प्रतिघात" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Elektri%C4%8Dna_reaktancija" title="Električna reaktancija – Croatian" lang="hr" hreflang="hr" data-title="Električna reaktancija" 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/Reaktansi_listrik" title="Reaktansi listrik – Indonesian" lang="id" hreflang="id" data-title="Reaktansi 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-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Launvi%C3%B0n%C3%A1m" title="Launviðnám – Icelandic" lang="is" hreflang="is" data-title="Launviðnám" 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/Reattanza" title="Reattanza – Italian" lang="it" hreflang="it" data-title="Reattanza" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he badge-Q70894304 mw-list-item" title=""><a href="https://he.wikipedia.org/wiki/%D7%94%D7%99%D7%92%D7%91" title="היגב – Hebrew" lang="he" hreflang="he" data-title="היגב" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Reakt%C4%ABv%C4%81_pretest%C4%ABba" title="Reaktīvā pretestība – Latvian" lang="lv" hreflang="lv" data-title="Reaktīvā pretestība" 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/Reaktyvioji_var%C5%BEa" title="Reaktyvioji varža – Lithuanian" lang="lt" hreflang="lt" data-title="Reaktyvioji varža" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Medd%C5%91_ellen%C3%A1ll%C3%A1s" title="Meddő ellenállás – Hungarian" lang="hu" hreflang="hu" data-title="Meddő ellenállás" 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%A0%D0%B5%D0%B0%D0%BA%D1%82%D0%B0%D0%BD%D1%81%D0%B0" title="Реактанса – Macedonian" lang="mk" hreflang="mk" data-title="Реактанса" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Reactantie" title="Reactantie – Dutch" lang="nl" hreflang="nl" data-title="Reactantie" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-new mw-list-item"><a href="https://new.wikipedia.org/wiki/%E0%A4%B0%E0%A4%BF%E0%A4%AF%E0%A4%BE%E0%A4%95%E0%A5%8D%E0%A4%9F%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%A8%E0%A5%8D%E0%A4%B8" title="रियाक्ट्यान्स – Newari" lang="new" hreflang="new" data-title="रियाक्ट्यान्स" data-language-autonym="नेपाल भाषा" data-language-local-name="Newari" class="interlanguage-link-target"><span>नेपाल भाषा</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%AA%E3%82%A2%E3%82%AF%E3%82%BF%E3%83%B3%E3%82%B9" title="リアクタンス – Japanese" lang="ja" hreflang="ja" data-title="リアクタンス" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Reaktans" title="Reaktans – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Reaktans" 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/Reaktans" title="Reaktans – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Reaktans" 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-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Reaktancja_(elektryczno%C5%9B%C4%87)" title="Reaktancja (elektryczność) – Polish" lang="pl" hreflang="pl" data-title="Reaktancja (elektryczność)" 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/Reat%C3%A2ncia" title="Reatância – Portuguese" lang="pt" hreflang="pt" data-title="Reatância" 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/Reactan%C8%9B%C4%83_electric%C4%83" title="Reactanță electrică – Romanian" lang="ro" hreflang="ro" data-title="Reactanță electrică" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A0%D0%B5%D0%B0%D0%BA%D1%82%D0%B8%D0%B2%D0%BD%D0%BE%D0%B5_%D1%81%D0%BE%D0%BF%D1%80%D0%BE%D1%82%D0%B8%D0%B2%D0%BB%D0%B5%D0%BD%D0%B8%D0%B5" title="Реактивное сопротивление – Russian" lang="ru" hreflang="ru" data-title="Реактивное сопротивление" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Reaktancia" title="Reaktancia – Slovak" lang="sk" hreflang="sk" data-title="Reaktancia" 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/Reaktanca" title="Reaktanca – Slovenian" lang="sl" hreflang="sl" data-title="Reaktanca" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/Elektri%C4%8Dna_reaktansa" title="Električna reaktansa – Serbian" lang="sr" hreflang="sr" data-title="Električna reaktansa" 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%8Dna_reaktansa" title="Električna reaktansa – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Električna reaktansa" 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/R%C3%A9aktansi" title="Réaktansi – Sundanese" lang="su" hreflang="su" data-title="Réaktansi" 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/Reaktanssi" title="Reaktanssi – Finnish" lang="fi" hreflang="fi" data-title="Reaktanssi" 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/Reaktans" title="Reaktans – Swedish" lang="sv" hreflang="sv" data-title="Reaktans" 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/Reaktansiya" title="Reaktansiya – Tagalog" lang="tl" hreflang="tl" data-title="Reaktansiya" 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%AE%E0%AE%B1%E0%AF%81%E0%AE%AA%E0%AF%8D%E0%AE%AA%E0%AF%81" title="மின்மறுப்பு – Tamil" lang="ta" hreflang="ta" data-title="மின்மறுப்பு" 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%A0%D0%B5%D0%B0%D0%BA%D1%82%D0%B8%D0%B2_%D0%BA%D0%B0%D1%80%D1%88%D1%8B%D0%BB%D1%8B%D0%BA" title="Реактив каршылык – Tatar" lang="tt" hreflang="tt" data-title="Реактив каршылык" 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-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Reaktans" title="Reaktans – Turkish" lang="tr" hreflang="tr" data-title="Reaktans" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A0%D0%B5%D0%B0%D0%BA%D1%82%D0%B8%D0%B2%D0%BD%D0%B8%D0%B9_%D0%BE%D0%BF%D1%96%D1%80" title="Реактивний опір – Ukrainian" lang="uk" hreflang="uk" data-title="Реактивний опір" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/%C4%90i%E1%BB%87n_kh%C3%A1ng" title="Điện kháng – Vietnamese" lang="vi" hreflang="vi" data-title="Điện kháng" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E7%94%B5%E6%8A%97" title="电抗 – Wu" lang="wuu" hreflang="wuu" data-title="电抗" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E9%9B%BB%E6%8A%97" title="電抗 – Cantonese" lang="yue" hreflang="yue" data-title="電抗" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%94%B5%E6%8A%97" title="电抗 – Chinese" lang="zh" hreflang="zh" data-title="电抗" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span 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(electronics)</a>)</span></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">Opposition to current by inductance or capacitance</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">"Reactance (physics)" redirects here. For other uses, see <a href="/wiki/Reactance_(disambiguation)" class="mw-redirect mw-disambig" title="Reactance (disambiguation)">Reactance</a>.</div> <p>In electrical circuits, <b>reactance</b> is the opposition presented to <a href="/wiki/Alternating_current" title="Alternating current">alternating current</a> by <a href="/wiki/Inductance" title="Inductance">inductance</a> and <a href="/wiki/Capacitance" title="Capacitance">capacitance</a>.<sup id="cite_ref-veley01_1-0" class="reference"><a href="#cite_note-veley01-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Along with resistance, it is one of two elements of <a href="/wiki/Electrical_impedance" title="Electrical impedance">impedance</a>; however, while both elements involve transfer of electrical energy, no <a href="/wiki/Joule_heating" title="Joule heating">dissipation of electrical energy as heat</a> occurs in reactance; instead, the reactance stores energy until a quarter-cycle later when the energy is returned to the circuit. Greater reactance gives smaller current for the same applied <a href="/wiki/Voltage" title="Voltage">voltage</a>. </p><p>Reactance is used to compute <a href="/wiki/Amplitude" title="Amplitude">amplitude</a> and <a href="/wiki/Phase_(waves)" title="Phase (waves)">phase</a> changes of <a href="/wiki/Sine_wave" title="Sine wave">sinusoidal</a> alternating current going through a circuit element. Like resistance, reactance is measured in <a href="/wiki/Ohm" title="Ohm">ohms</a>, with positive values indicating <i>inductive</i> reactance and negative indicating <i>capacitive</i> reactance. It is denoted by the symbol <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}" /></span>. An ideal <a href="/wiki/Resistor" title="Resistor">resistor</a> has zero reactance, whereas ideal reactors have no shunt conductance and no series resistance. As <a href="/wiki/Frequency" title="Frequency">frequency</a> increases, inductive reactance increases and capacitive reactance decreases. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Comparison_to_resistance">Comparison to resistance</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_reactance&action=edit&section=1" title="Edit section: Comparison to resistance"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Reactance is similar to resistance in that larger reactance leads to smaller currents for the same applied voltage. Further, a circuit made entirely of elements that have only reactance (and no resistance) can be treated the same way as a circuit made entirely of resistances. These same techniques can also be used to combine elements with reactance with elements with resistance but <a href="/wiki/Complex_number" title="Complex number">complex numbers</a> are typically needed. This is treated below in the section on <a href="/wiki/Electrical_impedance" title="Electrical impedance">impedance</a>. </p><p>There are several important differences between reactance and resistance, though. First, reactance changes the phase so that the current through the element is shifted by a quarter of a cycle relative to the phase of the voltage applied across the element. Second, power is not dissipated in a purely reactive element but is stored instead. Third, reactances can be negative so that they can 'cancel' each other out. Finally, the main circuit elements that have reactance (capacitors and inductors) have a frequency dependent reactance, unlike resistors which have the same resistance for all frequencies, at least in the ideal case. </p><p>The term <i>reactance</i> was first suggested by French engineer M. Hospitalier in <i>L'Industrie Electrique</i> on 10 May 1893. It was officially adopted by the <a href="/wiki/American_Institute_of_Electrical_Engineers" title="American Institute of Electrical Engineers">American Institute of Electrical Engineers</a> in May 1894.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Capacitive_reactance">Capacitive reactance</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_reactance&action=edit&section=2" title="Edit section: Capacitive reactance"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Capacitance" title="Capacitance">Capacitance</a></div> <p>A capacitor consists of two <a href="/wiki/Electric_conduction" class="mw-redirect" title="Electric conduction">conductors</a> separated by an <a href="/wiki/Electrical_insulation" class="mw-redirect" title="Electrical insulation">insulator</a>, also known as a <a href="/wiki/Dielectric" title="Dielectric">dielectric</a>. </p><p><i>Capacitive reactance</i> is an opposition to the change of voltage across an element. Capacitive reactance <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X_{C}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X_{C}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bbe98111b842bc759e8ca808cfc6a23d3b2b0317" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.406ex; height:2.509ex;" alt="{\displaystyle X_{C}}" /></span> is <a href="/wiki/Inversely_proportional" class="mw-redirect" title="Inversely proportional">inversely proportional</a> to the signal <a href="/wiki/Frequency" title="Frequency">frequency</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}" /></span> (or <a href="/wiki/Angular_frequency" title="Angular frequency">angular frequency</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48eff443f9de7a985bb94ca3bde20813ea737be8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.446ex; height:1.676ex;" alt="{\displaystyle \omega }" /></span>) and the <a href="/wiki/Capacitance" title="Capacitance">capacitance</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 C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4fc55753007cd3c18576f7933f6f089196732029" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}" /></span>.<sup id="cite_ref-Irwin_3-0" class="reference"><a href="#cite_note-Irwin-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>There are two choices in the literature for defining reactance for a capacitor. One is to use a uniform notion of reactance as the imaginary part of impedance, in which case the reactance of a capacitor is the negative number,<sup id="cite_ref-Irwin_3-1" class="reference"><a href="#cite_note-Irwin-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-Glisson_5-0" class="reference"><a href="#cite_note-Glisson-5"><span class="cite-bracket">[</span>5<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 X_{C}=-{\frac {1}{\omega C}}=-{\frac {1}{2\pi fC}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>ω</mi> <mi>C</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>π</mi> <mi>f</mi> <mi>C</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X_{C}=-{\frac {1}{\omega C}}=-{\frac {1}{2\pi fC}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b7998e89e869c9be0ff12c785390a9157d947cfd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:23.642ex; height:5.676ex;" alt="{\displaystyle X_{C}=-{\frac {1}{\omega C}}=-{\frac {1}{2\pi fC}}}" /></span>.</dd></dl> <p>Another choice is to define capacitive reactance as a positive number,<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-Hughes_7-0" class="reference"><a href="#cite_note-Hughes-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><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> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X_{C}={\frac {1}{\omega C}}={\frac {1}{2\pi fC}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>ω</mi> <mi>C</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>π</mi> <mi>f</mi> <mi>C</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X_{C}={\frac {1}{\omega C}}={\frac {1}{2\pi fC}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e33bdd36f50b2832a361a5982bb57c59ee58e6a2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:20.026ex; height:5.676ex;" alt="{\displaystyle X_{C}={\frac {1}{\omega C}}={\frac {1}{2\pi fC}}}" /></span>.</dd></dl> <p>In this case however one needs to remember to add a negative sign for the impedance of a capacitor, i.e. <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z_{c}=-jX_{c}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mi>j</mi> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z_{c}=-jX_{c}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/36d4ad65ca09b6f5898216cf89894223fe8b0a3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.265ex; height:2.509ex;" alt="{\displaystyle Z_{c}=-jX_{c}}" /></span>. </p><p>At <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1ee0fdf0f50fcba5afe3e856fcc7dc6acfa61014" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.54ex; height:2.509ex;" alt="{\displaystyle f=0}" /></span>, the magnitude of the capacitor's reactance is infinite, behaving like an <a href="https://en.wiktionary.org/wiki/open_circuit" class="extiw" title="wikt:open circuit">open circuit</a> (preventing any <a href="/wiki/Electric_current" title="Electric current">current</a> from flowing through the dielectric). As frequency increases, the magnitude of reactance decreases, allowing more current to flow. As <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}" /></span> approaches <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 \infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c26c105004f30c27aa7c2a9c601550a4183b1f21" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.676ex;" alt="{\displaystyle \infty }" /></span>, the capacitor's reactance approaches <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 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2aae8864a3c1fec9585261791a809ddec1489950" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 0}" /></span>, behaving like a <a href="/wiki/Short_circuit" title="Short circuit">short circuit</a>. </p><p>The application of a <a href="/wiki/Direct_current" title="Direct current">DC</a> voltage across a capacitor causes positive <a href="/wiki/Electrical_charge" class="mw-redirect" title="Electrical charge">charge</a> to accumulate on one side and negative <a href="/wiki/Electrical_charge" class="mw-redirect" title="Electrical charge">charge</a> to accumulate on the other side; the <a href="/wiki/Electric_field" title="Electric field">electric field</a> due to the accumulated charge is the source of the opposition to the current. When the <a href="/wiki/Potential" title="Potential">potential</a> associated with the charge exactly balances the applied voltage, the current goes to zero. </p><p>Driven by an AC supply (ideal AC current source), a capacitor will only accumulate a limited amount of charge before the potential difference changes polarity and the charge is returned to the source. The higher the frequency, the less charge will accumulate and the smaller the opposition to the current. </p> <div class="mw-heading mw-heading2"><h2 id="Inductive_reactance">Inductive reactance</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_reactance&action=edit&section=3" title="Edit section: Inductive reactance"><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/Inductance" title="Inductance">Inductance</a></div> <p>Inductive reactance is a property exhibited by an inductor, and inductive reactance exists based on the fact that an electric current produces a magnetic field around it. In the context of an AC circuit (although this concept applies any time current is changing), this magnetic field is constantly changing as a result of current that oscillates back and forth. It is this change in magnetic field that induces another electric current to flow in the same wire (counter-EMF), in a direction such as to oppose the flow of the current originally responsible for producing the magnetic field (known as <a href="/wiki/Lenz%27s_law" title="Lenz's law">Lenz's law</a>). Hence, <i>inductive reactance</i> is an opposition to the change of current through an element. </p><p>For an ideal inductor in an AC circuit, the inhibitive effect on change in current flow results in a delay, or a phase shift, of the alternating current with respect to alternating voltage. Specifically, an ideal inductor (with no resistance) will cause the current to lag the voltage by a quarter cycle, or 90°. </p><p>In electric power systems, inductive reactance (and capacitive reactance, however inductive reactance is more common) can limit the power capacity of an AC transmission line, because power is not completely transferred when voltage and current are out-of-phase (detailed above). That is, current will flow for an out-of-phase system, however real power at certain times will not be transferred, because there will be points during which instantaneous current is positive while instantaneous voltage is negative, or vice versa, implying negative power transfer. Hence, real work is not performed when power transfer is "negative". However, current still flows even when a system is out-of-phase, which causes transmission lines to heat up due to current flow. Consequently, transmission lines can only heat up so much (or else they would physically sag too much, due to the heat expanding the metal transmission lines), so transmission line operators have a "ceiling" on the amount of current that can flow through a given line, and excessive inductive reactance can limit the power capacity of a line. Power providers utilize capacitors to shift the phase and minimize the losses, based on usage patterns. </p><p>Inductive reactance <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X_{L}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X_{L}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59f14ed86135c464841bbc6fba36cfb3997df2ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.276ex; height:2.509ex;" alt="{\displaystyle X_{L}}" /></span> is <a href="/wiki/Proportionality_(mathematics)" title="Proportionality (mathematics)">proportional</a> to the sinusoidal signal <a href="/wiki/Frequency" title="Frequency">frequency</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}" /></span> and the <a href="/wiki/Inductance" title="Inductance">inductance</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 L}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/103168b86f781fe6e9a4a87b8ea1cebe0ad4ede8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.583ex; height:2.176ex;" alt="{\displaystyle L}" /></span>, which depends on the physical shape of the inductor: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X_{L}=\omega L=2\pi fL}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mo>=</mo> <mi>ω</mi> <mi>L</mi> <mo>=</mo> <mn>2</mn> <mi>π</mi> <mi>f</mi> <mi>L</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X_{L}=\omega L=2\pi fL}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a01029033173e630d9e2795da17b2b6e79d5bf6e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:17.857ex; height:2.509ex;" alt="{\displaystyle X_{L}=\omega L=2\pi fL}" /></span>. </p><p>The average current flowing through an <a href="/wiki/Inductance" title="Inductance">inductance</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 L}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/103168b86f781fe6e9a4a87b8ea1cebe0ad4ede8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.583ex; height:2.176ex;" alt="{\displaystyle L}" /></span> in series with a <a href="/wiki/Sinusoidal" class="mw-redirect" title="Sinusoidal">sinusoidal</a> AC voltage source of RMS <a href="/wiki/Amplitude" title="Amplitude">amplitude</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 A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" /></span> and frequency <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}" /></span> is equal to: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I_{L}={A \over \omega L}={A \over 2\pi fL}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>A</mi> <mrow> <mi>ω</mi> <mi>L</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>A</mi> <mrow> <mn>2</mn> <mi>π</mi> <mi>f</mi> <mi>L</mi> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{L}={A \over \omega L}={A \over 2\pi fL}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/99bc1e96bbe186fb150df0771d843575de109c64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:19.275ex; height:5.843ex;" alt="{\displaystyle I_{L}={A \over \omega L}={A \over 2\pi fL}.}" /></span></dd></dl> <p>Because a <a href="/wiki/Square_wave_(waveform)" title="Square wave (waveform)">square wave</a> has multiple amplitudes at sinusoidal <a href="/wiki/Harmonic" title="Harmonic">harmonics</a>, the average current flowing through an <a href="/wiki/Inductance" title="Inductance">inductance</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 L}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/103168b86f781fe6e9a4a87b8ea1cebe0ad4ede8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.583ex; height:2.176ex;" alt="{\displaystyle L}" /></span> in series with a square wave AC voltage source of RMS <a href="/wiki/Amplitude" title="Amplitude">amplitude</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 A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" /></span> and frequency <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}" /></span> is equal to: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I_{L}={A\pi ^{2} \over 8\omega L}={A\pi \over 16fL}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>A</mi> <msup> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>8</mn> <mi>ω</mi> <mi>L</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>A</mi> <mi>π</mi> </mrow> <mrow> <mn>16</mn> <mi>f</mi> <mi>L</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{L}={A\pi ^{2} \over 8\omega L}={A\pi \over 16fL}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4894bca448767285f2fa3d9ed33ca9304295a1c2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:19.621ex; height:6.176ex;" alt="{\displaystyle I_{L}={A\pi ^{2} \over 8\omega L}={A\pi \over 16fL}}" /></span></dd></dl> <p>making it appear as if the inductive reactance to a square wave was about 19% smaller <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X_{L}={16 \over \pi }fL}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>16</mn> <mi>π</mi> </mfrac> </mrow> <mi>f</mi> <mi>L</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X_{L}={16 \over \pi }fL}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dd9a8b5f2673c870960151d50591b77fd676dc3c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:12.397ex; height:5.176ex;" alt="{\displaystyle X_{L}={16 \over \pi }fL}" /></span> than the reactance to the AC sine wave. </p><p>Any conductor of finite dimensions has inductance; the inductance is made larger by the multiple turns in an <a href="/wiki/Electromagnetic_coil" title="Electromagnetic coil">electromagnetic coil</a>. <a href="/wiki/Faraday%27s_law_of_induction" title="Faraday's law of induction">Faraday's law</a> of electromagnetic induction gives the counter-<a href="/wiki/Electromotive_force" title="Electromotive force">emf</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 {\mathcal {E}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">E</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {E}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9c298ed828ff778065aeb5f0f305097f55bb9ae0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.311ex; height:2.176ex;" alt="{\displaystyle {\mathcal {E}}}" /></span> (voltage opposing current) due to a rate-of-change of <a href="/wiki/Magnetic_flux_density" class="mw-redirect" title="Magnetic flux density">magnetic flux density</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {B}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {B}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b8b91c469e83c445f3c1adfcee7d6a11dd6a051" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.247ex; height:1.676ex;" alt="{\displaystyle \scriptstyle {B}}" /></span> through a current loop. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {E}}=-{{d\Phi _{B}} \over dt}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">E</mi> </mrow> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> <msub> <mi mathvariant="normal">Φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {E}}=-{{d\Phi _{B}} \over dt}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e4ff61e87118da0be39e6932bbc467b69d456019" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:11.427ex; height:5.509ex;" alt="{\displaystyle {\mathcal {E}}=-{{d\Phi _{B}} \over dt}}" /></span></dd></dl> <p>For an inductor consisting of a coil with <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle N}" /></span> loops this gives: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {E}}=-N{d\Phi _{B} \over dt}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">E</mi> </mrow> </mrow> <mo>=</mo> <mo>−</mo> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <msub> <mi mathvariant="normal">Φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {E}}=-N{d\Phi _{B} \over dt}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a53a6a439e8dbdba1754e36c92d671e47d0b08e5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:13.491ex; height:5.509ex;" alt="{\displaystyle {\mathcal {E}}=-N{d\Phi _{B} \over dt}}" /></span>.</dd></dl> <p>The counter-emf is the source of the opposition to current flow. A constant <a href="/wiki/Direct_current" title="Direct current">direct current</a> has a zero rate-of-change, and sees an inductor as a <a href="/wiki/Short-circuit" class="mw-redirect" title="Short-circuit">short-circuit</a> (it is typically made from a material with a low <a href="/wiki/Resistivity" class="mw-redirect" title="Resistivity">resistivity</a>). An <a href="/wiki/Alternating_current" title="Alternating current">alternating current</a> has a time-averaged rate-of-change that is proportional to frequency, this causes the increase in inductive reactance with frequency. </p> <div class="mw-heading mw-heading2"><h2 id="Impedance">Impedance</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_reactance&action=edit&section=4" title="Edit section: Impedance"><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/Electrical_impedance" title="Electrical impedance">Electrical impedance</a></div> <p>Both reactance <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {X}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {X}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b304d4de2976f610f0bb24237028399681e16a81" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle {X}}" /></span> and <a href="/wiki/Electrical_resistance" class="mw-redirect" title="Electrical resistance">resistance</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {R}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {R}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3abe7f424f59ed9925c7f622af7aead87831412b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle {R}}" /></span> are components of <a href="/wiki/Electrical_impedance" title="Electrical impedance">impedance</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 {\mathbf {Z} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">Z</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathbf {Z} }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2da9988aa7959c6e2c145c7cc4d73c152d9ed50b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.634ex; height:2.176ex;" alt="{\displaystyle {\mathbf {Z} }}" /></span>. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {Z} =R+\mathbf {j} X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">Z</mi> </mrow> <mo>=</mo> <mi>R</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">j</mi> </mrow> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {Z} =R+\mathbf {j} X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fead8f66a1a2b1e1d001d7bdfbb918f3a76b0e60" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.133ex; height:2.509ex;" alt="{\displaystyle \mathbf {Z} =R+\mathbf {j} X}" /></span></dd></dl> <p>where: </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {Z} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">Z</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {Z} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b776aaf12c2da4b78ca777cb8295c2000bfd51f5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.634ex; height:2.176ex;" alt="{\displaystyle \mathbf {Z} }" /></span> is the complex <a href="/wiki/Electrical_impedance" title="Electrical impedance">impedance</a>, measured in <a href="/wiki/Ohm" title="Ohm">ohms</a>;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}" /></span> is the <a href="/wiki/Electrical_resistance" class="mw-redirect" title="Electrical resistance">resistance</a>, measured in ohms. It is the real part of the impedance: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {R={\text{Re}}{(\mathbf {Z} )}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>Re</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">Z</mi> </mrow> <mo stretchy="false">)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {R={\text{Re}}{(\mathbf {Z} )}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4e40f2419cf510e737d38682fb487a9233f7adb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.049ex; height:2.843ex;" alt="{\displaystyle {R={\text{Re}}{(\mathbf {Z} )}}}" /></span></li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}" /></span> is the reactance, measured in ohms. It is the imaginary part of the impedance: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {X={\text{Im}}{(\mathbf {Z} )}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>Im</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">Z</mi> </mrow> <mo stretchy="false">)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {X={\text{Im}}{(\mathbf {Z} )}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6c01889ffcc7a5b1a9f4bd6629459024ab827804" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.297ex; height:2.843ex;" alt="{\displaystyle {X={\text{Im}}{(\mathbf {Z} )}}}" /></span></li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {j} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">j</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {j} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ca5d874dbb32b8b33e83ca521f592808387a486e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.164ex; width:0.98ex; height:2.509ex;" alt="{\displaystyle \mathbf {j} }" /></span> is the <a href="/wiki/Square_root_of_minus_one" class="mw-redirect" title="Square root of minus one">square root of minus one</a>, usually represented 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 \mathbf {i} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">i</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {i} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dc909dd0c91a68cdb9cda4ae133fa1f82c987c01" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.742ex; height:2.176ex;" alt="{\displaystyle \mathbf {i} }" /></span> in non-electrical formulas. <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 {j} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">j</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {j} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ca5d874dbb32b8b33e83ca521f592808387a486e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.164ex; width:0.98ex; height:2.509ex;" alt="{\displaystyle \mathbf {j} }" /></span> is used so as not to confuse the imaginary unit with current, commonly represented 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 \mathbf {i} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">i</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {i} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dc909dd0c91a68cdb9cda4ae133fa1f82c987c01" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.742ex; height:2.176ex;" alt="{\displaystyle \mathbf {i} }" /></span>.</li></ul> <p>When both a capacitor and an inductor are placed in series in a circuit, their contributions to the total circuit impedance are opposite. Capacitive reactance <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X_{C}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X_{C}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bbe98111b842bc759e8ca808cfc6a23d3b2b0317" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.406ex; height:2.509ex;" alt="{\displaystyle X_{C}}" /></span> and inductive reactance <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X_{L}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X_{L}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59f14ed86135c464841bbc6fba36cfb3997df2ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.276ex; height:2.509ex;" alt="{\displaystyle X_{L}}" /></span> contribute to the total reactance <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}" /></span> as follows: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {X=X_{L}+X_{C}=\omega L-{\frac {1}{\omega C}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> <mo>=</mo> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mo>=</mo> <mi>ω</mi> <mi>L</mi> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>ω</mi> <mi>C</mi> </mrow> </mfrac> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {X=X_{L}+X_{C}=\omega L-{\frac {1}{\omega C}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b290c32d1611d25d9ae55bcb51613fece517395" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:27.616ex; height:5.343ex;" alt="{\displaystyle {X=X_{L}+X_{C}=\omega L-{\frac {1}{\omega C}}}}" /></span></dd></dl> <p>where: </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X_{L}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X_{L}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59f14ed86135c464841bbc6fba36cfb3997df2ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.276ex; height:2.509ex;" alt="{\displaystyle X_{L}}" /></span> is the <a href="/wiki/Inductance" title="Inductance">inductive</a> reactance, measured in ohms;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X_{C}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X_{C}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bbe98111b842bc759e8ca808cfc6a23d3b2b0317" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.406ex; height:2.509ex;" alt="{\displaystyle X_{C}}" /></span> is the <a href="/wiki/Capacitance" title="Capacitance">capacitive</a> reactance, measured in ohms;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48eff443f9de7a985bb94ca3bde20813ea737be8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.446ex; height:1.676ex;" alt="{\displaystyle \omega }" /></span> is the angular frequency, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2\pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2\pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/73efd1f6493490b058097060a572606d2c550a06" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.494ex; height:2.176ex;" alt="{\displaystyle 2\pi }" /></span> times the frequency in <a href="/wiki/Hertz" title="Hertz">Hz</a>.</li></ul> <p>Hence:<sup id="cite_ref-Glisson_5-1" class="reference"><a href="#cite_note-Glisson-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <ul><li>if <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 \scriptstyle X>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mi>X</mi> <mo>></mo> <mn>0</mn> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle X>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b09089317f0bb52f32ddcd9785bdf7c3b1baaeac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.501ex; height:1.676ex;" alt="{\displaystyle \scriptstyle X>0}" /></span>, the total reactance is said to be inductive;</li> <li>if <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 \scriptstyle X=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mi>X</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle X=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72fca0f827b97a232a7c709be397b6fba57f68ae" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.501ex; height:1.676ex;" alt="{\displaystyle \scriptstyle X=0}" /></span>, then the impedance is purely resistive;</li> <li>if <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 \scriptstyle X<0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mi>X</mi> <mo><</mo> <mn>0</mn> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle X<0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/647cd6433bf7c6d44c93244e0f961228162849b6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.501ex; height:1.676ex;" alt="{\displaystyle \scriptstyle X<0}" /></span>, the total reactance is said to be capacitive.</li></ul> <p>Note however that if <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X_{L}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X_{L}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59f14ed86135c464841bbc6fba36cfb3997df2ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.276ex; height:2.509ex;" alt="{\displaystyle X_{L}}" /></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X_{C}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X_{C}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bbe98111b842bc759e8ca808cfc6a23d3b2b0317" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.406ex; height:2.509ex;" alt="{\displaystyle X_{C}}" /></span> are assumed both positive by definition, then the intermediary formula changes to a difference:<sup id="cite_ref-Hughes_7-1" class="reference"><a href="#cite_note-Hughes-7"><span class="cite-bracket">[</span>7<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 {X=X_{L}-X_{C}=\omega L-{\frac {1}{\omega C}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> <mo>=</mo> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mo>=</mo> <mi>ω</mi> <mi>L</mi> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>ω</mi> <mi>C</mi> </mrow> </mfrac> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {X=X_{L}-X_{C}=\omega L-{\frac {1}{\omega C}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1e53a041b82181563d2847ae24cde6bfa8308ad5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:27.616ex; height:5.343ex;" alt="{\displaystyle {X=X_{L}-X_{C}=\omega L-{\frac {1}{\omega C}}}}" /></span></dd></dl> <p>but the ultimate value is the same. </p> <div class="mw-heading mw-heading3"><h3 id="Phase_relationship">Phase relationship</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_reactance&action=edit&section=5" title="Edit section: Phase relationship"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The phase of the voltage across a purely reactive device (i.e. with zero <a href="/wiki/Parasitic_element_(electrical_networks)" class="mw-redirect" title="Parasitic element (electrical networks)">parasitic resistance</a>) <i>lags</i> the current 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 {\tfrac {\pi }{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {\pi }{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4e31a202557dfbf326b44ebcc914ba3ab08fff1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:1.778ex; height:3.176ex;" alt="{\displaystyle {\tfrac {\pi }{2}}}" /></span> radians for a capacitive reactance and <i>leads</i> the current 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 {\tfrac {\pi }{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {\pi }{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4e31a202557dfbf326b44ebcc914ba3ab08fff1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:1.778ex; height:3.176ex;" alt="{\displaystyle {\tfrac {\pi }{2}}}" /></span> radians for an inductive reactance. Without knowledge of both the resistance and reactance the relationship between voltage and current cannot be determined. </p><p>The origin of the different signs for capacitive and inductive reactance is the phase factor <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e^{\pm \mathbf {j} {\frac {\pi }{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>±</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">j</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> </mrow> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e^{\pm \mathbf {j} {\frac {\pi }{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/08f425d79db0dc62f584ed73df010769f077396b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.772ex; height:3.176ex;" alt="{\displaystyle e^{\pm \mathbf {j} {\frac {\pi }{2}}}}" /></span> in the impedance. </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}\mathbf {Z} _{C}&={1 \over \omega C}e^{-\mathbf {j} {\pi \over 2}}=\mathbf {j} \left({-{\frac {1}{\omega C}}}\right)=\mathbf {j} X_{C}\\\mathbf {Z} _{L}&=\omega Le^{\mathbf {j} {\pi \over 2}}=\mathbf {j} \omega L=\mathbf {j} X_{L}\quad \end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>ω</mi> <mi>C</mi> </mrow> </mfrac> </mrow> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">j</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> </mrow> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">j</mi> </mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>ω</mi> <mi>C</mi> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">j</mi> </mrow> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>ω</mi> <mi>L</mi> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">j</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> </mrow> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">j</mi> </mrow> <mi>ω</mi> <mi>L</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">j</mi> </mrow> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mspace width="1em"></mspace> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}\mathbf {Z} _{C}&={1 \over \omega C}e^{-\mathbf {j} {\pi \over 2}}=\mathbf {j} \left({-{\frac {1}{\omega C}}}\right)=\mathbf {j} X_{C}\\\mathbf {Z} _{L}&=\omega Le^{\mathbf {j} {\pi \over 2}}=\mathbf {j} \omega L=\mathbf {j} X_{L}\quad \end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a862fa55b807a3f30b99eb4cfd1ea064ee4f7005" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.338ex; width:36.686ex; height:9.843ex;" alt="{\displaystyle {\begin{aligned}\mathbf {Z} _{C}&={1 \over \omega C}e^{-\mathbf {j} {\pi \over 2}}=\mathbf {j} \left({-{\frac {1}{\omega C}}}\right)=\mathbf {j} X_{C}\\\mathbf {Z} _{L}&=\omega Le^{\mathbf {j} {\pi \over 2}}=\mathbf {j} \omega L=\mathbf {j} X_{L}\quad \end{aligned}}}" /></span></dd></dl> <p>For a reactive component the sinusoidal voltage across the component is in quadrature (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 {\tfrac {\pi }{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {\pi }{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4e31a202557dfbf326b44ebcc914ba3ab08fff1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:1.778ex; height:3.176ex;" alt="{\displaystyle {\tfrac {\pi }{2}}}" /></span> phase difference) with the sinusoidal current through the component. The component alternately absorbs energy from the circuit and then returns energy to the circuit, thus a pure reactance does not dissipate power. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_reactance&action=edit&section=6" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Magnetic_reactance" class="mw-redirect" title="Magnetic reactance">Magnetic reactance</a></li> <li><a href="/wiki/Susceptance" class="mw-redirect" title="Susceptance">Susceptance</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_reactance&action=edit&section=7" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Shamieh C. and McComb G., <i>Electronics for Dummies,</i> John Wiley & Sons, 2011.</li> <li>Meade R., <i>Foundations of Electronics,</i> Cengage Learning, 2002.</li> <li><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="CITEREFYoung,_Hugh_D.Roger_A._FreedmanA._Lewis_Ford2004" class="citation book cs1">Young, Hugh D.; Roger A. Freedman; A. Lewis Ford (2004) [1949]. <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/relativity00unse"><i>Sears and Zemansky's University Physics</i></a></span> (11 ed.). <a href="/wiki/San_Francisco" title="San Francisco">San Francisco</a>: <a href="/wiki/Addison_Wesley" class="mw-redirect" title="Addison Wesley">Addison Wesley</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-8053-9179-7" title="Special:BookSources/0-8053-9179-7"><bdi>0-8053-9179-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Sears+and+Zemansky%27s+University+Physics&rft.place=San+Francisco&rft.edition=11&rft.pub=Addison+Wesley&rft.date=2004&rft.isbn=0-8053-9179-7&rft.au=Young%2C+Hugh+D.&rft.au=Roger+A.+Freedman&rft.au=A.+Lewis+Ford&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Frelativity00unse&rfr_id=info%3Asid%2Fen.wikipedia.org%3AElectrical+reactance" class="Z3988"></span></li></ul> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-veley01-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-veley01_1-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFVeley1987" class="citation book cs1">Veley, Victor F. C. (1987). <a rel="nofollow" class="external text" href="https://archive.org/details/benchtopelectron00vele"><i>The Benchtop Electronics Reference Manual</i></a> (1st ed.). New York: Tab Books. pp. 229, 232.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Benchtop+Electronics+Reference+Manual&rft.place=New+York&rft.pages=229%2C+232&rft.edition=1st&rft.pub=Tab+Books&rft.date=1987&rft.aulast=Veley&rft.aufirst=Victor+F.+C.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbenchtopelectron00vele&rfr_id=info%3Asid%2Fen.wikipedia.org%3AElectrical+reactance" 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"><a href="/wiki/Charles_Proteus_Steinmetz" title="Charles Proteus Steinmetz">Charles Proteus Steinmetz</a>, Frederick Bedell, <a rel="nofollow" class="external text" href="https://ieeexplore.ieee.org/document/4763812">"Reactance"</a>, <i>Transactions of the American Institute of Electrical Engineers</i>, vol. 11, pp. 640–648, January–December 1894.</span> </li> <li id="cite_note-Irwin-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-Irwin_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Irwin_3-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Irwin, D. (2002). <i>Basic Engineering Circuit Analysis</i>, page 274. New York: John Wiley & Sons, Inc.</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">Hayt, W.H., Kimmerly J.E. (2007). <i>Engineering Circuit Analysis</i>, 7th ed., McGraw-Hill, p. 388</span> </li> <li id="cite_note-Glisson-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-Glisson_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Glisson_5-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Glisson, T.H. (2011). <i>Introduction to Circuit Analysis and Design</i>, Springer, p. 408</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">Horowitz P., Hill W. (2015). <i><a href="/wiki/The_Art_of_Electronics" title="The Art of Electronics">The Art of Electronics</a></i>, 3rd ed., p. 42</span> </li> <li id="cite_note-Hughes-7"><span class="mw-cite-backlink">^ <a href="#cite_ref-Hughes_7-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Hughes_7-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Hughes E., Hiley J., Brown K., Smith I.McK., (2012). <i>Hughes Electrical and Electronic Technology</i>, 11th edition, Pearson, pp. 237-241</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">Robbins, A.H., Miller W. (2012). <i>Circuit Analysis: Theory and Practice</i>, 5th ed., Cengage Learning, pp. 554-558</span> </li> </ol></div></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=Electrical_reactance&action=edit&section=8" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://nationalmaglab.org/magnet-academy/watch-play/interactive-tutorials/inductive-reactance/">National magnet lab, inductive reactance </a></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output 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