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<span class="vector-toc-numb">2</span> <span>Conductors and resistors</span> </div> </a> <ul id="toc-Conductors_and_resistors-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ohm's_law" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ohm's_law"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Ohm's law</span> </div> </a> <ul id="toc-Ohm's_law-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Relation_to_resistivity_and_conductivity" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Relation_to_resistivity_and_conductivity"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Relation to resistivity and conductivity</span> </div> </a> <ul id="toc-Relation_to_resistivity_and_conductivity-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Measurement" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Measurement"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Measurement</span> </div> </a> <ul id="toc-Measurement-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Typical_values" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Typical_values"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Typical values</span> </div> </a> <ul id="toc-Typical_values-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Static_and_differential_resistance" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Static_and_differential_resistance"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Static and differential resistance</span> </div> </a> <ul id="toc-Static_and_differential_resistance-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-AC_circuits" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#AC_circuits"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>AC circuits</span> </div> </a> <button aria-controls="toc-AC_circuits-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle AC circuits subsection</span> </button> <ul id="toc-AC_circuits-sublist" class="vector-toc-list"> <li id="toc-Impedance_and_admittance" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Impedance_and_admittance"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.1</span> <span>Impedance and admittance</span> </div> </a> <ul id="toc-Impedance_and_admittance-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Frequency_dependence" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Frequency_dependence"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.2</span> <span>Frequency dependence</span> </div> </a> <ul id="toc-Frequency_dependence-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Energy_dissipation_and_Joule_heating" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Energy_dissipation_and_Joule_heating"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Energy dissipation and Joule heating</span> </div> </a> <ul id="toc-Energy_dissipation_and_Joule_heating-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Dependence_on_other_conditions" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Dependence_on_other_conditions"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Dependence on other conditions</span> </div> </a> <button aria-controls="toc-Dependence_on_other_conditions-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Dependence on other conditions subsection</span> </button> <ul id="toc-Dependence_on_other_conditions-sublist" class="vector-toc-list"> <li id="toc-Temperature_dependence" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Temperature_dependence"> <div class="vector-toc-text"> <span class="vector-toc-numb">10.1</span> <span>Temperature dependence</span> </div> </a> <ul id="toc-Temperature_dependence-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Strain_dependence" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Strain_dependence"> <div class="vector-toc-text"> <span class="vector-toc-numb">10.2</span> <span>Strain dependence</span> </div> </a> <ul id="toc-Strain_dependence-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Light_illumination_dependence" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Light_illumination_dependence"> <div class="vector-toc-text"> <span class="vector-toc-numb">10.3</span> <span>Light illumination dependence</span> </div> </a> <ul id="toc-Light_illumination_dependence-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Superconductivity" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Superconductivity"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>Superconductivity</span> </div> </a> <ul id="toc-Superconductivity-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">12</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Footnotes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Footnotes"> <div class="vector-toc-text"> <span class="vector-toc-numb">13</span> <span>Footnotes</span> </div> </a> <ul id="toc-Footnotes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">14</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">15</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table of Contents" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet 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Available in 15 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-15" 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">15 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Elektriese_weerstand_en_konduktansie" title="Elektriese weerstand en konduktansie – Afrikaans" lang="af" hreflang="af" data-title="Elektriese weerstand en konduktansie" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A7%D9%84%D9%85%D9%82%D8%A7%D9%88%D9%85%D8%A9_%D9%88%D8%A7%D9%84%D9%85%D9%88%D8%A7%D8%B5%D9%84%D8%A9_%D8%A7%D9%84%D9%83%D9%87%D8%B1%D8%A8%D8%A7%D8%A6%D9%8A%D8%A9" title="المقاومة والمواصلة الكهربائية – Arabic" lang="ar" hreflang="ar" data-title="المقاومة والمواصلة الكهربائية" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AC%E0%A7%88%E0%A6%A6%E0%A7%8D%E0%A6%AF%E0%A7%81%E0%A6%A4%E0%A6%BF%E0%A6%95_%E0%A6%B0%E0%A7%8B%E0%A6%A7_%E0%A6%93_%E0%A6%AA%E0%A6%B0%E0%A6%BF%E0%A6%AC%E0%A6%BE%E0%A6%B9%E0%A6%BF%E0%A6%A4%E0%A6%BE" title="বৈদ্যুতিক রোধ ও পরিবাহিতা – Bangla" lang="bn" hreflang="bn" data-title="বৈদ্যুতিক রোধ ও পরিবাহিতা" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Resist%C3%A8ncia_el%C3%A8ctrica_i_conduct%C3%A0ncia" title="Resistència elèctrica i conductància – Catalan" lang="ca" hreflang="ca" data-title="Resistència elèctrica i conductància" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%D9%82%D8%A7%D9%88%D9%85%D8%AA_%D9%88_%D8%B1%D8%B3%D8%A7%D9%86%D8%A7%DB%8C%DB%8C_%D8%A7%D9%84%DA%A9%D8%AA%D8%B1%DB%8C%DA%A9%DB%8C" title="مقاومت و رسانایی الکتریکی – Persian" lang="fa" hreflang="fa" data-title="مقاومت و رسانایی الکتریکی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Friota%C3%ADocht_agus_seoltas_leictreach" title="Friotaíocht agus seoltas leictreach – Irish" lang="ga" hreflang="ga" data-title="Friotaíocht agus seoltas leictreach" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A6%D0%B0%D1%85%D0%B8%D0%BB%D0%B3%D0%B0%D0%B0%D0%BD%D1%8B_%D1%8D%D1%81%D1%8D%D1%80%D0%B3%D2%AF%D2%AF%D1%86%D1%8D%D0%BB" title="Цахилгааны эсэргүүцэл – Mongolian" lang="mn" hreflang="mn" data-title="Цахилгааны эсэргүүцэл" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Electrical_reseestance_an_conductance" title="Electrical reseestance an conductance – Scots" lang="sco" hreflang="sco" data-title="Electrical reseestance an conductance" data-language-autonym="Scots" data-language-local-name="Scots" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Electrical_resistance_and_conductance" title="Electrical resistance and conductance – Simple English" lang="en-simple" hreflang="en-simple" data-title="Electrical resistance and conductance" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Elektri%C4%8Dni_otpor_i_vodljivost" title="Električni otpor i vodljivost – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Električni otpor i vodljivost" 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-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%B5%E0%B0%BF%E0%B0%A6%E0%B1%8D%E0%B0%AF%E0%B1%81%E0%B0%A8%E0%B1%8D%E0%B0%A8%E0%B0%BF%E0%B0%B0%E0%B1%8B%E0%B0%A7%E0%B0%82,_%E0%B0%B5%E0%B0%BE%E0%B0%B9%E0%B0%95%E0%B0%A4%E0%B1%8D%E0%B0%B5%E0%B0%82" title="విద్యున్నిరోధం, వాహకత్వం – Telugu" lang="te" hreflang="te" data-title="విద్యున్నిరోధం, వాహకత్వం" data-language-autonym="తెలుగు" data-language-local-name="Telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%84%E0%B8%A7%E0%B8%B2%E0%B8%A1%E0%B8%95%E0%B9%89%E0%B8%B2%E0%B8%99%E0%B8%97%E0%B8%B2%E0%B8%99%E0%B9%81%E0%B8%A5%E0%B8%B0%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%99%E0%B8%B3%E0%B9%84%E0%B8%9F%E0%B8%9F%E0%B9%89%E0%B8%B2" title="ความต้านทานและการนำไฟฟ้า – Thai" lang="th" hreflang="th" data-title="ความต้านทานและการนำไฟฟ้า" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Elektriksel_%C3%B6zdiren%C3%A7_ve_iletkenlik" title="Elektriksel özdirenç ve iletkenlik – Turkish" lang="tr" hreflang="tr" data-title="Elektriksel özdirenç ve iletkenlik" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%A8%D8%B1%D9%82%DB%8C_%D9%85%D8%B2%D8%A7%D8%AD%D9%85%D8%AA_%D8%A7%D9%88%D8%B1_%D8%A7%DB%8C%D8%B5%D8%A7%D9%84%DB%8C%D8%AA" title="برقی مزاحمت اور ایصالیت – Urdu" lang="ur" hreflang="ur" data-title="برقی مزاحمت اور ایصالیت" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/%C4%90i%E1%BB%87n_tr%E1%BB%9F_v%C3%A0_%C4%91i%E1%BB%87n_d%E1%BA%ABn" title="Điện trở và điện dẫn – Vietnamese" lang="vi" hreflang="vi" data-title="Điện trở và điện dẫn" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q106603432#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespaces"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul 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searchaux" style="display:none">Opposition to the passage of an electric current</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">This article is about specific applications of conductivity and resistivity in electrical elements. For other types of conductivity, see <a href="/wiki/Conductivity_(disambiguation)" class="mw-redirect mw-disambig" title="Conductivity (disambiguation)">Conductivity</a>. For electrical conductivity in general, see <a href="/wiki/Electrical_resistivity_and_conductivity" title="Electrical resistivity and conductivity">Electrical resistivity and conductivity</a>.</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">"Resistive" redirects here. 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title="Direct current">Direct current</a></li> <li><a href="/wiki/Electric_current" title="Electric current">Electric current</a></li> <li><a href="/wiki/Electric_power" title="Electric power">Electric power</a></li> <li><a href="/wiki/Electrolysis" title="Electrolysis">Electrolysis</a></li> <li><a href="/wiki/Electromotive_force" title="Electromotive force">Electromotive force</a></li> <li><a href="/wiki/Electrical_impedance" title="Electrical impedance">Impedance</a></li> <li><a href="/wiki/Inductance" title="Inductance">Inductance</a></li> <li><a href="/wiki/Joule_heating" title="Joule heating">Joule heating</a></li> <li><a href="/wiki/Kirchhoff%27s_circuit_laws" title="Kirchhoff's circuit laws">Kirchhoff laws</a></li> <li><a href="/wiki/Network_analysis_(electrical_circuits)" title="Network analysis (electrical circuits)">Network analysis</a></li> <li><a href="/wiki/Ohm%27s_law" title="Ohm's law">Ohm law</a></li> <li><a href="/wiki/Series_and_parallel_circuits#Parallel_circuits" title="Series and parallel circuits">Parallel circuit</a></li> <li><a class="mw-selflink selflink">Resistance</a></li> <li><a href="/wiki/Resonator#Electromagnetics" title="Resonator">Resonant cavities</a></li> <li><a href="/wiki/Series_and_parallel_circuits#Series_circuits" title="Series and parallel circuits">Series circuit</a></li> <li><a href="/wiki/Voltage" title="Voltage">Voltage</a></li> <li><a href="/wiki/Watt" title="Watt">Watt</a></li> <li><a href="/wiki/Waveguide_(radio_frequency)" title="Waveguide (radio frequency)">Waveguides</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Magnetic_circuit" title="Magnetic circuit">Magnetic circuit</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/AC_motor" title="AC motor">AC motor</a></li> <li><a href="/wiki/DC_motor" title="DC motor">DC motor</a></li> <li><a href="/wiki/Electric_machine" title="Electric machine">Electric machine</a></li> <li><a href="/wiki/Electric_motor" title="Electric motor">Electric motor</a></li> <li><a href="/wiki/Gyrator%E2%80%93capacitor_model" title="Gyrator–capacitor model">Gyrator–capacitor</a></li> <li><a href="/wiki/Induction_motor" title="Induction motor">Induction motor</a></li> <li><a href="/wiki/Linear_motor" title="Linear motor">Linear motor</a></li> <li><a href="/wiki/Magnetomotive_force" title="Magnetomotive force">Magnetomotive force</a></li> <li><a href="/wiki/Permeance" title="Permeance">Permeance</a></li> <li><a href="/wiki/Magnetic_complex_reluctance" title="Magnetic complex reluctance">Reluctance (complex)</a></li> <li><a href="/wiki/Magnetic_reluctance" title="Magnetic reluctance">Reluctance (real)</a></li> <li><a href="/wiki/Rotor_(electric)" title="Rotor (electric)">Rotor</a></li> <li><a href="/wiki/Stator" title="Stator">Stator</a></li> <li><a href="/wiki/Transformer" title="Transformer">Transformer</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Covariant_formulation_of_classical_electromagnetism" title="Covariant formulation of classical electromagnetism">Covariant formulation</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Electromagnetic_tensor" title="Electromagnetic tensor">Electromagnetic tensor</a></li> <li><a href="/wiki/Classical_electromagnetism_and_special_relativity" title="Classical electromagnetism and special relativity">Electromagnetism and special relativity</a></li> <li><a href="/wiki/Four-current" title="Four-current">Four-current</a></li> <li><a href="/wiki/Electromagnetic_four-potential" title="Electromagnetic four-potential">Four-potential</a></li> <li><a href="/wiki/Mathematical_descriptions_of_the_electromagnetic_field" title="Mathematical descriptions of the electromagnetic field">Mathematical descriptions</a></li> <li><a href="/wiki/Maxwell%27s_equations_in_curved_spacetime" title="Maxwell's equations in curved spacetime">Maxwell equations in curved spacetime</a></li> <li><a href="/wiki/Relativistic_electromagnetism" title="Relativistic electromagnetism">Relativistic electromagnetism</a></li> <li><a href="/wiki/Electromagnetic_stress%E2%80%93energy_tensor" title="Electromagnetic stress–energy tensor">Stress–energy tensor</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)">Scientists</div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Andr%C3%A9-Marie_Amp%C3%A8re" title="André-Marie Ampère">Ampère</a></li> <li><a href="/wiki/Jean-Baptiste_Biot" title="Jean-Baptiste Biot">Biot</a></li> <li><a href="/wiki/Charles-Augustin_de_Coulomb" title="Charles-Augustin de Coulomb">Coulomb</a></li> <li><a href="/wiki/Humphry_Davy" title="Humphry Davy">Davy</a></li> <li><a href="/wiki/Albert_Einstein" title="Albert Einstein">Einstein</a></li> <li><a href="/wiki/Michael_Faraday" title="Michael Faraday">Faraday</a></li> <li><a href="/wiki/Hippolyte_Fizeau" title="Hippolyte Fizeau">Fizeau</a></li> <li><a href="/wiki/Carl_Friedrich_Gauss" title="Carl Friedrich Gauss">Gauss</a></li> <li><a href="/wiki/Oliver_Heaviside" title="Oliver Heaviside">Heaviside</a></li> <li><a href="/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz">Helmholtz</a></li> <li><a href="/wiki/Joseph_Henry" title="Joseph Henry">Henry</a></li> <li><a href="/wiki/Heinrich_Hertz" title="Heinrich Hertz">Hertz</a></li> <li><a href="/wiki/John_Hopkinson" title="John Hopkinson">Hopkinson</a></li> <li><a href="/wiki/Oleg_D._Jefimenko" title="Oleg D. Jefimenko">Jefimenko</a></li> <li><a href="/wiki/James_Prescott_Joule" title="James Prescott Joule">Joule</a></li> <li><a href="/wiki/Lord_Kelvin" title="Lord Kelvin">Kelvin</a></li> <li><a href="/wiki/Gustav_Kirchhoff" title="Gustav Kirchhoff">Kirchhoff</a></li> <li><a href="/wiki/Joseph_Larmor" title="Joseph Larmor">Larmor</a></li> <li><a href="/wiki/Emil_Lenz" title="Emil Lenz">Lenz</a></li> <li><a href="/wiki/Alfred-Marie_Li%C3%A9nard" title="Alfred-Marie Liénard">Liénard</a></li> <li><a href="/wiki/Hendrik_Lorentz" title="Hendrik Lorentz">Lorentz</a></li> <li><a href="/wiki/James_Clerk_Maxwell" title="James Clerk Maxwell">Maxwell</a></li> <li><a href="/wiki/Franz_Ernst_Neumann" title="Franz Ernst Neumann">Neumann</a></li> <li><a href="/wiki/Georg_Ohm" title="Georg Ohm">Ohm</a></li> <li><a href="/wiki/Hans_Christian_%C3%98rsted" title="Hans Christian Ørsted">Ørsted</a></li> <li><a href="/wiki/Sim%C3%A9on_Denis_Poisson" title="Siméon Denis Poisson">Poisson</a></li> <li><a href="/wiki/John_Henry_Poynting" title="John Henry Poynting">Poynting</a></li> <li><a href="/wiki/William_Ritchie_(physicist)" title="William Ritchie (physicist)">Ritchie</a></li> <li><a href="/wiki/F%C3%A9lix_Savart" title="Félix Savart">Savart</a></li> <li><a href="/wiki/George_Singer" title="George Singer">Singer</a></li> <li><a href="/wiki/Charles_Proteus_Steinmetz" title="Charles Proteus Steinmetz">Steinmetz</a></li> <li><a href="/wiki/Nikola_Tesla" title="Nikola Tesla">Tesla</a></li> <li><a href="/wiki/J._J._Thomson" title="J. J. Thomson">Thomson</a></li> <li><a href="/wiki/Alessandro_Volta" title="Alessandro Volta">Volta</a></li> <li><a href="/wiki/Wilhelm_Eduard_Weber" title="Wilhelm Eduard Weber">Weber</a></li> <li><a href="/wiki/Emil_Wiechert" title="Emil Wiechert">Wiechert</a></li></ul></div></div></td> </tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Electromagnetism" title="Template:Electromagnetism"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Electromagnetism" title="Template talk:Electromagnetism"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Electromagnetism" title="Special:EditPage/Template:Electromagnetism"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox"><tbody><tr><th colspan="2" class="infobox-above">Electric resistance</th></tr><tr><th scope="row" class="infobox-label"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;">Common symbols</div></th><td class="infobox-data"><span class="texhtml mvar" style="font-style:italic;">R</span></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/SI_unit" class="mw-redirect" title="SI unit">SI unit</a></th><td class="infobox-data">ohm (Ω)</td></tr><tr><th scope="row" class="infobox-label">In <a href="/wiki/SI_base_unit" title="SI base unit"><span class="wrap">SI base units</span></a></th><td class="infobox-data">kg⋅m<sup>2</sup>⋅s<sup>−3</sup>⋅A<sup>−2</sup></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Dimensional_analysis#Formulation" title="Dimensional analysis">Dimension</a></th><td class="infobox-data"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathsf {M}}{\mathsf {L}}^{2}{\mathsf {T}}^{-3}{\mathsf {I}}^{-2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">M</mi> </mrow> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">L</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">T</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>3</mn> </mrow> </msup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">I</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathsf {M}}{\mathsf {L}}^{2}{\mathsf {T}}^{-3}{\mathsf {I}}^{-2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add5ced798822a94c30cf7c66708116889e54359" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.243ex; height:2.676ex;" alt="{\displaystyle {\mathsf {M}}{\mathsf {L}}^{2}{\mathsf {T}}^{-3}{\mathsf {I}}^{-2}}" /></span></td></tr></tbody></table> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1257001546" /><table class="infobox"><tbody><tr><th colspan="2" class="infobox-above">Electric conductance</th></tr><tr><th scope="row" class="infobox-label"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;">Common symbols</div></th><td class="infobox-data"><span class="texhtml mvar" style="font-style:italic;">G</span></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/SI_unit" class="mw-redirect" title="SI unit">SI unit</a></th><td class="infobox-data">siemens (S)</td></tr><tr><th scope="row" class="infobox-label">In <a href="/wiki/SI_base_unit" title="SI base unit"><span class="wrap">SI base units</span></a></th><td class="infobox-data">kg<sup>−1</sup>⋅m<sup>−2</sup>⋅s<sup>3</sup>⋅A<sup>2</sup></td></tr><tr><th scope="row" class="infobox-label"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;">Derivations from<br />other quantities</div></th><td class="infobox-data"><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 G={\frac {1}{R}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>R</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G={\frac {1}{R}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a782828bf4a2a9b53c1c26a8ab189a16e89326dd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:7.525ex; height:5.343ex;" alt="{\displaystyle G={\frac {1}{R}}}" /></span></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Dimensional_analysis#Formulation" title="Dimensional analysis">Dimension</a></th><td class="infobox-data"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathsf {M}}^{-1}{\mathsf {L}}^{-2}{\mathsf {T}}^{3}{\mathsf {I}}^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">M</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">L</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> </mrow> </msup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">T</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">I</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathsf {M}}^{-1}{\mathsf {L}}^{-2}{\mathsf {T}}^{3}{\mathsf {I}}^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a3fe666149a8b21f0db455155242699c704db842" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:12.297ex; height:2.676ex;" alt="{\displaystyle {\mathsf {M}}^{-1}{\mathsf {L}}^{-2}{\mathsf {T}}^{3}{\mathsf {I}}^{2}}" /></span></td></tr></tbody></table> <p>The <b>electrical resistance</b> of an object is a measure of its opposition to the flow of <a href="/wiki/Electric_current" title="Electric current">electric current</a>. Its <a href="/wiki/Multiplicative_inverse" title="Multiplicative inverse">reciprocal</a> quantity is <b><style data-mw-deduplicate="TemplateStyles:r1238216509">.mw-parser-output .vanchor>:target~.vanchor-text{background-color:#b1d2ff}@media screen{html.skin-theme-clientpref-night .mw-parser-output .vanchor>:target~.vanchor-text{background-color:#0f4dc9}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .vanchor>:target~.vanchor-text{background-color:#0f4dc9}}</style><span class="vanchor"><span id="electrical_conductance"></span><span id="CONDUCTANCE"></span><span class="vanchor-text">electrical conductance</span></span></b>, measuring the ease with which an electric current passes. Electrical resistance shares some conceptual parallels with mechanical <a href="/wiki/Friction" title="Friction">friction</a>. The <a href="/wiki/International_System_of_Units" title="International System of Units">SI</a> unit of electrical resistance is the <a href="/wiki/Ohm" title="Ohm">ohm</a> (<span class="texhtml"><a href="/wiki/Omega" title="Omega">Ω</a></span>), while electrical conductance is measured in <a href="/wiki/Siemens_(unit)" title="Siemens (unit)">siemens</a> (S) (formerly called the 'mho' and then represented by <span class="texhtml">℧</span>). </p><p>The resistance of an object depends in large part on the material it is made of. Objects made of <a href="/wiki/Electrical_insulator" class="mw-redirect" title="Electrical insulator">electrical insulators</a> like <a href="/wiki/Rubber" class="mw-redirect" title="Rubber">rubber</a> tend to have very high resistance and low conductance, while objects made of <a href="/wiki/Electrical_conductor" title="Electrical conductor">electrical conductors</a> like metals tend to have very low resistance and high conductance. This relationship is quantified by <a href="/wiki/Electrical_resistivity_and_conductivity" title="Electrical resistivity and conductivity">resistivity or conductivity</a>. The nature of a material is not the only factor in resistance and conductance, however; it also depends on the size and shape of an object because these properties are <a href="/wiki/Intensive_and_extensive_properties" title="Intensive and extensive properties">extensive rather than intensive</a>. For example, a wire's resistance is higher if it is long and thin, and lower if it is short and thick. All objects resist electrical current, except for <a href="/wiki/Superconductor" class="mw-redirect" title="Superconductor">superconductors</a>, which have a resistance of zero. </p><p>The resistance <span class="texhtml mvar" style="font-style:italic;">R</span> of an object is defined as the ratio of <a href="/wiki/Voltage" title="Voltage">voltage</a> <span class="texhtml mvar" style="font-style:italic;">V</span> across it to <a href="/wiki/Electric_current" title="Electric current">current</a> <span class="texhtml mvar" style="font-style:italic;">I</span> through it, while the conductance <span class="texhtml mvar" style="font-style:italic;">G</span> is the reciprocal: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R={\frac {V}{I}},\qquad G={\frac {I}{V}}={\frac {1}{R}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>V</mi> <mi>I</mi> </mfrac> </mrow> <mo>,</mo> <mspace width="2em"></mspace> <mi>G</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>I</mi> <mi>V</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>R</mi> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R={\frac {V}{I}},\qquad G={\frac {I}{V}}={\frac {1}{R}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/58d90d834dfad220cc899a56dbfce44bfcf4eadd" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:27.059ex; height:5.343ex;" alt="{\displaystyle R={\frac {V}{I}},\qquad G={\frac {I}{V}}={\frac {1}{R}}.}" /></span> </p><p>For a wide variety of materials and conditions, <span class="texhtml mvar" style="font-style:italic;">V</span> and <span class="texhtml mvar" style="font-style:italic;">I</span> are directly proportional to each other, and therefore <span class="texhtml mvar" style="font-style:italic;">R</span> and <span class="texhtml mvar" style="font-style:italic;">G</span> are <a href="/wiki/Constant_(mathematics)" title="Constant (mathematics)">constants</a> (although they will depend on the size and shape of the object, the material it is made of, and other factors like temperature or <a href="/wiki/Deformation_(mechanics)" class="mw-redirect" title="Deformation (mechanics)">strain</a>). This proportionality is called <a href="/wiki/Ohm%27s_law" title="Ohm's law">Ohm's law</a>, and materials that satisfy it are called <i>ohmic</i> materials. </p><p>In other cases, such as a <a href="/wiki/Transformer" title="Transformer">transformer</a>, <a href="/wiki/Diode" title="Diode">diode</a> or <a href="/wiki/Battery_(electricity)" class="mw-redirect" title="Battery (electricity)">battery</a>, <span class="texhtml mvar" style="font-style:italic;">V</span> and <span class="texhtml mvar" style="font-style:italic;">I</span> are not directly proportional. The ratio <span class="texhtml mvar" style="font-style:italic;"><style data-mw-deduplicate="TemplateStyles:r1214402035">.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="sfrac">⁠<span class="tion"><span class="num">V</span><span class="sr-only">/</span><span class="den">I</span></span>⁠</span></span> is sometimes still useful, and is referred to as a <i>chordal resistance</i> or <i>static resistance</i>,<sup id="cite_ref-brown_1-0" class="reference"><a href="#cite_note-brown-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-kaiser_2-0" class="reference"><a href="#cite_note-kaiser-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> since it corresponds to the inverse slope of a <a href="/wiki/Chord_(geometry)" title="Chord (geometry)">chord</a> between the origin and an <a href="/wiki/Current%E2%80%93voltage_characteristic" title="Current–voltage characteristic"><span class="texhtml mvar" style="font-style:italic;">I</span>–<span class="texhtml mvar" style="font-style:italic;">V</span> curve</a>. In other situations, the <a href="/wiki/Derivative" title="Derivative">derivative</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle {\frac {\mathrm {d} V}{\mathrm {d} I}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>V</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>I</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle {\frac {\mathrm {d} V}{\mathrm {d} I}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cf201e60955e1cedc71362ab16bc8f3494a8806e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:3.014ex; height:3.843ex;" alt="{\textstyle {\frac {\mathrm {d} V}{\mathrm {d} I}}}" /></span> may be most useful; this is called the <i>differential resistance</i>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Introduction">Introduction</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_resistance_and_conductance&action=edit&section=1" title="Edit section: Introduction"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:ResistanceHydraulicAnalogy.svg" class="mw-file-description"><img alt="analogy of resistance" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d0/ResistanceHydraulicAnalogy.svg/350px-ResistanceHydraulicAnalogy.svg.png" decoding="async" width="350" height="246" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d0/ResistanceHydraulicAnalogy.svg/525px-ResistanceHydraulicAnalogy.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d0/ResistanceHydraulicAnalogy.svg/700px-ResistanceHydraulicAnalogy.svg.png 2x" data-file-width="1233" data-file-height="865" /></a><figcaption>The <a href="/wiki/Hydraulic_analogy" title="Hydraulic analogy">hydraulic analogy</a> compares electric current flowing through circuits to water flowing through pipes. When a pipe (left) is filled with hair (right), it takes a larger pressure to achieve the same flow of water. Pushing electric current through a large resistance is like pushing water through a pipe clogged with hair: It requires a larger push (<a href="/wiki/Electromotive_force" title="Electromotive force">electromotive force</a>) to drive the same flow (<a href="/wiki/Electric_current" title="Electric current">electric current</a>).</figcaption></figure> <p>In the <a href="/wiki/Hydraulic_analogy" title="Hydraulic analogy">hydraulic analogy</a>, current flowing through a wire (or <a href="/wiki/Resistor" title="Resistor">resistor</a>) is like water flowing through a pipe, and the <a href="/wiki/Voltage_drop" title="Voltage drop">voltage drop</a> across the wire is like the <a href="/wiki/Pressure_drop" title="Pressure drop">pressure drop</a> that pushes water through the pipe. Conductance is proportional to how much flow occurs for a given pressure, and resistance is proportional to how much pressure is required to achieve a given flow. </p><p>The <a href="/wiki/Voltage_drop" title="Voltage drop">voltage drop</a> (i.e., difference between voltages on one side of the resistor and the other), not the <a href="/wiki/Voltage" title="Voltage">voltage</a> itself, provides the driving force pushing current through a resistor. In hydraulics, it is similar: the pressure difference between two sides of a pipe, not the pressure itself, determines the flow through it. For example, there may be a large water pressure above the pipe, which tries to push water down through the pipe. But there may be an equally large water pressure below the pipe, which tries to push water back up through the pipe. If these pressures are equal, no water flows. (In the image at right, the water pressure below the pipe is zero.) </p><p>The resistance and conductance of a wire, resistor, or other element is mostly determined by two properties: </p> <ul><li>geometry (shape), and</li> <li>material</li></ul> <p>Geometry is important because it is more difficult to push water through a long, narrow pipe than a wide, short pipe. In the same way, a long, thin copper wire has higher resistance (lower conductance) than a short, thick copper wire. </p><p>Materials are important as well. A pipe filled with hair restricts the flow of water more than a clean pipe of the same shape and size. Similarly, <a href="/wiki/Electron" title="Electron">electrons</a> can flow freely and easily through a <a href="/wiki/Copper" title="Copper">copper</a> wire, but cannot flow as easily through a <a href="/wiki/Steel" title="Steel">steel</a> wire of the same shape and size, and they essentially cannot flow at all through an <a href="/wiki/Insulator_(electrical)" class="mw-redirect" title="Insulator (electrical)">insulator</a> like <a href="/wiki/Rubber" class="mw-redirect" title="Rubber">rubber</a>, regardless of its shape. The difference between copper, steel, and rubber is related to their microscopic structure and <a href="/wiki/Electron_configuration" title="Electron configuration">electron configuration</a>, and is quantified by a property called <a href="/wiki/Resistivity" class="mw-redirect" title="Resistivity">resistivity</a>. </p><p>In addition to geometry and material, there are various other factors that influence resistance and conductance, such as temperature; see <a href="#Dependence_on_other_conditions">below</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Conductors_and_resistors">Conductors and resistors</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_resistance_and_conductance&action=edit&section=2" title="Edit section: Conductors and resistors"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Metal_film_resistor.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Metal_film_resistor.jpg/250px-Metal_film_resistor.jpg" decoding="async" width="250" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Metal_film_resistor.jpg/375px-Metal_film_resistor.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Metal_film_resistor.jpg/500px-Metal_film_resistor.jpg 2x" data-file-width="2181" data-file-height="240" /></a><figcaption>A 75 Ω <a href="/wiki/Resistor" title="Resistor">resistor</a>, as identified by its <a href="/wiki/Electronic_color_code" title="Electronic color code">electronic color code</a> (violet–green–black–gold–red). An <a href="/wiki/Ohmmeter" title="Ohmmeter">ohmmeter</a> could be used to verify this value.</figcaption></figure> <p>Substances in which electricity can flow are called <a href="/wiki/Electrical_conductor" title="Electrical conductor">conductors</a>. A piece of conducting material of a particular resistance meant for use in a circuit is called a <a href="/wiki/Resistor" title="Resistor">resistor</a>. Conductors are made of high-<a href="/wiki/Electrical_resistivity_and_conductivity" title="Electrical resistivity and conductivity">conductivity</a> materials such as metals, in particular copper and aluminium. Resistors, on the other hand, are made of a wide variety of materials depending on factors such as the desired resistance, amount of energy that it needs to dissipate, precision, and costs. </p> <div class="mw-heading mw-heading2"><h2 id="Ohm's_law"><span id="Ohm.27s_law"></span>Ohm's law</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_resistance_and_conductance&action=edit&section=3" title="Edit section: Ohm's law"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Ohm%27s_law" title="Ohm's law">Ohm's law</a></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:FourIVcurves.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d7/FourIVcurves.svg/500px-FourIVcurves.svg.png" decoding="async" width="500" height="102" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d7/FourIVcurves.svg/750px-FourIVcurves.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d7/FourIVcurves.svg/1000px-FourIVcurves.svg.png 2x" data-file-width="1536" data-file-height="314" /></a><figcaption>The <a href="/wiki/Current%E2%80%93voltage_characteristic" title="Current–voltage characteristic">current–voltage characteristics</a> of four devices: Two <a href="/wiki/Resistor" title="Resistor">resistors</a>, a <a href="/wiki/Diode" title="Diode">diode</a>, and a <a href="/wiki/Battery_(electricity)" class="mw-redirect" title="Battery (electricity)">battery</a>. The horizontal axis is <a href="/wiki/Voltage_drop" title="Voltage drop">voltage drop</a>, the vertical axis is <a href="/wiki/Electric_current" title="Electric current">current</a>. Ohm's law is satisfied when the graph is a straight line through the origin. Therefore, the two resistors are <i>ohmic</i>, but the diode and battery are not.</figcaption></figure> <p>For many materials, the current <span class="texhtml mvar" style="font-style:italic;">I</span> through the material is proportional to the voltage <span class="texhtml mvar" style="font-style:italic;">V</span> applied across it: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I\propto V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> <mo>∝</mo> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I\propto V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9dd58b600d89aad7e1a54fa604337590634f4c89" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.057ex; height:2.176ex;" alt="{\displaystyle I\propto V}" /></span> over a wide range of voltages and currents. Therefore, the resistance and conductance of objects or electronic components made of these materials is constant. This relationship is called <a href="/wiki/Ohm%27s_law" title="Ohm's law">Ohm's law</a>, and materials which obey it are called <i>ohmic</i> materials. Examples of ohmic components are wires and <a href="/wiki/Resistor" title="Resistor">resistors</a>. The <a href="/wiki/Current%E2%80%93voltage_characteristic" title="Current–voltage characteristic">current–voltage graph</a> of an ohmic device consists of a straight line through the origin with positive <a href="/wiki/Slope_(mathematics)" class="mw-redirect" title="Slope (mathematics)">slope</a>. </p><p>Other components and materials used in electronics do not obey Ohm's law; the current is not proportional to the voltage, so the resistance varies with the voltage and current through them. These are called <i>nonlinear</i> or <i>non-ohmic</i>. Examples include <a href="/wiki/Diode" title="Diode">diodes</a> and <a href="/wiki/Fluorescent_lamp" title="Fluorescent lamp">fluorescent lamps</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Relation_to_resistivity_and_conductivity">Relation to resistivity and conductivity</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_resistance_and_conductance&action=edit&section=4" title="Edit section: Relation to resistivity and conductivity"><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_resistivity_and_conductivity" title="Electrical resistivity and conductivity">Electrical resistivity and conductivity</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Resistivity_geometry.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/68/Resistivity_geometry.png/220px-Resistivity_geometry.png" decoding="async" width="220" height="198" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/68/Resistivity_geometry.png/330px-Resistivity_geometry.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/68/Resistivity_geometry.png/440px-Resistivity_geometry.png 2x" data-file-width="471" data-file-height="424" /></a><figcaption>A piece of resistive material with electrical contacts on both ends.</figcaption></figure> <p>The resistance of a given object depends primarily on two factors: what material it is made of, and its shape. For a given material, the resistance is inversely proportional to the cross-sectional area; for example, a thick copper wire has lower resistance than an otherwise-identical thin copper wire. Also, for a given material, the resistance is proportional to the length; for example, a long copper wire has higher resistance than an otherwise-identical short copper wire. The resistance <span class="texhtml">R</span> and conductance <span class="texhtml">G</span> of a conductor of uniform cross section, therefore, can be computed as </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}R&=\rho {\frac {\ell }{A}},\\[5pt]G&=\sigma {\frac {A}{\ell }}\,.\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="0.8em 0.3em" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>R</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>ℓ</mi> <mi>A</mi> </mfrac> </mrow> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mi>G</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>A</mi> <mi>ℓ</mi> </mfrac> </mrow> <mspace width="thinmathspace"></mspace> <mo>.</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}R&=\rho {\frac {\ell }{A}},\\[5pt]G&=\sigma {\frac {A}{\ell }}\,.\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b24667605c2703efd09de736ebc63d30be931418" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.505ex; width:10.62ex; height:12.176ex;" alt="{\displaystyle {\begin{aligned}R&=\rho {\frac {\ell }{A}},\\[5pt]G&=\sigma {\frac {A}{\ell }}\,.\end{aligned}}}" /></span> </p><p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ell }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ℓ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ell }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f066e981e530bacc07efc6a10fa82deee985929e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.97ex; height:2.176ex;" alt="{\displaystyle \ell }" /></span> is the length of the conductor, measured in <a href="/wiki/Metre" title="Metre">metres</a> (m), <span class="texhtml mvar" style="font-style:italic;">A</span> is the cross-sectional area of the conductor measured in <a href="/wiki/Square_metre" title="Square metre">square metres</a> (m<sup>2</sup>), <span class="texhtml mvar" style="font-style:italic;">σ</span> (<a href="/wiki/Sigma_(letter)" class="mw-redirect" title="Sigma (letter)">sigma</a>) is the <a href="/wiki/Electrical_conductivity" class="mw-redirect" title="Electrical conductivity">electrical conductivity</a> measured in <a href="/wiki/Siemens_(unit)" title="Siemens (unit)">siemens</a> per meter (S·m<sup>−1</sup>), and <span class="texhtml mvar" style="font-style:italic;">ρ</span> (<a href="/wiki/Rho_(letter)" class="mw-redirect" title="Rho (letter)">rho</a>) is the <a href="/wiki/Electrical_resistivity" class="mw-redirect" title="Electrical resistivity">electrical resistivity</a> (also called <i>specific electrical resistance</i>) of the material, measured in ohm-metres (Ω·m). The resistivity and conductivity are proportionality constants, and therefore depend only on the material the wire is made of, not the geometry of the wire. Resistivity and conductivity are <a href="/wiki/Multiplicative_inverse" title="Multiplicative inverse">reciprocals</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 \rho =1/\sigma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> <mo>=</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>σ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho =1/\sigma }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/013cda0a0b4ce975766b55aff950830a04776469" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.955ex; height:2.843ex;" alt="{\displaystyle \rho =1/\sigma }" /></span>. Resistivity is a measure of the material's ability to oppose electric current. </p><p>This formula is not exact, as it assumes the <a href="/wiki/Current_density" title="Current density">current density</a> is totally uniform in the conductor, which is not always true in practical situations. However, this formula still provides a good approximation for long thin conductors such as wires. </p><p>Another situation for which this formula is not exact is with <a href="/wiki/Alternating_current" title="Alternating current">alternating current</a> (AC), because the <a href="/wiki/Skin_effect" title="Skin effect">skin effect</a> inhibits current flow near the center of the conductor. For this reason, the <i>geometrical</i> cross-section is different from the <i>effective</i> cross-section in which current actually flows, so resistance is higher than expected. Similarly, if two conductors near each other carry AC current, their resistances increase due to the <a href="/wiki/Proximity_effect_(electromagnetism)" title="Proximity effect (electromagnetism)">proximity effect</a>. At <a href="/wiki/Utility_frequency" title="Utility frequency">commercial power frequency</a>, these effects are significant for large conductors carrying large currents, such as <a href="/wiki/Busbar" title="Busbar">busbars</a> in an <a href="/wiki/Electrical_substation" class="mw-redirect" title="Electrical substation">electrical substation</a>,<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> or large power cables carrying more than a few hundred amperes. </p><p>The resistivity of different materials varies by an enormous amount: For example, the conductivity of <a href="/wiki/PTFE" class="mw-redirect" title="PTFE">teflon</a> is about 10<sup>30</sup> times lower than the conductivity of copper. Loosely speaking, this is because metals have large numbers of "delocalized" electrons that are not stuck in any one place, so they are free to move across large distances. In an insulator, such as Teflon, each electron is tightly bound to a single molecule so a great force is required to pull it away. <a href="/wiki/Semiconductor" title="Semiconductor">Semiconductors</a> lie between these two extremes. More details can be found in the article: <a href="/wiki/Electrical_resistivity_and_conductivity" title="Electrical resistivity and conductivity">Electrical resistivity and conductivity</a>. For the case of <a href="/wiki/Electrolyte" title="Electrolyte">electrolyte</a> solutions, see the article: <a href="/wiki/Conductivity_(electrolytic)" title="Conductivity (electrolytic)">Conductivity (electrolytic)</a>. </p><p>Resistivity varies with temperature. In semiconductors, resistivity also changes when exposed to light. See <a href="#Dependence_on_other_conditions">below</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Measurement">Measurement</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_resistance_and_conductance&action=edit&section=5" title="Edit section: Measurement"><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/Ohmmeter" title="Ohmmeter">Ohmmeter</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Sanwa_SM-1005s.jpg" class="mw-file-description"><img alt="photograph of an ohmmeter" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a7/Sanwa_SM-1005s.jpg/220px-Sanwa_SM-1005s.jpg" decoding="async" width="220" height="295" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a7/Sanwa_SM-1005s.jpg/330px-Sanwa_SM-1005s.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a7/Sanwa_SM-1005s.jpg/440px-Sanwa_SM-1005s.jpg 2x" data-file-width="796" data-file-height="1066" /></a><figcaption>An <a href="/wiki/Ohmmeter" title="Ohmmeter">ohmmeter</a></figcaption></figure> <p>An instrument for measuring resistance is called an <a href="/wiki/Ohmmeter" title="Ohmmeter">ohmmeter</a>. Simple ohmmeters cannot measure low resistances accurately because the resistance of their measuring leads causes a voltage drop that interferes with the measurement, so more accurate devices use <a href="/wiki/Four-terminal_sensing" title="Four-terminal sensing">four-terminal sensing</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Typical_values">Typical values</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_resistance_and_conductance&action=edit&section=6" title="Edit section: Typical values"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Electrical_resistivities_of_the_elements_(data_page)" title="Electrical resistivities of the elements (data page)">Electrical resistivities of the elements (data page)</a> and <a href="/wiki/Electrical_resistivity_and_conductivity" title="Electrical resistivity and conductivity">Electrical resistivity and conductivity</a></div> <table class="wikitable"> <caption>Typical resistance values for selected objects </caption> <tbody><tr> <th scope="col">Component </th> <th scope="col">Resistance (Ω) </th></tr> <tr> <td>1 meter of copper wire with 1 mm diameter </td> <td>0.02<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>a<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td><span class="nowrap"><span data-sort-value="7003100000000000000♠"></span>1 km</span> <a href="/wiki/Overhead_power_line" title="Overhead power line">overhead power line</a> (<i>typical</i>) </td> <td>0.03<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td><a href="/wiki/AA_battery" title="AA battery">AA battery</a> (<i>typical <a href="/wiki/Internal_resistance" title="Internal resistance">internal resistance</a></i>) </td> <td>0.1<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>b<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td><a href="/wiki/Incandescent_light_bulb" title="Incandescent light bulb">Incandescent light bulb</a> filament (<i>typical</i>) </td> <td>200–1000<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>c<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td>Human body </td> <td>1000–100,000<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>d<span class="cite-bracket">]</span></a></sup> </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Static_and_differential_resistance">Static and differential resistance</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_resistance_and_conductance&action=edit&section=7" title="Edit section: Static and differential resistance"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Small-signal_model" title="Small-signal model">Small-signal model</a></div> <style data-mw-deduplicate="TemplateStyles:r1273380762/mw-parser-output/.tmulti">.mw-parser-output .tmulti .multiimageinner{display:flex;flex-direction:column}.mw-parser-output .tmulti .trow{display:flex;flex-direction:row;clear:left;flex-wrap:wrap;width:100%;box-sizing:border-box}.mw-parser-output .tmulti .tsingle{margin:1px;float:left}.mw-parser-output .tmulti .theader{clear:both;font-weight:bold;text-align:center;align-self:center;background-color:transparent;width:100%}.mw-parser-output .tmulti .thumbcaption{background-color:transparent}.mw-parser-output .tmulti .text-align-left{text-align:left}.mw-parser-output .tmulti .text-align-right{text-align:right}.mw-parser-output .tmulti .text-align-center{text-align:center}@media all and (max-width:720px){.mw-parser-output .tmulti .thumbinner{width:100%!important;box-sizing:border-box;max-width:none!important;align-items:center}.mw-parser-output .tmulti .trow{justify-content:center}.mw-parser-output .tmulti .tsingle{float:none!important;max-width:100%!important;box-sizing:border-box;text-align:center}.mw-parser-output .tmulti .tsingle .thumbcaption{text-align:left}.mw-parser-output .tmulti .trow>.thumbcaption{text-align:center}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .tmulti .multiimageinner span:not(.skin-invert-image):not(.skin-invert):not(.bg-transparent) img{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .tmulti .multiimageinner span:not(.skin-invert-image):not(.skin-invert):not(.bg-transparent) img{background-color:white}}</style><div class="thumb tmulti tright"><div class="thumbinner multiimageinner" style="width:408px;max-width:408px"><div class="trow"><div class="tsingle" style="width:202px;max-width:202px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:DifferentialChordalResistance.svg" class="mw-file-description"><img alt="Differential versus chordal resistance" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/57/DifferentialChordalResistance.svg/200px-DifferentialChordalResistance.svg.png" decoding="async" width="200" height="132" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/57/DifferentialChordalResistance.svg/300px-DifferentialChordalResistance.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/57/DifferentialChordalResistance.svg/400px-DifferentialChordalResistance.svg.png 2x" data-file-width="374" data-file-height="246" /></a></span></div><div class="thumbcaption">The <a href="/wiki/Current%E2%80%93voltage_characteristic" title="Current–voltage characteristic">current–voltage curve</a> of a non-ohmic device (purple). The <b>static resistance</b> at point <i>A</i> is the <a href="/wiki/Multiplicative_inverse" title="Multiplicative inverse">inverse</a> <a href="/wiki/Slope" title="Slope">slope</a> of line <i>B</i> through the origin. The <b>differential resistance</b> at <i>A</i> is the inverse slope of <a href="/wiki/Tangent_line" class="mw-redirect" title="Tangent line">tangent line</a> <i>C</i>.</div></div><div class="tsingle" style="width:202px;max-width:202px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Negative_differential_resistance.svg" class="mw-file-description"><img alt="Negative differential resistance" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/54/Negative_differential_resistance.svg/200px-Negative_differential_resistance.svg.png" decoding="async" width="200" height="182" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/54/Negative_differential_resistance.svg/300px-Negative_differential_resistance.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/54/Negative_differential_resistance.svg/400px-Negative_differential_resistance.svg.png 2x" data-file-width="524" data-file-height="478" /></a></span></div><div class="thumbcaption">The <a href="/wiki/Current%E2%80%93voltage_characteristic" title="Current–voltage characteristic">current–voltage curve</a> of a component with <a href="/wiki/Negative_resistance" title="Negative resistance">negative differential resistance</a>, an unusual phenomenon where the current–voltage curve is non-<a href="/wiki/Monotonic_function" title="Monotonic function">monotonic</a>.</div></div></div></div></div> <p>Many electrical elements, such as <a href="/wiki/Diode" title="Diode">diodes</a> and <a href="/wiki/Battery_(electricity)" class="mw-redirect" title="Battery (electricity)">batteries</a> do <em>not</em> satisfy <a href="/wiki/Ohm%27s_law" title="Ohm's law">Ohm's law</a>. These are called <i>non-ohmic</i> or <i>non-linear</i>, and their <a href="/wiki/Current%E2%80%93voltage_characteristic" title="Current–voltage characteristic">current–voltage curves</a> are <em>not</em> straight lines through the origin. </p><p>Resistance and conductance can still be defined for non-ohmic elements. However, unlike ohmic resistance, non-linear resistance is not constant but varies with the voltage or current through the device; i.e., its <a href="/wiki/Biasing" title="Biasing">operating point</a>. There are two types of resistance:<sup id="cite_ref-brown_1-1" class="reference"><a href="#cite_note-brown-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-kaiser_2-1" class="reference"><a href="#cite_note-kaiser-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <style data-mw-deduplicate="TemplateStyles:r1228772891">.mw-parser-output .glossary dt{margin-top:0.4em}.mw-parser-output .glossary dt+dt{margin-top:-0.2em}.mw-parser-output .glossary .templatequote{margin-top:0;margin-bottom:-0.5em}</style> <dl class="glossary"> <dt id="static_resistance"><dfn>Static resistance</dfn></dt> <dd><p class="glossary-hatnote"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><span role="note" class="hatnote navigation-not-searchable selfref">Also called <b>chordal</b> or <b>DC resistance</b></span></p> <p>This corresponds to the usual definition of resistance; the voltage divided by the current <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{\mathrm {static} }={V \over I}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">c</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>V</mi> <mi>I</mi> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{\mathrm {static} }={V \over I}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eafa591c42ec4f29af7209ea8b48b8ec60b9024b" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:12.302ex; height:5.176ex;" alt="{\displaystyle R_{\mathrm {static} }={V \over I}.}" /></span> </p> It is the slope of the line (<a href="/wiki/Chord_(geometry)" title="Chord (geometry)">chord</a>) from the origin through the point on the curve. Static resistance determines the power dissipation in an electrical component. Points on the current–voltage curve located in the 2nd or 4th quadrants, for which the slope of the chordal line is negative, have <i>negative static resistance</i>. <a href="/wiki/Passivity_(engineering)" title="Passivity (engineering)">Passive</a> devices, which have no source of energy, cannot have negative static resistance. However active devices such as transistors or <a href="/wiki/Op-amp" class="mw-redirect" title="Op-amp">op-amps</a> can synthesize negative static resistance with feedback, and it is used in some circuits such as <a href="/wiki/Gyrator" title="Gyrator">gyrators</a>.</dd> <dt id="differential_resistance"><dfn>Differential resistance</dfn></dt> <dd><p class="glossary-hatnote"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><span role="note" class="hatnote navigation-not-searchable selfref">Also called <b>dynamic</b>, <b>incremental</b>, or <b>small-signal resistance</b></span></p> <p>It is the derivative of the voltage with respect to the current; the <a href="/wiki/Slope" title="Slope">slope</a> of the current–voltage curve at a point <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{\mathrm {diff} }={{\mathrm {d} V} \over {\mathrm {d} I}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">f</mi> <mi mathvariant="normal">f</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>V</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>I</mi> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{\mathrm {diff} }={{\mathrm {d} V} \over {\mathrm {d} I}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/41836d313154d34848ad531ee3b68df62f26ac1b" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:12.252ex; height:5.509ex;" alt="{\displaystyle R_{\mathrm {diff} }={{\mathrm {d} V} \over {\mathrm {d} I}}.}" /></span> </p> If the current–voltage curve is non-<a href="/wiki/Monotonic" class="mw-redirect" title="Monotonic">monotonic</a> (with peaks and troughs), the curve has a negative slope in some regions—so in these regions the device has <i><a href="/wiki/Negative_differential_resistance" class="mw-redirect" title="Negative differential resistance">negative differential resistance</a></i>. Devices with negative differential resistance can amplify a signal applied to them, and are used to make amplifiers and oscillators. These include <a href="/wiki/Tunnel_diode" title="Tunnel diode">tunnel diodes</a>, <a href="/wiki/Gunn_diode" title="Gunn diode">Gunn diodes</a>, <a href="/wiki/IMPATT_diode" title="IMPATT diode">IMPATT diodes</a>, <a href="/wiki/Magnetron" class="mw-redirect" title="Magnetron">magnetron</a> tubes, and <a href="/wiki/Unijunction_transistor" title="Unijunction transistor">unijunction transistors</a>.</dd> </dl> <div class="mw-heading mw-heading2"><h2 id="AC_circuits">AC circuits</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_resistance_and_conductance&action=edit&section=8" title="Edit section: AC circuits"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Impedance_and_admittance">Impedance and admittance</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_resistance_and_conductance&action=edit&section=9" title="Edit section: Impedance and admittance"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Electrical_impedance" title="Electrical impedance">Electrical impedance</a> and <a href="/wiki/Admittance" title="Admittance">Admittance</a></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:VI_phase.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/71/VI_phase.svg/300px-VI_phase.svg.png" decoding="async" width="300" height="257" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/71/VI_phase.svg/450px-VI_phase.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/71/VI_phase.svg/600px-VI_phase.svg.png 2x" data-file-width="700" data-file-height="600" /></a><figcaption>The voltage (red) and current (blue) versus time (horizontal axis) for a <a href="/wiki/Capacitor" title="Capacitor">capacitor</a> (top) and <a href="/wiki/Inductor" title="Inductor">inductor</a> (bottom). Since the <a href="/wiki/Amplitude" title="Amplitude">amplitude</a> of the current and voltage <a href="/wiki/Sine_wave" title="Sine wave">sinusoids</a> are the same, the <a href="/wiki/Absolute_value" title="Absolute value">absolute value</a> of <a href="/wiki/Electrical_impedance" title="Electrical impedance">impedance</a> is 1 for both the capacitor and the inductor (in whatever units the graph is using). On the other hand, the <a href="/wiki/Phase_(waves)" title="Phase (waves)">phase difference</a> between current and voltage is −90° for the capacitor; therefore, the <a href="/wiki/Argument_(complex_analysis)" title="Argument (complex analysis)">complex phase</a> of the <a href="/wiki/Electrical_impedance" title="Electrical impedance">impedance</a> of the capacitor is −90°. Similarly, the <a href="/wiki/Phase_(waves)" title="Phase (waves)">phase difference</a> between current and voltage is +90° for the inductor; therefore, the complex phase of the impedance of the inductor is +90°.</figcaption></figure> <p>When an alternating current flows through a circuit, the relation between current and voltage across a circuit element is characterized not only by the ratio of their magnitudes, but also the difference in their <a href="/wiki/Phase_(waves)" title="Phase (waves)">phases</a>. For example, in an ideal <a href="/wiki/Resistor" title="Resistor">resistor</a>, the moment when the voltage reaches its maximum, the current also reaches its maximum (current and voltage are oscillating in phase). But for a <a href="/wiki/Capacitor" title="Capacitor">capacitor</a> or <a href="/wiki/Inductor" title="Inductor">inductor</a>, the maximum current flow occurs as the voltage passes through zero and vice versa (current and voltage are oscillating 90° out of phase, see image below). <a href="/wiki/Complex_number" title="Complex number">Complex numbers</a> are used to keep track of both the phase and magnitude of current and voltage: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{array}{cl}u(t)&=\operatorname {\mathcal {R_{e}}} \left(U_{0}\cdot e^{j\omega t}\right)\\i(t)&=\operatorname {\mathcal {R_{e}}} \left(I_{0}\cdot e^{j(\omega t+\varphi )}\right)\\Z&={\frac {U}{\ I\ }}\\Y&={\frac {\ 1\ }{Z}}={\frac {\ I\ }{U}}\end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="center left" rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>u</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mtd> <mtd> <mo>=</mo> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi class="MJX-tex-caligraphic" mathvariant="script">R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">e</mi> </mrow> </msub> </mrow> </mrow> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>⋅</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mi>ω</mi> <mi>t</mi> </mrow> </msup> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>i</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mtd> <mtd> <mo>=</mo> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi class="MJX-tex-caligraphic" mathvariant="script">R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">e</mi> </mrow> </msub> </mrow> </mrow> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>⋅</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mo stretchy="false">(</mo> <mi>ω</mi> <mi>t</mi> <mo>+</mo> <mi>φ</mi> <mo stretchy="false">)</mo> </mrow> </msup> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>Z</mi> </mtd> <mtd> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>U</mi> <mrow> <mtext> </mtext> <mi>I</mi> <mtext> </mtext> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>Y</mi> </mtd> <mtd> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mtext> </mtext> <mn>1</mn> <mtext> </mtext> </mrow> <mi>Z</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mtext> </mtext> <mi>I</mi> <mtext> </mtext> </mrow> <mi>U</mi> </mfrac> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{cl}u(t)&=\operatorname {\mathcal {R_{e}}} \left(U_{0}\cdot e^{j\omega t}\right)\\i(t)&=\operatorname {\mathcal {R_{e}}} \left(I_{0}\cdot e^{j(\omega t+\varphi )}\right)\\Z&={\frac {U}{\ I\ }}\\Y&={\frac {\ 1\ }{Z}}={\frac {\ I\ }{U}}\end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f85c0dc7d2649f25b9dae5ba9d0b85f4212e8d60" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -7.171ex; width:25.603ex; height:15.509ex;" alt="{\displaystyle {\begin{array}{cl}u(t)&=\operatorname {\mathcal {R_{e}}} \left(U_{0}\cdot e^{j\omega t}\right)\\i(t)&=\operatorname {\mathcal {R_{e}}} \left(I_{0}\cdot e^{j(\omega t+\varphi )}\right)\\Z&={\frac {U}{\ I\ }}\\Y&={\frac {\ 1\ }{Z}}={\frac {\ I\ }{U}}\end{array}}}" /></span> </p><p>where: </p> <ul><li><span class="texhtml mvar" style="font-style:italic;">t</span> is time;</li> <li><span class="texhtml"><i>u</i>(<i>t</i>)</span> and <span class="texhtml"><i>i</i>(<i>t</i>)</span> are the voltage and current as a function of time, respectively;</li> <li><span class="texhtml"><i>U</i><sub>0</sub></span> and <span class="texhtml"><i>I</i><sub>0</sub></span> indicate the amplitude of the voltage and current, respectively;</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 <a href="/wiki/Angular_frequency" title="Angular frequency">angular frequency</a> of the AC current;</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 \varphi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33ee699558d09cf9d653f6351f9fda0b2f4aaa3e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.52ex; height:2.176ex;" alt="{\displaystyle \varphi }" /></span> is the displacement angle;</li> <li><span class="texhtml mvar" style="font-style:italic;">U</span> and <span class="texhtml mvar" style="font-style:italic;">I</span> are the complex-valued voltage and current, respectively;</li> <li><span class="texhtml mvar" style="font-style:italic;">Z</span> and <span class="texhtml mvar" style="font-style:italic;">Y</span> are the complex <a href="/wiki/Electrical_impedance" title="Electrical impedance">impedance</a> and <a href="/wiki/Admittance" title="Admittance">admittance</a>, respectively;</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 {\mathcal {R_{e}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi class="MJX-tex-caligraphic" mathvariant="script">R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">e</mi> </mrow> </msub> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {R_{e}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/208b0efff2cecc0472be8287e3240e3d849fe6a7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.969ex; height:2.509ex;" alt="{\displaystyle {\mathcal {R_{e}}}}" /></span> indicates the <a href="/wiki/Real_part" class="mw-redirect" title="Real part">real part</a> of a <a href="/wiki/Complex_number" title="Complex number">complex number</a>; and</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle j\equiv {\sqrt {-1\ }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>j</mi> <mo>≡</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mo>−</mo> <mn>1</mn> <mtext> </mtext> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle j\equiv {\sqrt {-1\ }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ad9a404238e926263dcb6e161ee7a3baeea7d134" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.027ex; width:9.57ex; height:3.009ex;" alt="{\displaystyle j\equiv {\sqrt {-1\ }}}" /></span> is the <a href="/wiki/Imaginary_unit" title="Imaginary unit">imaginary unit</a>.</li></ul> <p>The impedance and admittance may be expressed as complex numbers that can be broken into real and imaginary parts: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}Z&=R+jX\\Y&=G+jB~.\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>Z</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>R</mi> <mo>+</mo> <mi>j</mi> <mi>X</mi> </mtd> </mtr> <mtr> <mtd> <mi>Y</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>G</mi> <mo>+</mo> <mi>j</mi> <mi>B</mi> <mtext> </mtext> <mo>.</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}Z&=R+jX\\Y&=G+jB~.\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86da8fd2198971a85669b338877444d90d2dfdfa" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:14.24ex; height:5.843ex;" alt="{\displaystyle {\begin{aligned}Z&=R+jX\\Y&=G+jB~.\end{aligned}}}" /></span> </p><p>where <span class="texhtml mvar" style="font-style:italic;">R</span> is resistance, <span class="texhtml mvar" style="font-style:italic;">G</span> is conductance, <span class="texhtml mvar" style="font-style:italic;">X</span> is <a href="/wiki/Electrical_reactance" title="Electrical reactance">reactance</a>, and <span class="texhtml mvar" style="font-style:italic;">B</span> is <a href="/wiki/Susceptance" class="mw-redirect" title="Susceptance">susceptance</a>. These lead to the <a href="/wiki/Complex_number" title="Complex number">complex number</a> identities <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}R&={\frac {G}{\ G^{2}+B^{2}\ }}\ ,\qquad &X={\frac {-B~}{\ G^{2}+B^{2}\ }}\ ,\\G&={\frac {R}{\ R^{2}+X^{2}\ }}\ ,\qquad &B={\frac {-X~}{\ R^{2}+X^{2}\ }}\ ,\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>R</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>G</mi> <mrow> <mtext> </mtext> <msup> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mtext> </mtext> </mrow> </mfrac> </mrow> <mtext> </mtext> <mo>,</mo> <mspace width="2em"></mspace> </mtd> <mtd> <mi>X</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo>−</mo> <mi>B</mi> <mtext> </mtext> </mrow> <mrow> <mtext> </mtext> <msup> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mtext> </mtext> </mrow> </mfrac> </mrow> <mtext> </mtext> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mi>G</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>R</mi> <mrow> <mtext> </mtext> <msup> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mtext> </mtext> </mrow> </mfrac> </mrow> <mtext> </mtext> <mo>,</mo> <mspace width="2em"></mspace> </mtd> <mtd> <mi>B</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo>−</mo> <mi>X</mi> <mtext> </mtext> </mrow> <mrow> <mtext> </mtext> <msup> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mtext> </mtext> </mrow> </mfrac> </mrow> <mtext> </mtext> <mo>,</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}R&={\frac {G}{\ G^{2}+B^{2}\ }}\ ,\qquad &X={\frac {-B~}{\ G^{2}+B^{2}\ }}\ ,\\G&={\frac {R}{\ R^{2}+X^{2}\ }}\ ,\qquad &B={\frac {-X~}{\ R^{2}+X^{2}\ }}\ ,\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec9b96053c28b4180c65cc92d6f4b264de859f28" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.171ex; width:43.745ex; height:11.509ex;" alt="{\displaystyle {\begin{aligned}R&={\frac {G}{\ G^{2}+B^{2}\ }}\ ,\qquad &X={\frac {-B~}{\ G^{2}+B^{2}\ }}\ ,\\G&={\frac {R}{\ R^{2}+X^{2}\ }}\ ,\qquad &B={\frac {-X~}{\ R^{2}+X^{2}\ }}\ ,\end{aligned}}}" /></span> which are true in all cases, whereas <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=1/G\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>R</mi> <mo>=</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>G</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ R=1/G\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f883acb30022cc5b5fab384b0c87cc26bbcf4bf9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.175ex; height:2.843ex;" alt="{\displaystyle \ R=1/G\ }" /></span> is only true in the special cases of either DC or reactance-free current. </p><p>The <a href="/wiki/Argument_(complex_analysis)" title="Argument (complex analysis)">complex angle</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 \ \theta =\arg(Z)=-\arg(Y)\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>θ</mi> <mo>=</mo> <mi>arg</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>Z</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo>−</mo> <mi>arg</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>Y</mi> <mo stretchy="false">)</mo> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \theta =\arg(Z)=-\arg(Y)\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d4f74c6ef74808d09d8862df9fc0d1a1ab01f28e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:24.189ex; height:2.843ex;" alt="{\displaystyle \ \theta =\arg(Z)=-\arg(Y)\ }" /></span> is the phase difference between the voltage and current passing through a component with impedance <span class="texhtml mvar" style="font-style:italic;">Z</span>. For <a href="/wiki/Capacitor" title="Capacitor">capacitors</a> and <a href="/wiki/Inductor" title="Inductor">inductors</a>, this angle is exactly -90° or +90°, respectively, and <span class="texhtml mvar" style="font-style:italic;">X</span> and <span class="texhtml mvar" style="font-style:italic;">B</span> are nonzero. Ideal resistors have an angle of 0°, since <span class="texhtml mvar" style="font-style:italic;">X</span> is zero (and hence <span class="texhtml mvar" style="font-style:italic;">B</span> also), and <span class="texhtml mvar" style="font-style:italic;">Z</span> and <span class="texhtml mvar" style="font-style:italic;">Y</span> reduce to <span class="texhtml mvar" style="font-style:italic;">R</span> and <span class="texhtml mvar" style="font-style:italic;">G</span> respectively. In general, AC systems are designed to keep the phase angle close to 0° as much as possible, since it reduces the <a href="/wiki/AC_power#Reactive_power" title="AC power">reactive power</a>, which does no useful work at a load. In a simple case with an inductive load (causing the phase to increase), a capacitor may be added for compensation at one frequency, since the capacitor's phase shift is negative, bringing the total impedance phase closer to 0° again. </p><p><span class="texhtml mvar" style="font-style:italic;">Y</span> is the reciprocal of <span class="texhtml mvar" style="font-style:italic;">Z</span> (<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=1/Y\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>Z</mi> <mo>=</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>Y</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ Z=1/Y\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5dcc79822e0035215224b253074698dea90b58f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.038ex; height:2.843ex;" alt="{\displaystyle \ Z=1/Y\ }" /></span>) for all circuits, just 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 R=1/G}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <mo>=</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>G</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R=1/G}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53ac96b2fbd95f288fa7318ab3a8d53f16df5281" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.014ex; height:2.843ex;" alt="{\displaystyle R=1/G}" /></span> for DC circuits containing only resistors, or AC circuits for which either the reactance or susceptance happens to be zero (<span class="texhtml mvar" style="font-style:italic;">X</span> or <span class="texhtml"><i>B</i> = 0</span>, respectively) (if one is zero, then for realistic systems both must be zero). </p> <div class="mw-heading mw-heading3"><h3 id="Frequency_dependence">Frequency dependence</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_resistance_and_conductance&action=edit&section=10" title="Edit section: Frequency dependence"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A key feature of AC circuits is that the resistance and conductance can be frequency-dependent, a phenomenon known as the <a href="/wiki/Universal_dielectric_response" title="Universal dielectric response">universal dielectric response</a>.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> One reason, mentioned above is the <a href="/wiki/Skin_effect" title="Skin effect">skin effect</a> (and the related <a href="/wiki/Proximity_effect_(electromagnetism)" title="Proximity effect (electromagnetism)">proximity effect</a>). Another reason is that the resistivity itself may depend on frequency (see <a href="/wiki/Drude_model" title="Drude model">Drude model</a>, <a href="/wiki/Deep-level_trap" title="Deep-level trap">deep-level traps</a>, <a href="/wiki/Resonant_frequency" class="mw-redirect" title="Resonant frequency">resonant frequency</a>, <a href="/wiki/Kramers%E2%80%93Kronig_relations" title="Kramers–Kronig relations">Kramers–Kronig relations</a>, etc.) </p> <div class="mw-heading mw-heading2"><h2 id="Energy_dissipation_and_Joule_heating">Energy dissipation and Joule heating</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_resistance_and_conductance&action=edit&section=11" title="Edit section: Energy dissipation and Joule heating"><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/Joule_heating" title="Joule heating">Joule heating</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Cartridge-heater-hot.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/92/Cartridge-heater-hot.jpg/220px-Cartridge-heater-hot.jpg" decoding="async" width="220" height="124" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/92/Cartridge-heater-hot.jpg/330px-Cartridge-heater-hot.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/92/Cartridge-heater-hot.jpg/440px-Cartridge-heater-hot.jpg 2x" data-file-width="3200" data-file-height="1800" /></a><figcaption>Running current through a material with resistance creates heat, in a phenomenon called <a href="/wiki/Joule_heating" title="Joule heating">Joule heating</a>. In this picture, a <a href="/wiki/Cartridge_heater" title="Cartridge heater">cartridge heater</a>, warmed by Joule heating, is <a href="/wiki/Incandescence" class="mw-redirect" title="Incandescence">glowing red hot</a>.</figcaption></figure> <p>Resistors (and other elements with resistance) oppose the flow of electric current; therefore, electrical energy is required to push current through the resistance. This electrical energy is dissipated, heating the resistor in the process. This is called <i><a href="/wiki/Joule_heating" title="Joule heating">Joule heating</a></i> (after <a href="/wiki/James_Prescott_Joule" title="James Prescott Joule">James Prescott Joule</a>), also called <i>ohmic heating</i> or <i>resistive heating</i>. </p><p>The dissipation of electrical energy is often undesired, particularly in the case of <a href="/wiki/Electric_power_transmission" title="Electric power transmission">transmission losses</a> in <a href="/wiki/Overhead_power_line" title="Overhead power line">power lines</a>. <a href="/wiki/Electric_power_transmission" title="Electric power transmission">High voltage transmission</a> helps reduce the losses by reducing the current for a given power. </p><p>On the other hand, Joule heating is sometimes useful, for example in <a href="/wiki/Electric_stove" title="Electric stove">electric stoves</a> and other <a href="/wiki/Electric_heating" title="Electric heating">electric heaters</a> (also called <i>resistive heaters</i>). As another example, <a href="/wiki/Incandescent_lamp" class="mw-redirect" title="Incandescent lamp">incandescent lamps</a> rely on Joule heating: the filament is heated to such a high temperature that it glows "white hot" with <a href="/wiki/Thermal_radiation" title="Thermal radiation">thermal radiation</a> (also called <a href="/wiki/Incandescence" class="mw-redirect" title="Incandescence">incandescence</a>). </p><p>The formula for Joule heating is: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P=I^{2}R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo>=</mo> <msup> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P=I^{2}R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c7bed4a958579256904b5a8728616b2100c1d8f5" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.879ex; height:2.676ex;" alt="{\displaystyle P=I^{2}R}" /></span> where <span class="texhtml mvar" style="font-style:italic;">P</span> is the <a href="/wiki/Electric_power" title="Electric power">power</a> (energy per unit time) converted from electrical energy to thermal energy, <span class="texhtml mvar" style="font-style:italic;">R</span> is the resistance, and <span class="texhtml mvar" style="font-style:italic;">I</span> is the current through the resistor. </p> <div class="mw-heading mw-heading2"><h2 id="Dependence_on_other_conditions">Dependence on other conditions</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_resistance_and_conductance&action=edit&section=12" title="Edit section: Dependence on other conditions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Temperature_dependence">Temperature dependence</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_resistance_and_conductance&action=edit&section=13" title="Edit section: Temperature dependence"><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_resistivity_and_conductivity#Temperature_dependence" title="Electrical resistivity and conductivity">Electrical resistivity and conductivity § Temperature dependence</a></div> <p>Near room temperature, the resistivity of metals typically increases as temperature is increased, while the resistivity of semiconductors typically decreases as temperature is increased. The resistivity of insulators and electrolytes may increase or decrease depending on the system. For the detailed behavior and explanation, see <a href="/wiki/Electrical_resistivity_and_conductivity" title="Electrical resistivity and conductivity">Electrical resistivity and conductivity</a>. </p><p>As a consequence, the resistance of wires, resistors, and other components often change with temperature. This effect may be undesired, causing an electronic circuit to malfunction at extreme temperatures. In some cases, however, the effect is put to good use. When temperature-dependent resistance of a component is used purposefully, the component is called a <a href="/wiki/Resistance_thermometer" title="Resistance thermometer">resistance thermometer</a> or <a href="/wiki/Thermistor" title="Thermistor">thermistor</a>. (A resistance thermometer is made of metal, usually platinum, while a thermistor is made of ceramic or polymer.) </p><p>Resistance thermometers and thermistors are generally used in two ways. First, they can be used as <a href="/wiki/Thermometer" title="Thermometer">thermometers</a>: by measuring the resistance, the temperature of the environment can be inferred. Second, they can be used in conjunction with <a href="/wiki/Joule_heating" title="Joule heating">Joule heating</a> (also called self-heating): if a large current is running through the resistor, the resistor's temperature rises and therefore its resistance changes. Therefore, these components can be used in a circuit-protection role similar to <a href="/wiki/Fuse_(electrical)" title="Fuse (electrical)">fuses</a>, or for <a href="/wiki/Feedback" title="Feedback">feedback</a> in circuits, or for many other purposes. In general, self-heating can turn a resistor into a <a href="/wiki/Nonlinear_element" class="mw-redirect" title="Nonlinear element">nonlinear</a> and <a href="/wiki/Hysteresis" title="Hysteresis">hysteretic</a> circuit element. For more details see <a href="/wiki/Thermistor#Self-heating_effects" title="Thermistor">Thermistor#Self-heating effects</a>. </p><p>If the temperature <span class="texhtml mvar" style="font-style:italic;">T</span> does not vary too much, a <a href="/wiki/Linear_approximation" title="Linear approximation">linear approximation</a> is typically used: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R(T)=R_{0}[1+\alpha (T-T_{0})]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <mo stretchy="false">(</mo> <mi>T</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">[</mo> <mn>1</mn> <mo>+</mo> <mi>α</mi> <mo stretchy="false">(</mo> <mi>T</mi> <mo>−</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R(T)=R_{0}[1+\alpha (T-T_{0})]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5b6622ab35566bd32d26736effa752dc8ace798d" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:26.608ex; height:2.843ex;" alt="{\displaystyle R(T)=R_{0}[1+\alpha (T-T_{0})]}" /></span> where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }" /></span> is called the <i>temperature coefficient of resistance</i>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/55b9e7d7b96196b5a6a26f4349caa3ac82fd67e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.412ex; height:2.509ex;" alt="{\displaystyle T_{0}}" /></span> is a fixed reference temperature (usually room temperature), 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 R_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b8916196f182fcbaaca54f931176a4a4f5769cc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.818ex; height:2.509ex;" alt="{\displaystyle R_{0}}" /></span> is the resistance at temperature <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/55b9e7d7b96196b5a6a26f4349caa3ac82fd67e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.412ex; height:2.509ex;" alt="{\displaystyle T_{0}}" /></span>. The parameter <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 \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }" /></span> is an empirical parameter fitted from measurement data. Because the linear approximation is only an approximation, <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 \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }" /></span> is different for different reference temperatures. For this reason it is usual to specify the temperature that <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 \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }" /></span> was measured at with a suffix, such 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 \alpha _{15}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>15</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha _{15}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2e93f2a04a064beebf70cf0756e0cb1c8fb5a1bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.364ex; height:2.009ex;" alt="{\displaystyle \alpha _{15}}" /></span>, and the relationship only holds in a range of temperatures around the reference.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>The temperature coefficient <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 \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }" /></span> is typically <span class="nowrap"><span data-sort-value="6997300000000000000♠"></span>+3<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−3</sup> K−1</span> to <span class="nowrap"><span data-sort-value="6997600000000000000♠"></span>+6<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−3</sup> K−1</span> for metals near room temperature. It is usually negative for semiconductors and insulators, with highly variable magnitude.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>e<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Strain_dependence">Strain dependence</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_resistance_and_conductance&action=edit&section=14" title="Edit section: Strain dependence"><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/Strain_gauge" title="Strain gauge">Strain gauge</a></div> <p>Just as the resistance of a conductor depends upon temperature, the resistance of a conductor depends upon <a href="/wiki/Strain_(materials_science)" class="mw-redirect" title="Strain (materials science)">strain</a>.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> By placing a conductor under <a href="/wiki/Tension_(mechanics)" class="mw-redirect" title="Tension (mechanics)">tension</a> (a form of <a href="/wiki/Stress_(physics)" class="mw-redirect" title="Stress (physics)">stress</a> that leads to strain in the form of stretching of the conductor), the length of the section of conductor under tension increases and its cross-sectional area decreases. Both these effects contribute to increasing the resistance of the strained section of conductor. Under <a href="/wiki/Compression_(physics)" title="Compression (physics)">compression</a> (strain in the opposite direction), the resistance of the strained section of conductor decreases. See the discussion on <a href="/wiki/Strain_gauge" title="Strain gauge">strain gauges</a> for details about devices constructed to take advantage of this effect. </p> <div class="mw-heading mw-heading3"><h3 id="Light_illumination_dependence">Light illumination dependence</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_resistance_and_conductance&action=edit&section=15" title="Edit section: Light illumination dependence"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Photoresistor" title="Photoresistor">Photoresistor</a> and <a href="/wiki/Photoconductivity" title="Photoconductivity">Photoconductivity</a></div> <p>Some resistors, particularly those made from <a href="/wiki/Semiconductor" title="Semiconductor">semiconductors</a>, exhibit <i><a href="/wiki/Photoconductivity" title="Photoconductivity">photoconductivity</a></i>, meaning that their resistance changes when light is shining on them. Therefore, they are called <i><a href="/wiki/Photoresistor" title="Photoresistor">photoresistors</a></i> (or <i>light dependent resistors</i>). These are a common type of <a href="/wiki/Photodetector" title="Photodetector">light detector</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Superconductivity">Superconductivity</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_resistance_and_conductance&action=edit&section=16" title="Edit section: Superconductivity"><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/Superconductivity" title="Superconductivity">Superconductivity</a></div> <p><a href="/wiki/Superconductor" class="mw-redirect" title="Superconductor">Superconductors</a> are materials that have exactly zero resistance and infinite conductance, because they can have <span class="texhtml"><i>V</i> = 0</span> and <span class="texhtml"><i>I</i> ≠ 0</span>. This also means there is no <a href="/wiki/Joule_heating" title="Joule heating">joule heating</a>, or in other words no <a href="/wiki/Dissipation" title="Dissipation">dissipation</a> of electrical energy. Therefore, if superconductive wire is made into a closed loop, current flows around the loop forever. Superconductors require cooling to temperatures near <span class="nowrap"><span data-sort-value="7000400000000000000♠"></span>4 K</span> with <a href="/wiki/Liquid_helium" title="Liquid helium">liquid helium</a> for most metallic superconductors like <a href="/wiki/Niobium%E2%80%93tin" title="Niobium–tin">niobium–tin</a> alloys, or cooling to temperatures near <span class="nowrap"><span data-sort-value="7001770000000000000♠"></span>77 K</span> with <a href="/wiki/Liquid_nitrogen" title="Liquid nitrogen">liquid nitrogen</a> for the expensive, brittle and delicate ceramic <a href="/wiki/High_temperature_superconductors" class="mw-redirect" title="High temperature superconductors">high temperature superconductors</a>. Nevertheless, there are many <a href="/wiki/Technological_applications_of_superconductivity" title="Technological applications of superconductivity">technological applications of superconductivity</a>, including <a href="/wiki/Superconducting_magnet" title="Superconducting magnet">superconducting magnets</a>. </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_resistance_and_conductance&action=edit&section=17" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1266661725">.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px solid var(--border-color-base,#a2a9b1);padding:0.1em;background:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .portalbox-entry{display:table-row;font-size:85%;line-height:110%;height:1.9em;font-style:italic;font-weight:bold}.mw-parser-output .portalbox-image{display:table-cell;padding:0.2em;vertical-align:middle;text-align:center}.mw-parser-output .portalbox-link{display:table-cell;padding:0.2em 0.2em 0.2em 0.3em;vertical-align:middle}@media(min-width:720px){.mw-parser-output .portalleft{margin:0.5em 1em 0.5em 0}.mw-parser-output .portalright{clear:right;float:right;margin:0.5em 0 0.5em 1em}}</style><ul role="navigation" aria-label="Portals" class="noprint portalbox portalborder portalright"> <li class="portalbox-entry"><span class="portalbox-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Nuvola_apps_ksim.png" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Nuvola_apps_ksim.png/28px-Nuvola_apps_ksim.png" decoding="async" width="28" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Nuvola_apps_ksim.png/42px-Nuvola_apps_ksim.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Nuvola_apps_ksim.png/56px-Nuvola_apps_ksim.png 2x" data-file-width="128" data-file-height="128" /></a></span></span><span class="portalbox-link"><a href="/wiki/Portal:Electronics" title="Portal:Electronics">Electronics portal</a></span></li></ul> <ul><li><a href="/wiki/Conductance_quantum" title="Conductance quantum">Conductance quantum</a> <ul><li><a href="/wiki/Von_Klitzing_constant" class="mw-redirect" title="Von Klitzing constant">Von Klitzing constant</a> (its reciprocal)</li></ul></li> <li><a href="/wiki/Electrical_measurements" title="Electrical measurements">Electrical measurements</a></li> <li><a href="/wiki/Contact_resistance" title="Contact resistance">Contact resistance</a></li> <li><a href="/wiki/Electrical_resistivity_and_conductivity" title="Electrical resistivity and conductivity">Electrical resistivity and conductivity</a> for more information about the physical mechanisms for conduction in materials.</li> <li><a href="/wiki/Johnson%E2%80%93Nyquist_noise" title="Johnson–Nyquist noise">Johnson–Nyquist noise</a></li> <li><a href="/wiki/Quantum_Hall_effect" title="Quantum Hall effect">Quantum Hall effect</a>, a standard for high-accuracy resistance measurements.</li> <li><a href="/wiki/Resistor" title="Resistor">Resistor</a></li> <li><a href="/wiki/RKM_code" title="RKM code">RKM code</a></li> <li><a href="/wiki/Series_and_parallel_circuits" title="Series and parallel circuits">Series and parallel circuits</a></li> <li><a href="/wiki/Sheet_resistance" title="Sheet resistance">Sheet resistance</a></li> <li><a href="/wiki/SI_electromagnetism_units" class="mw-redirect" title="SI electromagnetism units">SI electromagnetism units</a></li> <li><a href="/wiki/Thermal_resistance" class="mw-redirect" title="Thermal resistance">Thermal resistance</a></li> <li><a href="/wiki/Voltage_divider" title="Voltage divider">Voltage divider</a></li> <li><a href="/wiki/Voltage_drop" title="Voltage drop">Voltage drop</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Footnotes">Footnotes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_resistance_and_conductance&action=edit&section=18" title="Edit section: Footnotes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width reflist-lower-alpha"> <ol class="references"> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text">The resistivity of copper is about <span class="nowrap"><span data-sort-value="6992170000000000000♠"></span>1.7<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−8</sup> Ω⋅m</span>.<sup id="cite_ref-Cutnell_4-0" class="reference"><a href="#cite_note-Cutnell-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup></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">For a fresh Energizer E91 AA alkaline battery, the internal resistance varies from <span class="nowrap"><span data-sort-value="6999900000000000000♠"></span>0.9 Ω</span> at <span class="nowrap"><span data-sort-value="7002233149999999999♠"></span>−40 °C</span>, to <span class="nowrap"><span data-sort-value="6999100000000000000♠"></span>0.1 Ω</span> at <span class="nowrap"><span data-sort-value="7002313150000000000♠"></span>+40 °C</span>.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text">A <span class="nowrap"><span data-sort-value="7001600000000000000♠"></span>60 W</span> light bulb (in the USA, with <span class="nowrap"><span data-sort-value="7002120000000000000♠"></span>120 V</span> <a href="/wiki/Mains_electricity" title="Mains electricity">mains electricity</a>) draws RMS current <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035" /><span class="sfrac">⁠<span class="tion"><span class="num"><span class="nowrap"><span data-sort-value="7001600000000000000♠"></span>60 W</span></span><span class="sr-only">/</span><span class="den"><span class="nowrap"><span data-sort-value="7002120000000000000♠"></span>120 V</span></span></span>⁠</span> = <span class="nowrap"><span data-sort-value="6999500000000000000♠"></span>500 mA</span>, so its resistance is <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035" /><span class="sfrac">⁠<span class="tion"><span class="num"><span class="nowrap"><span data-sort-value="7002120000000000000♠"></span>120 V</span></span><span class="sr-only">/</span><span class="den"><span class="nowrap"><span data-sort-value="6999500000000000000♠"></span>500 mA</span></span></span>⁠</span> = <span class="nowrap"><span data-sort-value="7002240000000000000♠"></span>240 Ω</span>. The resistance of a <span class="nowrap"><span data-sort-value="7001600000000000000♠"></span>60 W</span> light bulb in Europe (<span class="nowrap"><span data-sort-value="7002230000000000000♠"></span>230 V</span> mains) is <span class="nowrap"><span data-sort-value="7002900000000000000♠"></span>900 Ω</span>. The resistance of a filament is temperature-dependent; these values are for when the filament is already heated up and the light is already glowing.</span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><span class="nowrap"><span data-sort-value="7002100000000000000♠"></span>100 kΩ</span> for dry skin contact, <span class="nowrap"><span data-sort-value="7000100000000000000♠"></span>1 kΩ</span> for wet or broken skin contact. High voltage breaks down the skin, lowering resistance to <span class="nowrap"><span data-sort-value="7002500000000000000♠"></span>500 Ω</span>. Other factors and conditions are relevant as well. For more details, see the <a href="/wiki/Electric_shock" class="mw-redirect" title="Electric shock">electric shock</a> article, and NIOSH 98-131.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text">See <a href="/wiki/Electrical_resistivity_and_conductivity" title="Electrical resistivity and conductivity">Electrical resistivity and conductivity</a> for a table. The temperature coefficient of resistivity is similar but not identical to the temperature coefficient of resistance. The small difference is due to <a href="/wiki/Thermal_expansion" title="Thermal expansion">thermal expansion</a> changing the dimensions of the resistor.</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_resistance_and_conductance&action=edit&section=19" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626" /><div class="reflist reflist-columns references-column-width" style="column-width: 25em;"> <ol class="references"> <li id="cite_note-brown-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-brown_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-brown_1-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFBrown2006" class="citation book cs1">Brown, Forbes T. (2006). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=UzqX4j9VZWcC"><i>Engineering System Dynamics: A Unified Graph-Centered Approach</i></a> (2nd ed.). Boca Raton, Florida: CRC Press. p. 43. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8493-9648-9" title="Special:BookSources/978-0-8493-9648-9"><bdi>978-0-8493-9648-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Engineering+System+Dynamics%3A+A+Unified+Graph-Centered+Approach&rft.place=Boca+Raton%2C+Florida&rft.pages=43&rft.edition=2nd&rft.pub=CRC+Press&rft.date=2006&rft.isbn=978-0-8493-9648-9&rft.aulast=Brown&rft.aufirst=Forbes+T.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DUzqX4j9VZWcC&rfr_id=info%3Asid%2Fen.wikipedia.org%3AElectrical+resistance+and+conductance" class="Z3988"></span></span> </li> <li id="cite_note-kaiser-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-kaiser_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-kaiser_2-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFKaiser2004" class="citation book cs1">Kaiser, Kenneth L. (2004). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=nZzOAsroBIEC"><i>Electromagnetic Compatibility Handbook</i></a>. Boca Raton, Florida: CRC Press. pp. <span class="nowrap">13–</span>52. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8493-2087-3" title="Special:BookSources/978-0-8493-2087-3"><bdi>978-0-8493-2087-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Electromagnetic+Compatibility+Handbook&rft.place=Boca+Raton%2C+Florida&rft.pages=%3Cspan+class%3D%22nowrap%22%3E13-%3C%2Fspan%3E52&rft.pub=CRC+Press&rft.date=2004&rft.isbn=978-0-8493-2087-3&rft.aulast=Kaiser&rft.aufirst=Kenneth+L.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DnZzOAsroBIEC&rfr_id=info%3Asid%2Fen.wikipedia.org%3AElectrical+resistance+and+conductance" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFFinkBeaty1923" class="citation journal cs1">Fink & Beaty (1923). "Standard Handbook for Electrical Engineers". <i>Nature</i>. <b>111</b> (2788) (11th ed.): <span class="nowrap">17–</span>19. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1923Natur.111..458R">1923Natur.111..458R</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2F111458a0">10.1038/111458a0</a>. <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://hdl.handle.net/2027%2Fmdp.39015065357108">2027/mdp.39015065357108</a></span>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:26358546">26358546</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature&rft.atitle=Standard+Handbook+for+Electrical+Engineers&rft.volume=111&rft.issue=2788&rft.pages=%3Cspan+class%3D%22nowrap%22%3E17-%3C%2Fspan%3E19&rft.date=1923&rft_id=info%3Ahdl%2F2027%2Fmdp.39015065357108&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A26358546%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1038%2F111458a0&rft_id=info%3Abibcode%2F1923Natur.111..458R&rft.au=Fink&rft.au=Beaty&rfr_id=info%3Asid%2Fen.wikipedia.org%3AElectrical+resistance+and+conductance" class="Z3988"></span></span> </li> <li id="cite_note-Cutnell-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-Cutnell_4-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFCutnellJohnson1992" class="citation book cs1">Cutnell, John D.; <a href="/wiki/Kenneth_Alan_Johnson" title="Kenneth Alan Johnson">Johnson, Kenneth W.</a> (1992). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/physics00cutn/mode/2up?"><i>Physics</i></a></span> (2nd ed.). New York: Wiley. p. 559. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-52919-4" title="Special:BookSources/978-0-471-52919-4"><bdi>978-0-471-52919-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Physics&rft.place=New+York&rft.pages=559&rft.edition=2nd&rft.pub=Wiley&rft.date=1992&rft.isbn=978-0-471-52919-4&rft.aulast=Cutnell&rft.aufirst=John+D.&rft.au=Johnson%2C+Kenneth+W.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fphysics00cutn%2Fmode%2F2up%3F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AElectrical+resistance+and+conductance" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFMcDonald2016" class="citation book cs1">McDonald, John D. 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"Stress-dependent electrical transport and its universal scaling in granular materials". <i>Extreme Mechanics Letters</i>. <b>22</b>: <span class="nowrap">83–</span>88. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1712.05938">1712.05938</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2018ExML...22...83Z">2018ExML...22...83Z</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.eml.2018.05.005">10.1016/j.eml.2018.05.005</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:51912472">51912472</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Extreme+Mechanics+Letters&rft.atitle=Stress-dependent+electrical+transport+and+its+universal+scaling+in+granular+materials&rft.volume=22&rft.pages=%3Cspan+class%3D%22nowrap%22%3E83-%3C%2Fspan%3E88&rft.date=2018&rft_id=info%3Aarxiv%2F1712.05938&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A51912472%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1016%2Fj.eml.2018.05.005&rft_id=info%3Abibcode%2F2018ExML...22...83Z&rft.aulast=Zhai&rft.aufirst=Chongpu&rft.au=Gan%2C+Yixiang&rft.au=Hanaor%2C+Dorian&rft.au=Proust%2C+Gw%C3%A9na%C3%ABlle&rfr_id=info%3Asid%2Fen.wikipedia.org%3AElectrical+resistance+and+conductance" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFWard1971" class="citation book cs1">Ward, M.R. 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(2022), "Characterization of the deformation state of magnesium by electrical resistance", <i>Volume 215</i>, Scripta Materialia, vol. 215, p. 114712, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.scriptamat.2022.114712">10.1016/j.scriptamat.2022.114712</a></span>, <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:247959452">247959452</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Characterization+of+the+deformation+state+of+magnesium+by+electrical+resistance&rft.btitle=Volume+215&rft.series=Scripta+Materialia&rft.pages=114712&rft.date=2022&rft_id=info%3Adoi%2F10.1016%2Fj.scriptamat.2022.114712&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A247959452%23id-name%3DS2CID&rft.aulast=Meyer&rft.aufirst=Sebastian&rfr_id=info%3Asid%2Fen.wikipedia.org%3AElectrical+resistance+and+conductance" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Electrical_resistance_and_conductance&action=edit&section=20" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Commons-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Electrical_resistance_and_conductance" class="extiw" title="commons:Category:Electrical resistance and conductance">Electrical resistance and conductance</a></span>.</div></div> </div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20100711132344/http://www.cvel.clemson.edu/emc/calculators/Resistance_Calculator/index.html">"Resistance calculator"</a>. 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