{"id":4688,"date":"2025-04-18T12:04:10","date_gmt":"2025-04-18T06:34:10","guid":{"rendered":"https:\/\/study.madeeasy.in\/?p=4688"},"modified":"2025-07-22T14:58:28","modified_gmt":"2025-07-22T09:28:28","slug":"series-and-parallel-connection-of-coupled-coils","status":"publish","type":"post","link":"https:\/\/www.madeeasy.in\/study\/ee\/types-of-laws\/series-and-parallel-connection-of-coupled-coils","title":{"rendered":"Series and Parallel Connection of Coupled Coils"},"content":{"rendered":"<h2>Series and Parallel Connection of Coupled Coils<\/h2>\n<p style=\"text-align: justify;\">There are four possible ways of connecting coils in series and parallel. We will analyze each case one by one.<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_79_1 ez-toc-wrap-left counter-hierarchy ez-toc-counter ez-toc-light-blue ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.madeeasy.in\/study\/ee\/types-of-laws\/series-and-parallel-connection-of-coupled-coils\/#Case-I-Series-Aiding-Connection\" >Case-I : Series Aiding Connection<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.madeeasy.in\/study\/ee\/types-of-laws\/series-and-parallel-connection-of-coupled-coils\/#Case-II-Series-Opposing-Connection\" >Case-II : Series Opposing Connection<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.madeeasy.in\/study\/ee\/types-of-laws\/series-and-parallel-connection-of-coupled-coils\/#Case-III-Parallel-Connection-of-Coupled-Coils\" >Case-III : Parallel Connection of Coupled Coils<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.madeeasy.in\/study\/ee\/types-of-laws\/series-and-parallel-connection-of-coupled-coils\/#Case-IV-Parallel-Connection-of-Coupled-Coils\" >Case-IV : Parallel Connection of Coupled Coils<\/a><\/li><\/ul><\/nav><\/div>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Case-I-Series-Aiding-Connection\"><\/span>Case-I : Series Aiding Connection<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">Figure (a) shows the series connection of two coupled inductors with self inductance L1, L2 and mutual inductance M. The currents in both inductors at any instant of time are in same direction relative to the like terminals. This is called series aiding connection. To find out total inductance in this case, consider the circuit given in the figure (b). Writing KVL in the loop, by taking mutual <a href=\"https:\/\/study.madeeasy.in\/ec\/analog-circuits\/voltage-follower\/\" target=\"_blank\" rel=\"noopener\">voltage<\/a> into account.<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-4689 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2025\/04\/series-aiding-connection.jpg\" alt=\"Series Aiding Connection\" width=\"504\" height=\"362\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2025\/04\/series-aiding-connection.jpg 504w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2025\/04\/series-aiding-connection-300x215.jpg 300w\" sizes=\"auto, (max-width: 504px) 100vw, 504px\" \/><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Case-II-Series-Opposing-Connection\"><\/span>Case-II : Series Opposing Connection<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">Figure (c) given below shows the series connection of two coupled inductors with self inductance L1, L2 and <a href=\"https:\/\/study.madeeasy.in\/ee\/lti-systems\/mutual-inductance\/\" target=\"_blank\" rel=\"noopener\">mutual inductance<\/a> M. The currents in both inductors at any instant of time are in opposite direction relative to the like terminals. This is called series opposing connection. To find out a total inductance in this case, consider the circuit given in the figure (d). Writing KVL in the loop, by taking mutual voltage into account.<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-4690 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2025\/04\/Series-opposing-connection.jpg\" alt=\"Series opposing connection\" width=\"505\" height=\"355\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2025\/04\/Series-opposing-connection.jpg 505w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2025\/04\/Series-opposing-connection-300x211.jpg 300w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2025\/04\/Series-opposing-connection-130x90.jpg 130w\" sizes=\"auto, (max-width: 505px) 100vw, 505px\" \/><\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Case-III-Parallel-Connection-of-Coupled-Coils\"><\/span>Case-III : Parallel Connection of Coupled Coils<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">Figure shows the parallel connection of the coupled coils L1 and L2 having mutual inductance M. The equivalent inductance for the circuit shown below in figure (e) is<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-4691 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2025\/04\/coupled-coils.jpg\" alt=\"coupled coils\" width=\"230\" height=\"206\" \/><\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Case-IV-Parallel-Connection-of-Coupled-Coils\"><\/span>Case-IV : Parallel Connection of Coupled Coils<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">Figure (f) shows the parallel connection of the coupled coils L1 and L2 having mutual inductance M. The equivalent inductance for the <a href=\"https:\/\/study.madeeasy.in\/ee\/types-of-laws\/circuit-theorems\/\" target=\"_blank\" rel=\"noopener\">circuit<\/a> shown below in figure (f) is<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-4692 aligncenter\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2025\/04\/coupled-coils-.jpg\" alt=\"coupled coils \" width=\"216\" height=\"171\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Series and Parallel Connection of Coupled Coils There are four possible ways of connecting coils in series and parallel. We<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1362,5],"tags":[1403,1401,1402],"class_list":["post-4688","post","type-post","status-publish","format-standard","hentry","category-types-of-laws","category-ee","tag-parallel-connection-of-coupled-coils","tag-series-aiding-connection","tag-series-opposing-connection"],"_links":{"self":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/4688","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/comments?post=4688"}],"version-history":[{"count":0,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/4688\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/media?parent=4688"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/categories?post=4688"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/tags?post=4688"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}