{"id":1581,"date":"2024-07-12T19:20:32","date_gmt":"2024-07-12T13:50:32","guid":{"rendered":"https:\/\/study.madeeasy.in\/?p=1581"},"modified":"2025-07-16T15:06:22","modified_gmt":"2025-07-16T09:36:22","slug":"maximum-power-transfer","status":"publish","type":"post","link":"https:\/\/www.madeeasy.in\/study\/ec\/network-theory\/maximum-power-transfer","title":{"rendered":"Maximum Power Transfer"},"content":{"rendered":"<p style=\"text-align: justify;\">In many practical situations, a circuit is designed to provide power to a load. There are applications in areas such as communications where it is desirable to maximize the power delivered to a load. The Thevenin equivalent is useful in finding the maximum power a linear circuit can deliver to a load. We assume that we can\u00a0adjust the load resistance <em>R<sub>L<\/sub><\/em>. If the entire circuit is replaced by its Thevenin equivalent except for the load, as shown in figure, the power delivered to the load is<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1582 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/maximum-power-transfer.jpg\" alt=\"Maximum Power Transfer\" width=\"688\" height=\"366\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/maximum-power-transfer.jpg 688w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/maximum-power-transfer-300x160.jpg 300w\" sizes=\"auto, (max-width: 688px) 100vw, 688px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1584 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/power-transfer-.jpg\" alt=\"Power Transfer \" width=\"691\" height=\"140\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/power-transfer-.jpg 691w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/power-transfer--300x61.jpg 300w\" sizes=\"auto, (max-width: 691px) 100vw, 691px\" \/><\/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\/ec\/network-theory\/maximum-power-transfer\/#Superposition-Theorem\" >Superposition Theorem<\/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\/ec\/network-theory\/maximum-power-transfer\/#Compensation-Theorem\" >Compensation Theorem<\/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\/ec\/network-theory\/maximum-power-transfer\/#Consider-the-following-description\" >Consider the following description :\u00a0<\/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\/ec\/network-theory\/maximum-power-transfer\/#Tellegens-Theorem\" >Tellegen\u2019s Theorem<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.madeeasy.in\/study\/ec\/network-theory\/maximum-power-transfer\/#Note\" >Note:<\/a><\/li><\/ul><\/nav><\/div>\n<h3><span class=\"ez-toc-section\" id=\"Superposition-Theorem\"><\/span><strong>Superposition Theorem<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">It states that for a linear circuit containing two or more independent sources, any circuit voltage or current may be calculated as the algebraic sum of the individual currents or voltages caused by each independent source acting alone.<\/p>\n<p style=\"text-align: justify;\">Since ac circuits are linear, the superposition theorem applies to ac circuits the same way it applies to dc circuits. The theorem becomes important if the circuit has sources operating at different frequencies. In this case, since the impedances depend on frequency, we must have a different frequency domain circuit for each frequency. The total response must be obtained by adding the individual responses in the time domain. It is incorrect to try to add the responses in the phasor or frequency domain. So, when a circuit has sources operating at different frequencies, one must add the responses due to the individual frequencies in the time domain.<\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Compensation-Theorem\"><\/span><strong>Compensation Theorem<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">If we are interested in finding the corresponding changes in various voltages and currents of a network subjected to a change in one of its branches, then compensation theorem provides us a convenient method for determining such effects.<\/p>\n<p style=\"text-align: justify;\">In a linear time-invariant network when the impedance (Z) of an uncoupled branch, carrying a current (I), is changed by (\u2206Z), the currents in all the branches would change and can be obtained by assuming that an ideal voltage source of (V<sub>C<\/sub>) has been connected [such that V<sub>C<\/sub> = I (\u2206Z)] in series with (Z + \u2206Z) when all other sources in the network are replaced by their internal impedances.<\/p>\n<p>[The source voltage (V<sub>C<\/sub>) opposes the original current].<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Consider-the-following-description\"><\/span><strong>Consider the following description :\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1587 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/compensation-theorem.jpg\" alt=\"Compensation Theorem\" width=\"658\" height=\"530\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/compensation-theorem.jpg 658w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/compensation-theorem-300x242.jpg 300w\" sizes=\"auto, (max-width: 658px) 100vw, 658px\" \/><\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Tellegens-Theorem\"><\/span><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1589 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/same-value.jpg\" alt=\"Same Value\" width=\"660\" height=\"74\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/same-value.jpg 660w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/same-value-300x34.jpg 300w\" sizes=\"auto, (max-width: 660px) 100vw, 660px\" \/><strong>Tellegen\u2019s Theorem<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">Tellegen\u2019s theorem is remarkable and one of the most general theorems of circuit theory. The statement of theorem can be given as:<\/p>\n<ul>\n<li style=\"text-align: justify;\">For any given time, the sum of power delivered to each branch of any electric network is zero.<\/li>\n<li style=\"text-align: justify;\">The summation of instantaneous power or summation of complex power of sinusoidal sources in an electrical network is zero.<br \/>\nMathematically, for k<sup>th<\/sup> branch the theorem states that,<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1592 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/kirchhoff.png\" alt=\"Kirchhoff\u2019s laws\" width=\"648\" height=\"239\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/kirchhoff.png 648w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/kirchhoff-300x111.png 300w\" sizes=\"auto, (max-width: 648px) 100vw, 648px\" \/><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Note\"><\/span><strong>Note:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Tellegen\u2019s theorem is applicable for any network, i.e., linear, non-linear, bidirectional, unidirectional, time variant, time invariant.<\/p>\n<p style=\"text-align: center;\"><a class=\"btn btn-danger\" role=\"button\" href=\"https:\/\/study.madeeasy.in\/ec\/network-theory\/norton-theorem\/\" target=\"_blank\" rel=\"noopener\">&lt;&lt; Previous<\/a> | <a class=\"btn btn-success\" role=\"button\" href=\"https:\/\/study.madeeasy.in\/ec\/network-theory\/network-parameters\/\" target=\"_blank\" rel=\"noopener\"> Next &gt;&gt;<\/a><br \/>\n<strong> Must Read: <\/strong> <a href=\"https:\/\/study.madeeasy.in\/subjects\/what-is-network-theory\/\" target=\"_blank\" rel=\"noopener\"><strong>What is Network Theory?<\/strong><\/a><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In many practical situations, a circuit is designed to provide power to a load. There are applications in areas such<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[421,6],"tags":[447,445,446,448],"class_list":["post-1581","post","type-post","status-publish","format-standard","hentry","category-network-theory","category-ec","tag-compensation-theorem","tag-power-transfer","tag-superposition-theorem","tag-tellegens-theorem"],"_links":{"self":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/1581","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=1581"}],"version-history":[{"count":0,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/1581\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/media?parent=1581"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/categories?post=1581"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/tags?post=1581"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}