{"id":2646,"date":"2024-08-24T19:39:42","date_gmt":"2024-08-24T19:39:42","guid":{"rendered":"https:\/\/workhouse.sweetdishy.com\/?p=2646"},"modified":"2024-08-24T19:39:43","modified_gmt":"2024-08-24T19:39:43","slug":"co-efficient-of-coupling","status":"publish","type":"post","link":"https:\/\/workhouse.sweetdishy.com\/index.php\/2024\/08\/24\/co-efficient-of-coupling\/","title":{"rendered":"\u00a0CO-EFFICIENT OF COUPLING"},"content":{"rendered":"\n<p id=\"para-432\">When current flows through one coil, it produces flux (<em>f<\/em><sub>1<\/sub>). The whole of this flux may not be linking with the other coil coupled to it, as shown in\u00a0Figure 5.32. It may be reduced because of leakage flux f<em><sub>l<\/sub><\/em>\u00a0by a fraction\u00a0<em>k<\/em>\u00a0known as co-efficient of coupling.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332558311\/files\/images\/page241_1.png\" alt=\"image\"\/><\/figure>\n\n\n\n<p id=\"para-433\"><strong>Fig. 5.32&nbsp;&nbsp;<\/strong>Magnetic circuit for co-efficient of coupling<\/p>\n\n\n\n<p id=\"para-434\">Thus, the fraction of magnetic flux produced by the current in one coil that links with the other is known as co-efficient of coupling (<em>k<\/em>) between the two coils. If the flux produced by one coil completely links with the other, then the value of&nbsp;<em>k<\/em>&nbsp;is&nbsp;<em>1&nbsp;<\/em>and the coils are said to be magnetically tightly coupled. However, if the flux produced by one coil does not link at all with the other, then the value of&nbsp;<em>k<\/em>&nbsp;is zero and the coils are said to be magnetically isolated.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"h4-011\">5.22.1&nbsp;&nbsp;Mathematical Expression<\/h4>\n\n\n\n<p id=\"para-435\">Consider the magnetic circuit shown in\u00a0Figure 5.32. When current\u00a0<em>I<\/em><sub>1<\/sub>\u00a0flows through coil 1,<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332558311\/files\/images\/page241_2.png\" alt=\"image\"\/><\/figure>\n\n\n\n<p>(\u0398<em>\u0278<\/em><sub>12<\/sub>&nbsp;=&nbsp;<em>k\u0278<\/em><sub>1<\/sub>)<\/p>\n\n\n\n<p id=\"para-436\">Now, considering coil 2 carrying current&nbsp;<em>I<\/em><sub>2<\/sub>;<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332558311\/files\/images\/page241_3.png\" alt=\"image\"\/><\/figure>\n\n\n\n<p>(\u0398<em>\u0278<\/em><sub>21<\/sub>&nbsp;=&nbsp;<em>k\u0278<\/em><sub>2<\/sub>)<\/p>\n\n\n\n<p id=\"para-437\">Multiplying\u00a0Equations (5.3)\u00a0and\u00a0(5.4), we get<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332558311\/files\/images\/page241_4.png\" alt=\"image\"\/><\/figure>\n\n\n\n<p id=\"para-438\">or<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332558311\/files\/images\/page241_5.png\" alt=\"image\"\/><\/figure>\n\n\n\n<p id=\"para-439\">or<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332558311\/files\/images\/page241_6.png\" alt=\"image\"\/><\/figure>\n\n\n\n<p id=\"para-440\">The abovementioned expression gives a relation between mutual inductance between the two coils and their respective self-inductances.<\/p>\n\n\n\n<p id=\"para-441\">Expression (5.5)\u00a0can also be written as<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332558311\/files\/images\/page241_7.png\" alt=\"image\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>When current flows through one coil, it produces flux (f1). The whole of this flux may not be linking with the other coil coupled to it, as shown in\u00a0Figure 5.32. It may be reduced because of leakage flux fl\u00a0by a fraction\u00a0k\u00a0known as co-efficient of coupling. Fig. 5.32&nbsp;&nbsp;Magnetic circuit for co-efficient of coupling Thus, the fraction [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":2473,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[407],"tags":[],"class_list":["post-2646","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-magnetic-circuits"],"jetpack_featured_media_url":"https:\/\/workhouse.sweetdishy.com\/wp-content\/uploads\/2024\/08\/magnet_1653038.png","_links":{"self":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2646","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/comments?post=2646"}],"version-history":[{"count":1,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2646\/revisions"}],"predecessor-version":[{"id":2647,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2646\/revisions\/2647"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media\/2473"}],"wp:attachment":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media?parent=2646"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/categories?post=2646"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/tags?post=2646"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}