{"id":2857,"date":"2024-08-25T19:42:35","date_gmt":"2024-08-25T19:42:35","guid":{"rendered":"https:\/\/workhouse.sweetdishy.com\/?p=2857"},"modified":"2024-08-25T19:42:36","modified_gmt":"2024-08-25T19:42:36","slug":"transformer-with-winding-resistance","status":"publish","type":"post","link":"https:\/\/workhouse.sweetdishy.com\/index.php\/2024\/08\/25\/transformer-with-winding-resistance\/","title":{"rendered":"TRANSFORMER WITH WINDING RESISTANCE"},"content":{"rendered":"\n

In an actual transformer, the primary and secondary windings have some resistance represented by\u00a0R<\/em>1\u00a0<\/sub>and\u00a0R<\/em>2<\/sub>, respectively. These resistances are shown external to the windings in\u00a0Figure 10.19. The resistance of the two windings can be transferred to either side in order to simplify the calculations. The resistance is transferred from one side to the other in such a manner that percentage voltage drop remains the same when represented on either side.<\/p>\n\n\n\n

Let the primary resistance\u00a0R<\/em>1\u00a0<\/sub>be transferred to the secondary side and the new value of this resistance be\u00a0\"img\"\u00a0called equivalent resistance of primary referred to secondary side as shown in\u00a0Figure 10.20(a).\u00a0I<\/em>1\u00a0<\/sub>and\u00a0I<\/em>2\u00a0<\/sub>be the full-load primary and secondary currents, respectively.<\/p>\n\n\n\n

\"img\"\/<\/figure>\n\n\n\n

Fig. 10.19<\/strong>  Transformer with its windings resistances<\/p>\n\n\n\n

Then,<\/p>\n\n\n\n

\"img\"\/<\/figure>\n\n\n\n

or<\/p>\n\n\n\n

\"img\"\/<\/figure>\n\n\n\n

\u2234 Total equivalent resistance referred to secondary.<\/p>\n\n\n\n

R<\/em>es<\/sub> = R<\/em>2<\/sub> + \"img\" = R<\/em>2<\/sub> + K<\/em>2<\/sup>R<\/em>1<\/sub><\/p>\n\n\n\n

Now consider resistance R2<\/sub>, when it is transferred to primary, let its new value be\u00a0\"img\"\u00a0called equivalent resistance of secondary referred to primary as shown in\u00a0Figure 10.20(c).<\/p>\n\n\n\n

Then,<\/p>\n\n\n\n

\"img\"\/<\/figure>\n\n\n\n

\u2234 Total equivalent resistance referred to primary,<\/p>\n\n\n\n

\"img\"\/<\/figure>\n\n\n\n
\"img\"\/<\/figure>\n\n\n\n

Fig. 10.20<\/strong>  (a) and (b) Equivalent resistance when referred to secondary side (c) and (d) Equivalent resistance when referred to primary side<\/p>\n\n\n\n

10.12  MUTUAL AND LEAKAGE FLUXES<\/h5>\n\n\n\n

So far, it is assumed that when AC supply is given to the primary winding of a transformer, an alternating flux is set up in the core and whole of this flux links with both primary and secondary windings. However, in an actual transformer, both the windings produce some flux that links only with the winding that produces it.<\/p>\n\n\n\n

The flux that links with both windings of the transformer is called mutual flux and the flux that links only with one winding of the transformer and not to the other is called leakage flux.<\/p>\n\n\n\n

The primary ampere turns produce some flux\u00a0\u0278<\/em>l1<\/sub>\u00a0which is set up in air and links only with primary winding as shown in\u00a0Figure 10.21(a), is called primary leakage flux.<\/em><\/p>\n\n\n\n

\"img\"\/<\/figure>\n\n\n\n

Fig. 10.21<\/strong>  (a) Representation of leakage flux on primary and secondary side (b) Representation of primary and secondary reactances<\/p>\n\n\n\n

Similarly, secondary ampere turns produce some flux \u0278<\/em>l<\/em>2<\/sub> which is set up in air and links only with secondary winding is called secondary leakage flux.<\/em><\/p>\n\n\n\n

The primary leakage flux\u00a0\u0278<\/em>l<\/em>1<\/sub>\u00a0is proportional to the primary current\u00a0I<\/em>1\u00a0<\/sub>and secondary leakage flux\u00a0\u0278<\/em>l<\/em>2<\/sub>\u00a0is proportional to secondary current\u00a0I<\/em>2<\/sub>. The primary leakage flux\u00a0\u0278<\/em>l<\/em>1<\/sub>\u00a0produces self-inductance\u00a0L<\/em>1<\/sub>(=\u00a0N<\/em>1<\/sub>\u0278<\/em>1<\/sub>\/\u00a0I<\/em>1<\/sub>) which in turn produces leakage reactance\u00a0X<\/em>1<\/sub>(=2\u03c0\u00a0fL<\/em>1<\/sub>). Similarly, secondary leakage flux\u00a0\u0278<\/em>l<\/em>2<\/sub>\u00a0produces leakage reactance\u00a0X<\/em>2<\/sub>(=2\u03c0\u00a0fL<\/em>2<\/sub>). The leakage reactance (inductive) has been shown external to the windings in\u00a0Figure 10.21(b).<\/p>\n","protected":false},"excerpt":{"rendered":"

In an actual transformer, the primary and secondary windings have some resistance represented by\u00a0R1\u00a0and\u00a0R2, respectively. These resistances are shown external to the windings in\u00a0Figure 10.19. The resistance of the two windings can be transferred to either side in order to simplify the calculations. The resistance is transferred from one side to the other in such […]<\/p>\n","protected":false},"author":1,"featured_media":2841,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[413],"tags":[],"class_list":["post-2857","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-single-phase-transformers"],"jetpack_featured_media_url":"https:\/\/workhouse.sweetdishy.com\/wp-content\/uploads\/2024\/08\/power-transformer.png","_links":{"self":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2857","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=2857"}],"version-history":[{"count":1,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2857\/revisions"}],"predecessor-version":[{"id":2858,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2857\/revisions\/2858"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media\/2841"}],"wp:attachment":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media?parent=2857"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/categories?post=2857"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/tags?post=2857"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}