{"id":2881,"date":"2024-08-25T20:08:55","date_gmt":"2024-08-25T20:08:55","guid":{"rendered":"https:\/\/workhouse.sweetdishy.com\/?p=2881"},"modified":"2024-08-25T20:08:55","modified_gmt":"2024-08-25T20:08:55","slug":"saving-of-copper-in-an-autotransformer","status":"publish","type":"post","link":"https:\/\/workhouse.sweetdishy.com\/index.php\/2024\/08\/25\/saving-of-copper-in-an-autotransformer\/","title":{"rendered":"\u00a0SAVING OF COPPER IN AN AUTOTRANSFORMER"},"content":{"rendered":"\n

Volume, and hence weight of copper (or aluminium), is proportional to the length and area of X<\/em>-section of the conductor. The length of conductor is proportional to number of turns, whereas area of X<\/em>-section is proportional to the current flowing through it. Hence, the weight of copper is proportional to the product of current and number of turns.<\/p>\n\n\n\n

Now, with reference to\u00a0Figure 10.38(a), weight of copper required in an autotransformer.<\/p>\n\n\n\n

 <\/p>\n\n\n\n

Wt<\/em>a <\/sub>= weight of Cu in section AC + weight of Cu in section CB<\/p>\n\n\n\n

\u2234<\/p>\n\n\n\n

 <\/p>\n\n\n\n

Wta<\/sub><\/em> \u221e I<\/em>1<\/sub> (N<\/em>1<\/sub> \u2212 N<\/em>2<\/sub>) + (I<\/em>2<\/sub> \u2212 I<\/em>1<\/sub>) N<\/em>2<\/sub> \u221e I<\/em>1<\/sub>N<\/em>1<\/sub> + I<\/em>2<\/sub>N<\/em>2<\/sub> \u2212 <\/em>2I<\/em>1<\/sub>N<\/em>2<\/sub><\/p>\n\n\n\n

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

Fig. 10.38<\/strong>  (a) Electric circuit of an auto-transformer (b) Equivalent circuit<\/p>\n\n\n\n

If an ordinary two-winding transformer is to perform the same duty, then with reference to\u00a0Figure 10.38(b). Total weight of copper required in the ordinary transformer.<\/p>\n\n\n\n

 <\/p>\n\n\n\n

Wt<\/em>0<\/sub> = weight of Cu on its primary + weight of Cu on its secondary.<\/p>\n\n\n\n

\u2234<\/p>\n\n\n\n

 <\/p>\n\n\n\n

Wt<\/em>0<\/sub> \u221e I<\/em>1<\/sub>N<\/em>1<\/sub>+I<\/em>2<\/sub>N<\/em>2<\/sub><\/p>\n\n\n\n

Now, the ratio of weight of copper in autotransformer to the weight of copper in an ordinary transformer,<\/p>\n\n\n\n

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

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

 <\/p>\n\n\n\n

Wt<\/em>a<\/sub> = (1 \u2013 K<\/em>) Wt<\/em>0<\/sub><\/p>\n\n\n\n

Saving of copper affected by using an autotransformer<\/p>\n\n\n\n

= wt. of cu required in an ordinary transformer \u2013 wt. of copper required in an autotransformer.<\/p>\n\n\n\n

= Wt<\/em>0<\/sub> \u2013 Wt<\/em>a<\/sub> = Wt<\/em>0<\/sub> \u2013 (1 \u2013 K<\/em>) Wt<\/em>0 <\/sub>= K <\/em>\u00d7 Wt<\/em>0<\/sub><\/p>\n\n\n\n

\u2234 Saving = K <\/em>\u00d7 Wt. of copper required for two-winding transformer<\/p>\n\n\n\n

Hence, saving in copper increases as the transformation ratio approaches to unity, therefore, autotransformers are used when K <\/em>in nearly equal to unity.<\/p>\n","protected":false},"excerpt":{"rendered":"

Volume, and hence weight of copper (or aluminium), is proportional to the length and area of X-section of the conductor. The length of conductor is proportional to number of turns, whereas area of X-section is proportional to the current flowing through it. Hence, the weight of copper is proportional to the product of current and number of […]<\/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-2881","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\/2881","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=2881"}],"version-history":[{"count":1,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2881\/revisions"}],"predecessor-version":[{"id":2882,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2881\/revisions\/2882"}],"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=2881"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/categories?post=2881"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/tags?post=2881"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}