{"id":2549,"date":"2024-08-24T09:00:30","date_gmt":"2024-08-24T09:00:30","guid":{"rendered":"https:\/\/workhouse.sweetdishy.com\/?p=2549"},"modified":"2024-08-24T09:00:31","modified_gmt":"2024-08-24T09:00:31","slug":"source-transformation-conversion-of-voltage-source-to-current-source-and-vice-versa","status":"publish","type":"post","link":"https:\/\/workhouse.sweetdishy.com\/index.php\/2024\/08\/24\/source-transformation-conversion-of-voltage-source-to-current-source-and-vice-versa\/","title":{"rendered":"\u00a0\u00a0SOURCE TRANSFORMATION (CONVERSION OF VOLTAGE SOURCE TO CURRENT SOURCE AND VICE VERSA)"},"content":{"rendered":"\n

In fact, a voltage source can be converted into current source and vice versa. Consider a DC source connected to a load resistance\u00a0R<\/em>L<\/sub>, as shown in\u00a0Figure 2.13(a). The source can be treated as a voltage source, as shown in\u00a0Figure 2.13(b), or as a current source as shown in\u00a0Figure 2.13(c).\u00a0Both types of representations appear the same to the externally connected load resistance\u00a0R<\/em>L<\/sub>. They must give the same results.<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Fig. 2.13<\/strong>  (a) Load connected to source (b) Voltage source and (c) Current source<\/p>\n\n\n\n

The source is treated as voltage source as shown in\u00a0Figure 2.13(b). If the load resistance\u00a0R<\/em>L<\/sub>\u00a0is reduced to zero as shown in\u00a0Figure 2.14(a), (i.e., the terminal A and B are short circuited), the current supplied by the source is<\/p>\n\n\n\n

I<\/em>L<\/sub> (short circuit) = \"image\"<\/p>\n\n\n\n

The source is treated as a current source, as shown in\u00a0Figure 2.13(c). If the load resistance\u00a0R<\/em>L<\/sub>\u00a0is reduced to zero (the same resistance\u00a0R<\/em>i2<\/sub>\u00a0connected in parallel with the short circuit is as good as not being present), as shown in\u00a0Figure 2.14(b). However, the current obtained by shorting the terminals A and B simply source current\u00a0I<\/em>S<\/sub>. This current must be the same as supplied by the source when it is treated as voltage source.<\/p>\n\n\n\n

I<\/em>S<\/sub> = I<\/em>L<\/sub>(short circuit) = \"image\"<\/p>\n\n\n\n

E<\/em> = I<\/em>S<\/sub>R<\/em>i1<\/sub>        (2.1)<\/p>\n\n\n\n

Again, the two representations of the source must give same terminal voltage when the load resistance R<\/em>L<\/sub> is disconnected from the source (i.e., when the terminals A and B are open circuited).<\/p>\n\n\n\n

When the source is treated as voltage source (as shown in\u00a0Fig. 2.14(c)), the terminal voltage,<\/p>\n\n\n\n

 <\/p>\n\n\n\n

V <\/em>= E<\/em><\/p>\n\n\n\n

When the source is treated as a current source (as shown in\u00a0Fig. 2.14(d)), the terminal voltage,<\/p>\n\n\n\n

 <\/p>\n\n\n\n

V <\/em>= I<\/em>S<\/sub>R<\/em>i<\/sub>2<\/sub> = E <\/em>        (2.2)<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Fig. 2.14<\/strong>  (a) Voltage source on short-circuit (b) Current source on short-circuit (c) Voltage source on open-circuit and (d) Current source on open-circuit<\/p>\n\n\n\n

From\u00a0Equation (2.1)\u00a0and\u00a0(2.2), we get<\/p>\n\n\n\n

 <\/p>\n\n\n\n

I<\/em>S<\/sub>R<\/em>i<\/sub>1<\/sub> = I<\/em>S<\/sub>R<\/em>i<\/sub>2<\/sub><\/p>\n\n\n\n

 <\/p>\n\n\n\n

R<\/em>i<\/sub>1<\/sub> = R<\/em>i<\/sub>2<\/sub> = R<\/em>i<\/sub> (say)<\/p>\n\n\n\n

Both\u00a0Equation (2.1)\u00a0and\u00a0(2.2)\u00a0reduce to<\/p>\n\n\n\n

 <\/p>\n\n\n\n

E <\/em>= I<\/em>S<\/sub>R<\/em>i<\/sub>        (2.3)<\/p>\n\n\n\n

Hence, it is seen that in both the representations of the source, the source impedance as faced by the load resistance at the terminal AB is the same (i.e., R<\/em>i<\/sub>). Thus, it establishes the equivalence between the voltage source representation and the current source representation under short circuit and open circuit conditions.<\/p>\n\n\n\n

We can also test the equivalence at a given load resistance\u00a0R<\/em>L<\/sub>. In the case of voltage source representation, as shown in\u00a0Figure 2.14(b), the current through the load resistance<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

In the case of current source representation, as shown in\u00a0Figure 2.14(c), the current\u00a0I<\/em>S<\/sub>\u00a0is divided into two branches. Current through the load resistance,<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

The two currents\u00a0I<\/em>1<\/sub>\u00a0and\u00a0I<\/em>2<\/sub>\u00a0are exactly the same. Thus, we conclude that a given voltage source can be converted into its equivalent current source and vice versa by using\u00a0Equation (2.3).<\/p>\n\n\n\n

Example 2.1<\/strong><\/p>\n\n\n\n

Figure 2.15\u00a0shows a DC voltage source having an open-circuit voltage of 6 V and an internal resistance of 1\u03a9. Obtain its equivalent current source representation.<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Fig. 2.15<\/strong>  Voltage source<\/p>\n\n\n\n

Solution:<\/em><\/p>\n\n\n\n

If the terminals A and B of voltage source are short circuited, the current supplied by the source,<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

In the equivalent current source representation, the current source is of 6 A. The internal resistance of the source is represented in parallel with the current source as shown in\u00a0Figure 2.16.<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Fig. 2.16<\/strong>  Equivalent current source<\/p>\n\n\n\n

Example 2.2<\/strong><\/p>\n\n\n\n

Figure 2.17<\/a> shows a DC current source. Obtain its equivalent voltage source representation.<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Fig. 2.17<\/strong>  Current source<\/p>\n\n\n\n

Solution:<\/em><\/p>\n\n\n\n

The open-circuit voltage of the current source across the terminals A and B.<\/p>\n\n\n\n

 <\/p>\n\n\n\n

E <\/em>= I<\/em>S<\/sub>R<\/em>i<\/sub> = 2 \u00d7 100 = 200 V<\/p>\n\n\n\n

 <\/p>\n\n\n\n

This will be the generated emf or ideal voltage of the equivalent voltage source representation. The internal impedance (R<\/em>i<\/sub>\u00a0= 100 \u03a9) is connected in series with the ideal voltage source, as shown in\u00a0Figure 2.18.<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Fig. 2.18<\/strong>  Equivant voltage source<\/p>\n\n\n\n

This gives the equivalent voltage source representation of the given current source.<\/p>\n","protected":false},"excerpt":{"rendered":"

In fact, a voltage source can be converted into current source and vice versa. Consider a DC source connected to a load resistance\u00a0RL, as shown in\u00a0Figure 2.13(a). The source can be treated as a voltage source, as shown in\u00a0Figure 2.13(b), or as a current source as shown in\u00a0Figure 2.13(c).\u00a0Both types of representations appear the same […]<\/p>\n","protected":false},"author":1,"featured_media":2547,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[404],"tags":[],"class_list":["post-2549","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-dc-circuit-analysis-and-network-theorems"],"jetpack_featured_media_url":"https:\/\/workhouse.sweetdishy.com\/wp-content\/uploads\/2024\/08\/download-11.jpeg","_links":{"self":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2549","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=2549"}],"version-history":[{"count":1,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2549\/revisions"}],"predecessor-version":[{"id":2550,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2549\/revisions\/2550"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media\/2547"}],"wp:attachment":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media?parent=2549"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/categories?post=2549"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/tags?post=2549"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}