{"id":2877,"date":"2024-08-25T20:06:49","date_gmt":"2024-08-25T20:06:49","guid":{"rendered":"https:\/\/workhouse.sweetdishy.com\/?p=2877"},"modified":"2024-08-25T20:06:49","modified_gmt":"2024-08-25T20:06:49","slug":"autotransformers","status":"publish","type":"post","link":"https:\/\/workhouse.sweetdishy.com\/index.php\/2024\/08\/25\/autotransformers\/","title":{"rendered":"AUTOTRANSFORMERS"},"content":{"rendered":"\n

A transformer, in which a part of the winding is common to both primary and secondary circuits, is called an autotransformer. In a two-winding transformers, primary and secondary windings are electrically isolated, but in an autotransformer, the two windings are not electrically isolated rather a section of the same winding acts as secondary or primary of the transformer.<\/p>\n\n\n\n

10.24.1  Construction<\/h4>\n\n\n\n

The core of an autotransformer may be rectangular (Figure 10.35(a)) or circular ring type (Figure 10.36(a)) in shape. A single winding is wound around one or two limbs of the rectangular core as shown in\u00a0Figure 10.35(b)\u00a0or it is wound over the ring as shown in\u00a0Figure 10.36(b). Terminal \u2018B\u2019 is taken as a common point from which one terminal for primary and one terminal of the secondary is taken out. The second terminal of the secondary is connected to point \u2018C\u2019 which may be fixed or movable as shown in\u00a0Figure 10.35(b)\u00a0and\u00a010.36(b). The number of turns between AB are taken as\u00a0N<\/em>1<\/sub>\u00a0and the number of turns between BC are taken as\u00a0N<\/em>2<\/sub>\u00a0as shown in\u00a0Figure 10.35(c)\u00a0and\u00a010.36(c). Thus, one section of the same winding acts as a primary\u00a0and the other section of the same winding acts as a secondary. When the number of secondary turns\u00a0N<\/em>2<\/sub>\u00a0is less than the primary turns\u00a0N<\/em>1<\/sub>\u00a0(i.e.,\u00a0N<\/em>2<\/sub>\u00a0<\u00a0N<\/em>1<\/sub>) as shown in\u00a0Figure 10.35(c)\u00a0and\u00a010.36(c), the autotransformer works as step-down transformer, whereas it works as a step-up transformer if number of secondary turns\u00a0N<\/em>2<\/sub>\u00a0is more than primary turns\u00a0N<\/em>1<\/sub>\u00a0as shown in\u00a0Figure 10.35(d)\u00a0and\u00a010.36(d).<\/p>\n\n\n\n

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

Fig. 10.35<\/strong>  (a) Rectangular core of an auto-transformer (b) Single winding placed on the core (c) Electric circuit for step-down auto-transformer (d) Electric circuit for step-up auto-transformer (e) Electric circuit of an auto-transformer<\/p>\n\n\n\n

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

Fig. 10.36<\/strong>  (a) Circular core of an auto-transformer (b) Single winding placed on the core (c) electric circuit for step-down auto-transformer (d) Electric circuit for step-up auto-transformer (e) & (f) Pictorial view of an auto-transformer (or variac)<\/p>\n\n\n\n

The pictorial view of a single-phase autotransformer used in laboratories is shown in\u00a0Figure 10.36(e\u00a0&\u00a0f<\/a>). Here, point C is attached to a movable arm which carries a carbon brush. The brush moves over number of turns wound over a circular laminated core and its position determines the output voltage.<\/p>\n\n\n\n

10.24.2  Working<\/h4>\n\n\n\n

When AC voltage V<\/em>1<\/sub> is applied to winding AB, an exciting current starts flowing through the full winding AB if the internal impedance drop is neglected, then the voltage per turn in winding AB is V<\/em>1<\/sub>\/N<\/em>1<\/sub> and, therefore, the voltage across BC is (V<\/em>1<\/sub>\/N<\/em>1<\/sub>)N<\/em>2<\/sub>.<\/p>\n\n\n\n

<\/a>When switch S is closed, as shown in Fig. 10.37(a)<\/a>, a current I<\/em>2<\/sub> starts flowing through the load and current I<\/em>1<\/sub> is drawn from the source [see Fig. 10.37(b)<\/a>]. Neglecting losses,<\/p>\n\n\n\n

 <\/p>\n\n\n\n

Input power = Output power<\/p>\n\n\n\n

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

 <\/p>\n\n\n\n

V<\/em>1<\/sub>I<\/em>1<\/sub>cos \u0278<\/em>1<\/sub> = V<\/em>2<\/sub>I<\/em>2<\/sub>cos \u0278<\/em>2<\/sub><\/p>\n\n\n\n

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

Fig. 10.37<\/strong>  (a) Winding of an auto-transformer placed around a limit of the core (b) Electric circuit of an auto-transformer<\/p>\n\n\n\n

If internal (or leakage) impedance drops and losses are neglected, then<\/p>\n\n\n\n

 <\/p>\n\n\n\n

cos \u0278<\/em>1 <\/sub>= cos \u0278<\/em>2<\/sub><\/p>\n\n\n\n

Hence<\/p>\n\n\n\n

 <\/p>\n\n\n\n

V<\/em>1<\/sub>I<\/em>1 <\/sub>= V<\/em>2<\/sub>I<\/em>2<\/sub><\/p>\n\n\n\n

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

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

Here, K <\/em>is less than unity. The expression is identical to a two-winding transformer.<\/p>\n\n\n\n

Let at any instant, the exciting current flows from A <\/em>to B <\/em>and it establishes a working mmf directed vertically upward in the core. When switch S is closed, the current in winding BC must flow from B to C, in order to create an mmf opposing the exciting or working mmf, as per Lenz\u2019s law. Since the working mmf in a transformer remains constant at its no-load value, the primary must draw additional current I<\/em>1 <\/sub>from the source, in order to neutralise the effect of current I<\/em>BC<\/sub>. In winding AB, I<\/em>1 <\/sub>flows from A to B while in winding BC, I<\/em>2 <\/sub>flows from B to C. Therefore, the current in winding BC is I<\/em>1 <\/sub>from C to B and I<\/em>2<\/sub> from B to C. Here, the current I<\/em>2 <\/sub>is greater than I<\/em>1 <\/sub>(because V<\/em>2<\/sub> < V<\/em>1<\/sub>) and their mmfs. are opposing each other at every instant, therefore,<\/p>\n\n\n\n

 <\/p>\n\n\n\n

I<\/em>BC<\/sub> = I<\/em>2<\/sub> \u2212 I<\/em>1<\/sub><\/p>\n\n\n\n

mmf of winding<\/p>\n\n\n\n

 <\/p>\n\n\n\n

AC = I<\/em>1<\/sub>(N<\/em>1<\/sub>\u2212 N<\/em>2<\/sub>) = I<\/em>1<\/sub>N<\/em>1<\/sub> \u2212 I<\/em>1<\/sub>N<\/em>2<\/sub><\/p>\n\n\n\n

= I<\/em>2<\/sub>N<\/em>2<\/sub> \u2212 I<\/em>1<\/sub>N<\/em>2<\/sub> = (I<\/em>2<\/sub> \u2212 I<\/em>1<\/sub>) N<\/em>2<\/sub> [\u2234 I<\/em>1<\/sub>N<\/em>1 <\/sub>= I<\/em>2<\/sub>N<\/em>2<\/sub>]<\/p>\n\n\n\n

= mmf of winding CB.<\/p>\n\n\n\n

It is, therefore, seen that the transformer action takes place between winding, section AC and winding section BC. In other words, the volt-amperes across winding AC are transferred by transformer action to the load connected across winding BC.<\/p>\n\n\n\n

\u2234 Power transformed in VA = V<\/em>AC<\/sub>I<\/em>AC<\/sub> = (V<\/em>1<\/sub> \u2212 V<\/em>2<\/sub>) I<\/em>1<\/sub><\/p>\n\n\n\n

Total power to be transferred or input power in VA = V<\/em>1<\/sub>I<\/em>1<\/sub><\/p>\n\n\n\n

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

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

Power transformed <\/em>= (<\/em>1 \u2212 K) <\/em>\u00d7 power input<\/em><\/p>\n\n\n\n

Out of the input volt-amperes V<\/em>1<\/sub>I<\/em>1<\/sub>, only V<\/em>AC<\/sub>I<\/em>AC<\/sub> = (V<\/em>1 <\/sub>\u2212 V<\/em>2<\/sub>) I<\/em>1 <\/sub>is transformed to the output by transformer action. The remaining power in volt-ampere required for the output, are conducted directly to the secondary from the primary (due to electrical connection).<\/p>\n\n\n\n

\u2234 Power conducted in VA = Total power input in VA \u2212 transformed power in VA<\/p>\n\n\n\n

 <\/p>\n\n\n\n

= V<\/em>1<\/sub>I<\/em>1 <\/sub>\u2212 (V<\/em>1 <\/sub>\u2212 V<\/em>2<\/sub>) I<\/em>1 <\/sub>= V<\/em>2<\/sub>I<\/em>1<\/sub><\/p>\n\n\n\n

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

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

Power conducted <\/em>= K <\/em>\u00d7 power input<\/em><\/p>\n\n\n\n

Hence,<\/p>\n\n\n\n

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

And<\/p>\n\n\n\n

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

Considering eqn. (10.12),<\/p>\n\n\n\n

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

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

\"img\"\/<\/figure>\n\n\n\n
10.25  AUTOTRANSFORMER V\/S POTENTIAL DIVIDER<\/h5>\n\n\n\n

At first sight, an autotransformer appears to be similar to a resistance potential divider. But this is not so, as described below.<\/p>\n\n\n\n

    \n
  1. A resistive potential divider cannot step up the voltage, whereas it is possible in an autotransformer.<\/li>\n\n\n\n
  2. The potential divider has more losses and is, therefore, less efficient.<\/li>\n\n\n\n
  3. <\/a>In a potential divider, almost entire power to load flows by conduction, whereas in auto-transformer, a part of the power is conducted and the rest is transferred to load by transformer action.<\/li>\n\n\n\n
  4. In a potential divider, the input current, must always be more than the output current, this is not so in an autotransformer. If the output voltage in autotransformer is less than the input voltage, the load current is more than the input current.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

    A transformer, in which a part of the winding is common to both primary and secondary circuits, is called an autotransformer. In a two-winding transformers, primary and secondary windings are electrically isolated, but in an autotransformer, the two windings are not electrically isolated rather a section of the same winding acts as secondary or primary […]<\/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-2877","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\/2877","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=2877"}],"version-history":[{"count":1,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2877\/revisions"}],"predecessor-version":[{"id":2878,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2877\/revisions\/2878"}],"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=2877"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/categories?post=2877"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/tags?post=2877"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}

<\/a>= I<\/em>BC<\/sub>N<\/em>2<\/sub><\/p>\n\n\n\n