{"id":2735,"date":"2024-08-25T11:06:07","date_gmt":"2024-08-25T11:06:07","guid":{"rendered":"https:\/\/workhouse.sweetdishy.com\/?p=2735"},"modified":"2024-08-25T11:06:08","modified_gmt":"2024-08-25T11:06:08","slug":"ac-circuit-containing-pure-inductance-only","status":"publish","type":"post","link":"https:\/\/workhouse.sweetdishy.com\/index.php\/2024\/08\/25\/ac-circuit-containing-pure-inductance-only\/","title":{"rendered":"AC CIRCUIT CONTAINING PURE INDUCTANCE ONLY"},"content":{"rendered":"\n

The circuit containing a pure inductance of\u00a0L<\/em>\u00a0Henry is shown in\u00a0Figure 7.3.<\/p>\n\n\n\n

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

Fig. 7.3  <\/strong>Circuit containing pure inductance only<\/p>\n\n\n\n

Let the alternating voltage applied across the circuit be given by the equation;<\/p>\n\n\n\n

 <\/p>\n\n\n\n

\u03bd<\/em> = V<\/em>m<\/sub> sin \u03c9<\/em> t        <\/em>(7.4)<\/p>\n\n\n\n

As a result, an AC i<\/em> flows through the inductance that induces an emf in it, given by the relation;<\/p>\n\n\n\n

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

This induced emf is equal and opposite to the applied voltage.<\/p>\n\n\n\n

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

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

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

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

Integrating both sides<\/p>\n\n\n\n

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

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

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

where X<\/em>L<\/sub> = \u03c9<\/em> L<\/em> is the opposition offered to the flow of AC by a pure inductance and it is called inductive reactance.<\/p>\n\n\n\n

The value of current will be maximum when sin (\u03c9<\/em> t<\/em> \u2212 \u03c0<\/em>\/2) = 1; i.e., \"image\"<\/p>\n\n\n\n

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

 <\/p>\n\n\n\n

i<\/em> = I<\/em>m<\/sub> sin (\u03c9<\/em> t<\/em> \u2212 \u03c0<\/em>\/2)        (7.5)<\/p>\n\n\n\n

<\/a>7.3.1  Phase Angle<\/h4>\n\n\n\n

From Equations (7.4)<\/a> and (7.5)<\/a>, it is clear that current flowing through a pure inductive circuit lags behind the applied voltage \u03bd<\/em> by 90\u00b0. The phasor diagram is shown in Figure 7.4(a)<\/a> and 7.4(b)<\/a>, respectively.<\/p>\n\n\n\n

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

Fig. 7.4  <\/strong>(a) Phasor diagram (b) Wave diagram for voltage, current and power<\/p>\n\n\n\n

Hence, in an AC circuit containing pure inductance, current lags behind the voltage by 90\u00b0.<\/p>\n\n\n\n

7.3.2  Power<\/h4>\n\n\n\n

Instantaneous power, p<\/em> = vi<\/em> = V<\/em>m<\/sub> sin \u03c9<\/em> t<\/em> \u00d7 I<\/em>m<\/sub> sin (\u03c9<\/em> t<\/em> \u2212 \u03c0<\/em>\/2)<\/p>\n\n\n\n

= V<\/em>m<\/sub>I<\/em>m<\/sub> sin\u03c9<\/em>t cos\u03c9<\/em>t \"image\"<\/p>\n\n\n\n

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

Average power consumed in the circuit over a complete cycle,<\/p>\n\n\n\n

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

Hence, average power consumed in a pure inductive circuit is zero.<\/p>\n\n\n\n

7.3.3  Power Curve<\/h4>\n\n\n\n

The power curve for a pure inductive circuit is shown in\u00a0Figure 7.4(b). It is very clear that average power in a half cycle (one alternation) is zero, as the negative and positive loop area under the power curve is the same.<\/p>\n\n\n\n

It is interesting to note that during the first quarter cycle, whatever power (or energy) is supplied by the source to the inductance (or coil) is stored in the magnetic field set\u2212up around it. However, in the next quarter cycle, the magnetic field collapses and the power (or energy) stored in the field is returned to the source. This process is repeated in each and every alternation. Hence, no power or energy is consumed in this circuit.<\/p>\n","protected":false},"excerpt":{"rendered":"

The circuit containing a pure inductance of\u00a0L\u00a0Henry is shown in\u00a0Figure 7.3. Fig. 7.3  Circuit containing pure inductance only Let the alternating voltage applied across the circuit be given by the equation;   \u03bd = Vm sin \u03c9 t        (7.4) As a result, an AC i flows through the inductance that induces an emf in it, given by the relation; This induced emf is equal […]<\/p>\n","protected":false},"author":1,"featured_media":2481,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[410],"tags":[],"class_list":["post-2735","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-single-phase-ac-circuits"],"jetpack_featured_media_url":"https:\/\/workhouse.sweetdishy.com\/wp-content\/uploads\/2024\/08\/singlephase-network-energy-meter-connection-260nw-2444369485.jpg","_links":{"self":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2735","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=2735"}],"version-history":[{"count":1,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2735\/revisions"}],"predecessor-version":[{"id":2736,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2735\/revisions\/2736"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media\/2481"}],"wp:attachment":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media?parent=2735"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/categories?post=2735"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/tags?post=2735"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}