{"id":2741,"date":"2024-08-25T11:10:47","date_gmt":"2024-08-25T11:10:47","guid":{"rendered":"https:\/\/workhouse.sweetdishy.com\/?p=2741"},"modified":"2024-08-25T11:10:47","modified_gmt":"2024-08-25T11:10:47","slug":"r-l-series-circuit","status":"publish","type":"post","link":"https:\/\/workhouse.sweetdishy.com\/index.php\/2024\/08\/25\/r-l-series-circuit\/","title":{"rendered":"R\u2013L SERIES CIRCUIT"},"content":{"rendered":"\n

A circuit that contains a pure resistance R<\/em> \u03a9 connected in series with a coil having pure inductance of L<\/em> Henry is known as R\u2013L series circuit. This is the most general case that we come across in practice.<\/p>\n\n\n\n

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

Fig. 7.7<\/strong>  Circuit containing resistance and inductance in series<\/p>\n\n\n\n

An R\u2013L series circuit and its phasor diagram are shown in\u00a0Figures 7.7\u00a0and\u00a07.8, respectively. To draw the phasor diagram, current\u00a0I<\/em>\u00a0(rms value) is taken as the reference vector. Voltage drop in resistance\u00a0V<\/em>R<\/sub>\u00a0(=IR<\/em>) is taken in phase with current vector, whereas voltage drop in inductive reactance\u00a0V<\/em>L<\/sub>\u00a0(=IX<\/em>L<\/sub>) is taken 90\u00b0 ahead of the current vector (since current lags behind the voltage by 90\u00b0 in pure inductive circuit). The vector sum of these two voltages (drops) is equal to the applied voltage\u00a0V<\/em>\u00a0(rms value).<\/p>\n\n\n\n

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

Fig. 7.8<\/strong>  Phasor diagram<\/p>\n\n\n\n

Now, V<\/em>R<\/sub> = IR<\/em> and V<\/em>L<\/sub> = IX<\/em>L<\/sub> (where X<\/em>L<\/sub> = 2 \u03c0<\/em> f L<\/em>)<\/p>\n\n\n\n

In right\u2212angled triangle OAB,<\/p>\n\n\n\n

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

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

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

where \"image\" is the total opposition offered to the flow of AC by an R\u2013L series circuit and is called impedance of the circuit. It is measured in ohms.<\/p>\n\n\n\n

7.6.1  Phase Angle<\/h4>\n\n\n\n

From the phasor diagram shown in\u00a0Figure 7.8, it is clear that current in this circuit lags behind the applied voltage by an angle\u00a0\u0278<\/em>\u00a0called phase angle.<\/p>\n\n\n\n

From phasor diagram, \"image\"<\/p>\n\n\n\n

7.6.2  Power<\/h4>\n\n\n\n

If the alternating voltage applied across the circuit is 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><\/p>\n\n\n\n

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

 <\/p>\n\n\n\n

i<\/em> = I<\/em>m<\/sub> sin (\u03c9<\/em> t<\/em> \u2212 \u0278<\/em> )<\/p>\n\n\n\n

\u2234Instantaneous power, p<\/em> = vi<\/em><\/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

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

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

where cos \u0278<\/em> is called power factor of the circuit.<\/p>\n\n\n\n

From phasor diagram, \"image\"<\/p>\n\n\n\n

Therefore, power factor is defined as the cosine of the angle between the voltage and the current in an AC circuit. It may also be defined as the ratio of resistance to impedance of an AC circuit.<\/p>\n\n\n\n

<\/a>Alternatively, power, <\/em>\"image\"<\/p>\n\n\n\n

This shows that power is actually consumed in resistance only; inductance does not consume any power.<\/p>\n\n\n\n

7.6.3  Power Curve<\/h4>\n\n\n\n

The phasor diagram and wave diagram for voltage and current are shown in\u00a0Figure 7.9(a)\u00a0and\u00a0(b), respectively, where applied voltage (v<\/em>\u00a0=\u00a0V<\/em>m<\/sub>\u00a0sin\u00a0\u03c9 t<\/em>) is taken as reference quantity. The power curve for R\u2013L series circuit is also shown in\u00a0Figure 7.9(b). The points on the power curve are obtained from the product of the corresponding instantaneous values of voltage and current. It is clear that power is negative between angle 0 and\u00a0\u0278<\/em>\u00a0and between 180\u00b0 and (180 +\u00a0\u0278<\/em>). During rest of the cycle, the power is positive. Since the area under the positive loops is greater than that under the negative loops, the net power over a complete cycle is positive. Hence, a definite quantity of power is utilised or consumed by this circuit.<\/p>\n\n\n\n

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

Fig. 7.9<\/strong>  (a) Phasor diagram (b) Wave diagram for voltage, current and power<\/p>\n","protected":false},"excerpt":{"rendered":"

A circuit that contains a pure resistance R \u03a9 connected in series with a coil having pure inductance of L Henry is known as R\u2013L series circuit. This is the most general case that we come across in practice. Fig. 7.7  Circuit containing resistance and inductance in series An R\u2013L series circuit and its phasor diagram are shown in\u00a0Figures 7.7\u00a0and\u00a07.8, […]<\/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-2741","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\/2741","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=2741"}],"version-history":[{"count":1,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2741\/revisions"}],"predecessor-version":[{"id":2742,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2741\/revisions\/2742"}],"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=2741"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/categories?post=2741"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/tags?post=2741"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}