{"id":2751,"date":"2024-08-25T11:21:00","date_gmt":"2024-08-25T11:21:00","guid":{"rendered":"https:\/\/workhouse.sweetdishy.com\/?p=2751"},"modified":"2024-08-25T11:21:01","modified_gmt":"2024-08-25T11:21:01","slug":"r-l-c-series-circuit","status":"publish","type":"post","link":"https:\/\/workhouse.sweetdishy.com\/index.php\/2024\/08\/25\/r-l-c-series-circuit\/","title":{"rendered":"R\u2013L\u2013C SERIES CIRCUIT"},"content":{"rendered":"\n

A circuit that contains a pure resistance of R<\/em> \u03a9, a pure inductance of L<\/em> Henry, and a pure capacitor of capacitance C<\/em> Farad; all connected in series is known as R\u2013L\u2013C series circuit.<\/p>\n\n\n\n

An R\u2013L\u2013C series circuit is shown in\u00a0Figure 7.28.<\/p>\n\n\n\n

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

Fig. 7.28<\/strong>  Circuit containing resistance, inductance and capacitance in series<\/p>\n\n\n\n

Here, X<\/em>L<\/sub> = 2 \u03c0<\/em> \u0278<\/em> L<\/em> and X<\/em>C<\/sub> = 1\/2 \u03c0<\/em> f C<\/em><\/p>\n\n\n\n

<\/a>When a resulting current I<\/em> (rms value) flows through the circuit, the voltage across each component will be<\/p>\n\n\n\n

V<\/em>R<\/sub> = IR<\/em>, that is, voltage across R<\/em>……….. in phase with I<\/em>;<\/p>\n\n\n\n

V<\/em>L<\/sub> = IX<\/em>L<\/sub>, that is, voltage across L<\/em>……….. leads I <\/em>by 90\u00b0;<\/p>\n\n\n\n

V<\/em>C<\/sub> <\/em>= IX<\/em>C<\/sub>, that is, voltage across C<\/em>……….. lags I<\/em> by 90\u00b0;<\/p>\n\n\n\n

The phasor diagram is shown in Figure 7.29<\/a>, where current is taken as the reference phasor. Since voltage across inductance V<\/em>L<\/sub> leads the current vector I<\/em> by 90\u00b0 and voltage across capacitance V<\/em>C<\/sub> lags the current vector I<\/em> by 90\u00b0, they act opposite to each other. If V<\/em>L<\/sub> > V<\/em>C<\/sub>, in effect, the circuit behaves as an inductive circuit; however, when V<\/em>L<\/sub> < V<\/em>C<\/sub>, the circuit behaves as a capacitive circuit. Here, the phasor diagram is drawn for an inductive circuit (i.e., when V<\/em>L<\/sub> > V<\/em>C<\/sub>).<\/p>\n\n\n\n

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

Fig. 7.29<\/strong>  Phasor diagram<\/p>\n\n\n\n

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

or<\/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\u2013C series circuit and is called impedance of the circuit.<\/p>\n\n\n\n

7.12.1  Phase Angle<\/h4>\n\n\n\n

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

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

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

7.12.2  Power<\/h4>\n\n\n\n

Average power, P<\/em> = VI<\/em> cos \u0278<\/em> = I<\/em>2<\/sup> R<\/em><\/p>\n\n\n\n

Power factor, \"image\"<\/p>\n\n\n\n

The alternating voltage applied across the circuit is given by<\/p>\n\n\n\n

 <\/p>\n\n\n\n

v<\/em> = V<\/em>m<\/sub> sin \u03c9<\/em> t<\/em>,<\/p>\n\n\n\n

Therefore, the circuit current is represented by the equation as per the constants or parameters, as explained in the following three cases of R\u2013L\u2013C series circuit:<\/p>\n\n\n\n

    \n
  1. When X<\/em>L<\/sub> > X<\/em>C<\/sub>, the phase angle \u0278<\/em> is positive. In effect, the circuit behaves as an R\u2013L series circuit. The circuit current lags behind the applied voltage and pf is lagging. The current is given by the equation. i<\/em> = I<\/em>m<\/sub> sin (\u03c9<\/em> t<\/em> \u2212 \u0278<\/em>) <\/li>\n\n\n\n
  2. <\/a>When X<\/em>L<\/sub> < X<\/em>C<\/sub>, the phase angle \u0278<\/em> is negative. In effect, the circuit behaves as an R\u2013C series circuit. The circuit current leads the applied voltage and pf is leading. The current is given by the equation. i<\/em> = I<\/em>m<\/sub> sin (\u03c9<\/em> t<\/em> + \u0278<\/em>) <\/li>\n\n\n\n
  3. When X<\/em>L<\/sub> = X<\/em>C<\/sub>, the phase angle \u0278<\/em> is zero. In effect, the circuit behaves like a pure resistive circuit. The circuit current is in phase with applied voltage and pf is unity. The current is given by the equation. i<\/em> = I<\/em>m<\/sub> sin \u03c9<\/em> t<\/em> <\/li>\n<\/ol>\n\n\n\n

    7.12.3  Impedance Triangle<\/h4>\n\n\n\n

    Figure 7.30(a)\u00a0shows the impedance triangle of the circuit when\u00a0X<\/em>L<\/sub>\u00a0>\u00a0X<\/em>C<\/sub>, while Figure 7.30(b) shows the impedance triangle of the circuit when\u00a0X<\/em>L<\/sub>\u00a0<\u00a0X<\/em>C<\/sub>.<\/p>\n\n\n\n

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

    Fig. 7.30  (a) Impedance triangle (XL<\/sub> ><\/strong> XC<\/sub>) (b) Impedance triangle (XC<\/sub> ><\/strong> XL<\/sub>)<\/p>\n","protected":false},"excerpt":{"rendered":"

    A circuit that contains a pure resistance of R \u03a9, a pure inductance of L Henry, and a pure capacitor of capacitance C Farad; all connected in series is known as R\u2013L\u2013C series circuit. An R\u2013L\u2013C series circuit is shown in\u00a0Figure 7.28. Fig. 7.28  Circuit containing resistance, inductance and capacitance in series Here, XL = 2 \u03c0 \u0278 L and XC = 1\/2 \u03c0 f C When a resulting current I (rms value) flows […]<\/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-2751","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\/2751","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=2751"}],"version-history":[{"count":1,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2751\/revisions"}],"predecessor-version":[{"id":2752,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2751\/revisions\/2752"}],"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=2751"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/categories?post=2751"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/tags?post=2751"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}