{"id":2753,"date":"2024-08-25T11:23:22","date_gmt":"2024-08-25T11:23:22","guid":{"rendered":"https:\/\/workhouse.sweetdishy.com\/?p=2753"},"modified":"2024-08-25T11:23:22","modified_gmt":"2024-08-25T11:23:22","slug":"series-resonance","status":"publish","type":"post","link":"https:\/\/workhouse.sweetdishy.com\/index.php\/2024\/08\/25\/series-resonance\/","title":{"rendered":"SERIES RESONANCE"},"content":{"rendered":"\n

In an R\u2013L\u2013C series circuit, when circuit current is in phase with the applied voltage, the circuit is said to be in series resonance. This condition is obtained in an R\u2013L\u2013C circuit shown in\u00a0Figure 7.31,<\/p>\n\n\n\n

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

Fig. 7.31<\/strong>  R\u2013L\u2013C series circuit<\/p>\n\n\n\n

when<\/p>\n\n\n\n

 <\/p>\n\n\n\n

X<\/em>L<\/sub> <\/em>= X<\/em>C<\/sub> <\/em>(or X<\/em>L<\/sub> <\/em>\u2212 X<\/em>C<\/sub> <\/em>= 0)<\/p>\n\n\n\n

At resonance,    X<\/em>L<\/sub> <\/em>\u2212 X<\/em>C<\/sub> <\/em>= 0 or X<\/em>L<\/sub> <\/em>= X<\/em>C<\/sub><\/p>\n\n\n\n

Impedance, \"image\"<\/p>\n\n\n\n

Current,<\/p>\n\n\n\n

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

<\/a>Since at resonance, the opposition to the flow of current is only resistance (R<\/em>) of the circuit, the circuit draws maximum current under this condition.<\/p>\n\n\n\n

7.13.1  Resonant Frequency<\/h4>\n\n\n\n

The value of\u00a0X<\/em>L<\/sub>\u00a0<\/em>(= 2\u03c0f L<\/em>) and\u00a0XC\u00a0<\/em>(= 1\/2\u03c0f C<\/em>) can be changed by changing the supply frequency. When frequency increases, the value of\u00a0X<\/em>L<\/sub>\u00a0increases, whereas the value of\u00a0X<\/em>C<\/sub>\u00a0<\/em>decreases, and vice versa.\u00a0<\/em>Therefore, to obtain series resonance, the frequency is adjusted to\u00a0f<\/em>r<\/sub>,\u00a0<\/em>so that\u00a0X<\/em>L<\/sub>\u00a0<\/em>=\u00a0X<\/em>C<\/sub>, the condition at point\u00a0P\u00a0<\/em>shown in\u00a0Figure 7.32.<\/p>\n\n\n\n

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

Fig. 7.32<\/strong>  Phasor diagram for series resonant circuit<\/p>\n\n\n\n

At series resonance, X<\/em>L<\/sub> = X<\/em>C<\/sub><\/p>\n\n\n\n

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

where f<\/em>r<\/sub> <\/em>is the resonant frequency <\/em>in Hz when L <\/em>and C <\/em>are measured in Henry and Farad, respectively.<\/p>\n\n\n\n

7.13.2  Effects of Series Resonance<\/h4>\n\n\n\n

The following are the main effects of series resonance:<\/p>\n\n\n\n

    \n
  1. At resonance X<\/em>L<\/sub> <\/em>= X<\/em>C<\/sub>, and therefore, the impedance of the circuit is minimum and is reduced to the resistance of the circuit only, that is, Z<\/em>r<\/sub> <\/em>= R<\/em> <\/li>\n\n\n\n
  2. Since, impedance is minimum, the circuit current is maximum at resonance, that is I<\/em>r<\/sub> <\/em>= V<\/em>\/Z<\/em>r<\/sub> <\/em>= V\/R<\/em> <\/li>\n\n\n\n
  3. Power taken by the circuit is maximum, as I<\/em>r<\/sub> <\/em>is maximum, \"image\" <\/li>\n\n\n\n
  4. As the current drawn by the circuit, at resonance, is very large (maximum), the voltage drop across L <\/em>(i.e., V<\/em>L<\/sub> = IX<\/em>L<\/sub> = I<\/em> \u00d7 2\u03c0 fr<\/sub>L<\/em>) and (i.e., V<\/em>C<\/sub> = IX<\/em>C<\/sub> = I \u00d7 1\/2\u03c0f<\/em>r<\/sub>C<\/em>) are also very large. In power system, at resonance, the excessive voltage built up across the inductive and capacitive components (such as circuit breakers and reactors) may cause damage. Therefore, series resonance should be avoided in power system. However, in some of the electronic devices (such as antenna circuit of radio and TV receiver and tuning circuits), the principle of series resonance is used to increase the signal voltage and current at a desired frequency (f<\/em>r<\/sub>). Since a series resonant circuit has the capability to draw heavy current and power from the mains, it is often regarded as acceptor circuit.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

    In an R\u2013L\u2013C series circuit, when circuit current is in phase with the applied voltage, the circuit is said to be in series resonance. This condition is obtained in an R\u2013L\u2013C circuit shown in\u00a0Figure 7.31, Fig. 7.31  R\u2013L\u2013C series circuit when   XL = XC (or XL \u2212 XC = 0) At resonance,    XL \u2212 XC = 0 or XL = XC Impedance,  Current, Since at resonance, the opposition to […]<\/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-2753","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\/2753","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=2753"}],"version-history":[{"count":1,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2753\/revisions"}],"predecessor-version":[{"id":2754,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2753\/revisions\/2754"}],"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=2753"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/categories?post=2753"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/tags?post=2753"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}