{"id":2755,"date":"2024-08-25T11:26:26","date_gmt":"2024-08-25T11:26:26","guid":{"rendered":"https:\/\/workhouse.sweetdishy.com\/?p=2755"},"modified":"2024-08-25T11:26:27","modified_gmt":"2024-08-25T11:26:27","slug":"resonance-curve","status":"publish","type":"post","link":"https:\/\/workhouse.sweetdishy.com\/index.php\/2024\/08\/25\/resonance-curve\/","title":{"rendered":"RESONANCE CURVE"},"content":{"rendered":"\n

The curve obtained by plotting a graph between the current and the frequency is known as resonance curve. A resonance curve of a typical R\u2013L\u2013C series circuit is shown in\u00a0Figure 7.33.\u00a0It may be noted that current reaches its maximum value at the resonant frequency (f<\/em>r<\/sub>), falling off rapidly on either side of that point. It is because when the value of frequency is lower than resonance frequency,\u00a0X<\/em>C<\/sub>\u00a0>\u00a0X<\/em>L<\/sub>\u00a0and when the value of frequency is higher than\u00a0f<\/em>r<\/sub>,\u00a0X<\/em>C<\/sub>\u00a0<\u00a0X<\/em>L<\/sub>. In both the cases, impedance of the circuit increases (Z\u00a0<\/em>>\u00a0Z<\/em>r<\/sub>) and the value of current decreases.<\/p>\n\n\n\n

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

Fig. 7.33<\/strong>  Graph between f and I for R\u2013L\u2013C series circuit<\/p>\n\n\n\n

Note that resistance of the circuit also plays its own role. The smaller the resistance, the greater is the current at resonance.<\/p>\n\n\n\n

7.14.1  Bandwidth<\/h4>\n\n\n\n

The range of frequency over which circuit current is equal to or more than 70.7% of maximum value (i.e., I<\/em>r<\/sub>, current at resonance) is known as the bandwidth of a series resonant circuit.<\/p>\n\n\n\n

Figure 7.34\u00a0shows a resonance curve of a typical R\u2013L\u2013C circuit where the circuit current is equal to or greater\u00a0<\/em>than 70.7% of maximum current (i.e.,\u00a0I<\/em>r<\/sub>\u00a0<\/em>=\u00a0V<\/em>\/R<\/em>) between\u00a0<\/em>frequency range\u00a0f<\/em>1<\/sub>\u00a0to\u00a0f<\/em>2<\/sub>.<\/p>\n\n\n\n

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

Fig. 7.34<\/strong>  Graph representing band width in<\/p>\n\n\n\n

Bandwidth,<\/p>\n\n\n\n

 <\/p>\n\n\n\n

BW <\/em>= f<\/em>2<\/sub> \u2212 f<\/em>1<\/sub><\/p>\n\n\n\n

Here, the frequency f<\/em>1<\/sub> is called the lower cutoff frequency <\/em>and the frequency f<\/em>2 <\/sub>is called the upper cut\u2212off frequency. The bandwidth represents the frequency range <\/em>at which the circuit offers low impedance to circuit <\/em>current.<\/p>\n\n\n\n

The following points may be noted here:<\/p>\n\n\n\n

    \n
  1. If the resonant frequency is not located at the centre of upper and lower cut\u2212off frequency, then \"image\"<\/li>\n\n\n\n
  2. When the resonant frequency is located sufficiently near to the centre of the two cut\u2212off frequencies and Q <\/em>of the circuit is \u226510, then \"image\"<\/li>\n<\/ol>\n\n\n\n

    7.14.2  Selectivity<\/h4>\n\n\n\n

    From the resonance curve, it is clear that for smaller resistance the resonance curve is sharp and flat for the larger resistance. A sharper resonance curve provides smaller band of frequencies to give reasonable response, and hence, provides better selectivity. It also shows that selectivity is reciprocal of bandwidth.<\/p>\n","protected":false},"excerpt":{"rendered":"

    The curve obtained by plotting a graph between the current and the frequency is known as resonance curve. A resonance curve of a typical R\u2013L\u2013C series circuit is shown in\u00a0Figure 7.33.\u00a0It may be noted that current reaches its maximum value at the resonant frequency (fr), falling off rapidly on either side of that point. It […]<\/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-2755","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\/2755","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=2755"}],"version-history":[{"count":1,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2755\/revisions"}],"predecessor-version":[{"id":2756,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2755\/revisions\/2756"}],"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=2755"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/categories?post=2755"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/tags?post=2755"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}