{"id":9274,"date":"2026-03-12T06:18:47","date_gmt":"2026-03-12T00:48:47","guid":{"rendered":"https:\/\/www.goseeko.com\/blog\/?p=9274"},"modified":"2026-06-03T19:55:24","modified_gmt":"2026-06-03T14:25:24","slug":"series-and-parallel-resonance-in-electrical-engineering","status":"publish","type":"post","link":"https:\/\/www.goseeko.com\/blog\/series-and-parallel-resonance-in-electrical-engineering\/","title":{"rendered":"<strong>Series and parallel resonance in electrical engineering<\/strong>"},"content":{"rendered":"\n<p>The phenomenon of series and parallel resonance takes place in the series or parallel R-L-C circuit which leads to unity power factor. Voltage and current in R \u2013 L &#8211; C circuit are in phase with each other.<\/p>\n\n\n\n<p>Resonance is used in many communicate circuit such as radio receiver.<\/p>\n\n\n\n<p>Resonance in series RLC series resonance in parallel RLC anti resonance \/ parallel resonance.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Condition for resonance X<sub>L <\/sub>= X<sub>C<\/sub><\/strong><\/li>\n\n\n\n<li><strong>Resonant frequency (Fr):<\/strong> for given values of R-L-C the inductive reactance X<sub>L<\/sub> become exactly aqual to the capacitive reactance Xc only at one particular frequency. This frequency is called as resonant frequency and denoted by (fr)<\/li>\n\n\n\n<li><strong>Expression for resonant frequency(fr): we know thet X<sub>L<\/sub> = 2<\/strong><strong>\u019b<\/strong><strong> FL &#8211; Inductive reactance<\/strong><\/li>\n<\/ul>\n\n\n\n<p>Xc = <img loading=\"lazy\" decoding=\"async\" width=\"26\" height=\"29\" src=\"\">&nbsp;&nbsp; &#8211; capacitive reactance<\/p>\n\n\n\n<p>At a particular frequency \u0234 = fr, the Inductive and capacitive reactance are exactly equal<\/p>\n\n\n\n<p><img loading=\"lazy\" decoding=\"async\" width=\"9\" height=\"20\" src=\"\">&nbsp;X<sub>L <\/sub>= X<sub>C<\/sub>&nbsp; \u2026\u2026at \u0234 = fr<\/p>\n\n\n\n<p>Ie <img loading=\"lazy\" decoding=\"async\" width=\"28\" height=\"20\" src=\"\">&nbsp; L&nbsp; =&nbsp; <img loading=\"lazy\" decoding=\"async\" width=\"27\" height=\"29\" src=\"\"><\/p>\n\n\n\n<p><img loading=\"lazy\" decoding=\"async\" width=\"9\" height=\"20\" src=\"\">&nbsp;fr<sup>2<\/sup> = <img loading=\"lazy\" decoding=\"async\" width=\"33\" height=\"29\" src=\"\"><sup><\/sup><\/p>\n\n\n\n<p><img loading=\"lazy\" decoding=\"async\" width=\"9\" height=\"20\" src=\"\">&nbsp;fr =&nbsp; <img loading=\"lazy\" decoding=\"async\" width=\"33\" height=\"29\" src=\"\">&nbsp;&nbsp; H<sup>2<\/sup><\/p>\n\n\n\n<p>And <img loading=\"lazy\" decoding=\"async\" width=\"28\" height=\"20\" src=\"\">&nbsp;= wr = <img loading=\"lazy\" decoding=\"async\" width=\"21\" height=\"29\" src=\"\">&nbsp;&nbsp; rad\/sec<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Quality factor \/ Q factor<\/strong><\/h2>\n\n\n\n<p>The quality of resonance circuit is measured in terms of efficiency of L and C to stare energy and the efficiency of L and C to store energy as measured in terms of a factor called quality factor or Q factor it is expressed as<\/p>\n\n\n\n<p>Q = <img loading=\"lazy\" decoding=\"async\" width=\"25\" height=\"32\" src=\"\">&nbsp; and Q = <img loading=\"lazy\" decoding=\"async\" width=\"15\" height=\"29\" src=\"\"><\/p>\n\n\n\n<p>The sharpness of tuning of R-L-C series circuit or its selectivity is measured by value of Q. as the value of Q increases, sharpness of the curve also increases and the selectivity increases  <a href=\"https:\/\/link-slot88ku.one\/\">https:\/\/link-slot88ku.one\/<\/a><\/p>\n\n\n\n\n\n<p>Q factor in resonance<\/p>\n\n\n\n\n\n<p>Resonance frequency<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Bandwidth in resonance (BW) = f2 = b1<\/strong><\/h2>\n\n\n\n<p><img loading=\"lazy\" decoding=\"async\" width=\"14\" height=\"20\" src=\"\">&nbsp;and <img loading=\"lazy\" decoding=\"async\" width=\"14\" height=\"20\" src=\"\">&nbsp;are the frequency at which the power delivered to the resistor is reduced to 50% of the power delivered to it at resonance <img loading=\"lazy\" decoding=\"async\" width=\"9\" height=\"20\" src=\"\">&nbsp;these frequency are called as half power <a href=\"https:\/\/www.nephro-ulm.de\/\" style=\"color: black\">https:\/\/www.nephro-ulm.de\/<\/a> frequency<\/p>\n\n\n\n<p>Bw = fr\/Q<\/p>\n\n\n\n<p><strong>Resonance in Parallel circuit<\/strong><strong>:<\/strong><\/p>\n\n\n\n<p>When a coil is in parallel with a capacitor, as shown below. The circuit is said to be in resonance.<\/p>\n\n\n\n\n\n<p>Resonance in RLC circuit<\/p>\n\n\n\n<p>The resonant frequency for above circuit is fr =&nbsp; <img loading=\"lazy\" decoding=\"async\" width=\"33\" height=\"29\" src=\"\">&nbsp; Hz<\/p>\n\n\n\n<p>The current at resonance is I=<img loading=\"lazy\" decoding=\"async\" width=\"26\" height=\"33\" src=\"\">&nbsp;<\/p>\n\n\n\n<p>The value L\/RC is known as dynamic impedance.<\/p>\n\n\n\n\n\n<p>The current at resonance is minimum. The circuits&nbsp;admittance&nbsp;must be at its minimum and one of the characteristics of a parallel resonance circuit is that admittance is very low limiting the circuits current. Unlike the series resonance circuit, the resistor in a parallel resonance circuit has a damping effect on the circuit bandwidth making the circuit less selective.<\/p>\n\n\n\n<p>Also, since the circuit current is constant for any value of impedance,&nbsp;Z, the voltage across a parallel resonance circuit will have the same shape as the total impedance and for a parallel circuit the voltage waveform is generally taken from across the capacitor.<\/p>\n\n\n\n<p><strong>Bandwidth and selectivity:<\/strong><strong><\/strong><\/p>\n\n\n\n<p><img loading=\"lazy\" decoding=\"async\" width=\"14\" height=\"20\" src=\"\">&nbsp;and <img loading=\"lazy\" decoding=\"async\" width=\"14\" height=\"20\" src=\"\">&nbsp;are the frequency at which the power delivered to the resistor is reduced to 50% of the power <a href=\"https:\/\/www.ccit.tg\/job-offers\" style=\"color: black\">https:\/\/www.ccit.tg\/job-offers<\/a> delivered to it at resonance <img loading=\"lazy\" decoding=\"async\" width=\"9\" height=\"20\" src=\"\">these frequency are called as half power frequency<\/p>\n\n\n\n<p>Bw = fr\/Q<\/p>\n\n\n\n<p>Q = <img loading=\"lazy\" decoding=\"async\" width=\"27\" height=\"31\" src=\"\">&nbsp;= <img loading=\"lazy\" decoding=\"async\" width=\"19\" height=\"20\" src=\"\">fCR = R<img loading=\"lazy\" decoding=\"async\" width=\"18\" height=\"29\" src=\"\"><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Resonant Frequency:<\/strong><\/h2>\n\n\n\n<p>The resonant frequency for parallel resonant circuit is given as<\/p>\n\n\n\n<p>f<sub>R<\/sub>= <img loading=\"lazy\" decoding=\"async\" width=\"93\" height=\"29\" src=\"\"><\/p>\n\n\n\n<p>Where L= inductance of the coil<\/p>\n\n\n\n<p>C = is the capacitance<\/p>\n\n\n\n<p>R<sub>s<\/sub> = Resistive value of coil.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">&nbsp;<\/h2>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Previous year solved questions on the topic<\/strong><\/h2>\n\n\n\n<p>1) A coil takes a current of 6A when connected to 24V dc supply. To obtain the same current with 50HZ ac, the voltage required was 30V. Calculate inductance and p.f of coil?<\/p>\n\n\n\n<p>Sol: The coil will offer only resistance to dc voltage and impedance to ac voltage<\/p>\n\n\n\n<p>R =24\/6 = 4ohm<\/p>\n\n\n\n<p>Z= 30\/6 = 5ohm<\/p>\n\n\n\n<p>X<sub>L<\/sub> = <img loading=\"lazy\" decoding=\"async\" width=\"65\" height=\"21\" src=\"\"><\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp; = 3ohm<\/p>\n\n\n\n<p>cos\u03c6 = <img loading=\"lazy\" decoding=\"async\" width=\"8\" height=\"27\" src=\"\">&nbsp;= 4\/5 = 0.8 lagging<\/p>\n\n\n\n<p>2) The potential difference measured across a coil is 4.5V, when it carries a dc current of 8A. The same coil when carries ac current of 8A at 25Hz, the potential difference is 24V. Find current and power when supplied by 50V,50Hz supply?<\/p>\n\n\n\n<p>Sol: R=V\/I= 4.5\/8 = 0.56ohm<\/p>\n\n\n\n<p>At 25Hz, Z= V\/I=24\/8 =3ohms<\/p>\n\n\n\n<p>X<sub>L<\/sub> = <img loading=\"lazy\" decoding=\"async\" width=\"65\" height=\"21\" src=\"\"><\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp; = 2.93ohm<\/p>\n\n\n\n<p>X<sub>L<\/sub> = 2<img loading=\"lazy\" decoding=\"async\" width=\"10\" height=\"19\" src=\"\">fL = 2<img loading=\"lazy\" decoding=\"async\" width=\"10\" height=\"19\" src=\"\">x 25x L = 2.93<\/p>\n\n\n\n<p>L=0.0187ohm<\/p>\n\n\n\n<p>At 50Hz<\/p>\n\n\n\n<p>X<sub>L<\/sub> = 2&#215;3 =6ohm<\/p>\n\n\n\n<p>Z = <img loading=\"lazy\" decoding=\"async\" width=\"66\" height=\"21\" src=\"\">&nbsp;= 5.97ohm<\/p>\n\n\n\n<p>I= 50\/5.97 = 8.37A<\/p>\n\n\n\n<p>Power = I<sup>2<\/sup>R = 39.28W<\/p>\n\n\n\n<p>3) A coil having inductance of 50mH an resistance 10ohmis connected in series with a 25<img loading=\"lazy\" decoding=\"async\" width=\"9\" height=\"19\" src=\"\">F capacitor across a 200V ac supply. Calculate resonant frequency and current flowing at resonance?<\/p>\n\n\n\n<p>Sol: f<sub>0<\/sub>=<img loading=\"lazy\" decoding=\"async\" width=\"35\" height=\"27\" src=\"\">&nbsp;= 142.3Hz<\/p>\n\n\n\n<p>I<sub>0<\/sub> = V\/R = 200\/10 = 20A<\/p>\n\n\n\n<p>Que) A 15mH inductor is in series with a parallel combination of 80ohm resistor and 20<img loading=\"lazy\" decoding=\"async\" width=\"13\" height=\"19\" src=\"\">F capacitor. If the angular frequency of the applied voltage is 1000rad\/s find admittance?<\/p>\n\n\n\n<p>Sol: X<sub>L<\/sub> = 2<img loading=\"lazy\" decoding=\"async\" width=\"10\" height=\"19\" src=\"\">fL = 1000x15x10<sup>-3<\/sup> = 15ohm<\/p>\n\n\n\n<p>&nbsp;X<sub>L<\/sub> = 1\/<img loading=\"lazy\" decoding=\"async\" width=\"12\" height=\"19\" src=\"\">C = 50ohm<\/p>\n\n\n\n<p>Impedance of parallel combination Z = 80||-j50 = 22.5-j36<\/p>\n\n\n\n<p>Total impedance = j15+22.5-j36 = 22.5-j21<\/p>\n\n\n\n<p>Admittance Y= 1\/Z = 0.023-j0.022 siemens<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Access more from <a href=\"https:\/\/www.goseeko.com\/reader\/question-bank\/other-univ\/engineering\/computer-engineering-1\/first-year\/null\/basic-electrical-engineering-87\/unit-3-single-phase-ac-circuits-38\">QB here<\/a><\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Test your knowledge with some MCQ on the topic&nbsp;<\/strong><\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li>The current flowing through an insulating medium is called<\/li>\n\n\n\n<li>Conduction<\/li>\n\n\n\n<li>Convection<\/li>\n\n\n\n<li>Radiation<\/li>\n\n\n\n<li>None<\/li>\n\n\n\n<li>In a parallel circuit, we consider _____________ instead of impedance.<\/li>\n\n\n\n<li>Resistance<\/li>\n\n\n\n<li>Capacitance<\/li>\n\n\n\n<li>Inductance<\/li>\n\n\n\n<li>None<\/li>\n<\/ol>\n\n\n\n<p>You can attempt more here: <a href=\"https:\/\/www.goseeko.com\/studymaterial\/mcq\/other-univ\/engineering\/computer-engineering-1\/first-year\/null\/basic-electrical-engineering-87\/unit-3-single-phase-ac-circuits-39\">MCQ Test link<\/a><\/p>\n\n\n\n<p>To learn more <a href=\"https:\/\/www.bing.com\/ck\/a?!&amp;&amp;p=3ef667f0cc62fcb1JmltdHM9MTY2MDY0MTY0NyZpZ3VpZD04MTgzMWM0Zi04YTZhLTQwZmQtYTMwMi1lOWEzNTQ0NWQyNmYmaW5zaWQ9NTE0OA&amp;ptn=3&amp;hsh=3&amp;fclid=b66c3ac4-1d44-11ed-8710-087333a75597&amp;u=a1aHR0cHM6Ly93d3cuZGlmZmVyZW5jZS53aWtpL3Nlcmllcy1yZXNvbmFuY2UtdnMtcGFyYWxsZWwtcmVzb25hbmNlLw&amp;ntb=1\">click here<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The phenomenon of series and parallel resonance takes place in the series or parallel R-L-C circuit which leads to unity power factor.&hellip;<\/p>\n","protected":false},"author":28,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-9274","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.3.1 - 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