{"id":149333,"date":"2024-03-04T19:20:43","date_gmt":"2024-03-04T13:50:43","guid":{"rendered":"https:\/\/www.mapsofindia.com\/my-india\/?p=149333"},"modified":"2024-03-04T19:20:43","modified_gmt":"2024-03-04T13:50:43","slug":"mention-the-factors-on-which-the-resonant-frequency-of-a-series-lcr","status":"publish","type":"post","link":"https:\/\/www.mapsofindia.com\/my-india\/quiz\/mention-the-factors-on-which-the-resonant-frequency-of-a-series-lcr","title":{"rendered":"Mention the factors on which the resonant frequency of a series LCR…"},"content":{"rendered":"

Mention the factors on which the resonant frequency of a series LCR circuit depends. Plot a graph showing variation of impedance of a series LCR circuit with the frequency of the applied a.c. source.<\/h3>\n

Ans.<\/h3>\n

Factors affecting the resonant frequency of a series LCR circuit:<\/h3>\n
    \n
  1. \n

    Inductance (L):<\/strong> Higher inductance lowers the resonant frequency.<\/h3>\n<\/li>\n
  2. \n

    Capacitance (C):<\/strong> Higher capacitance increases the resonant frequency.<\/h3>\n<\/li>\n
  3. \n

    Resistance (R):<\/strong> Higher resistance broadens the resonance curve and reduces the amplitude of the current at resonance.<\/h3>\n<\/li>\n
  4. \n

    Quality factor (Q):<\/strong> Higher Q factors indicate sharper resonance peaks and narrower bandwidths.<\/h3>\n<\/li>\n<\/ol>\n

    The resonant frequency \ufffd0<\/span>f<\/span>0<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> of a series LCR circuit: \ufffd0=12\ufffd\ufffd\ufffd<\/span>f<\/span>0<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>2\u03c0<\/span>L<\/span>C<\/span><\/span>\u200b<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/h3>\n

    To plot the variation of impedance of a series LCR circuit with the frequency of the applied AC source:<\/h3>\n
      \n
    1. \n

      Choose a range of frequencies \ufffd<\/span>f<\/span><\/span><\/span><\/span><\/span> for the x-axis.<\/h3>\n<\/li>\n
    2. \n

      Calculate the inductive reactance \ufffd\ufffd<\/span>X<\/span>L<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> and capacitive reactance \ufffd\ufffd<\/span>X<\/span>C<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> for each frequency.<\/h3>\n<\/li>\n
    3. \n

      Use the impedance formula \ufffd=\ufffd2+(\ufffd\ufffd\u2212\ufffd\ufffd)2<\/span>Z<\/span>=<\/span><\/span>R<\/span>2<\/span><\/span><\/span><\/span>+<\/span>(<\/span>X<\/span>L<\/span><\/span>\u200b<\/span><\/span>\u2212<\/span>X<\/span>C<\/span><\/span>\u200b<\/span><\/span>)2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> to calculate the impedance \ufffd<\/span>Z<\/span><\/span><\/span><\/span><\/span> for each frequency.<\/h3>\n<\/li>\n
    4. \n

      Plot the impedance \ufffd<\/span>Z<\/span><\/span><\/span><\/span><\/span> against the frequency \ufffd<\/span>f<\/span><\/span><\/span><\/span><\/span>.<\/h3>\n<\/li>\n<\/ol>\n

      The resulting graph typically shows a peak at the resonant frequency \ufffd0<\/span>f<\/span>0<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>, where the impedance is minimized. As the frequency deviates from the resonant frequency, the impedance increases due to the combined effects of inductive and capacitive reactance.<\/h3>\n","protected":false},"excerpt":{"rendered":"

      Mention the factors on which the resonant frequency of a series LCR circuit depends. Plot a graph showing variation of impedance of a series LCR circuit with the frequency of the applied a.c. source. Ans. Factors affecting the resonant frequency of a series LCR circuit: Inductance (L): Higher inductance lowers the resonant frequency. Capacitance (C): […]<\/p>\n","protected":false},"author":21830,"featured_media":114041,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12119],"tags":[],"class_list":{"0":"post-149333","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-quiz"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/149333","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/users\/21830"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/comments?post=149333"}],"version-history":[{"count":1,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/149333\/revisions"}],"predecessor-version":[{"id":149335,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/149333\/revisions\/149335"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/media\/114041"}],"wp:attachment":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/media?parent=149333"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/categories?post=149333"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/tags?post=149333"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}