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Resonance frequency in an LCR circuit

  1. May 16, 2006 #1
    Hello everyone!

    I've been trying to derive the expression

    w = sqrt( (1/(LC)) - (R_l^2 / L^2) )

    where w is the resonace frequency, L is the inductance of the inductor, R_l is the resistance in the inductor, R is the resistance of the resistor and C is the capacitance of the capacitator.

    for this circuit:

    http://web.telia.com/~u18412273/lcr.JPG [Broken]

    I'm not sure how to attack the problem and I can't find any good texts about it.
    I know how to do it in series circuits. I've been trying to do it in a correspondning way for this one but I can't quite do it.

    Any help is appreciated
    Last edited by a moderator: May 2, 2017
  2. jcsd
  3. May 16, 2006 #2


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    Homework Helper

    Set up an expression for the complex impedance of the circuit (you can forget about the R since it doesn't affect the analysis). Find the omega for which the impedance of the capacitor in parallel with (series inductance + resistance) becomes a pure real number. At this point the reactive component disappears, the load is purely resistive and resonance is achieved.
    Last edited by a moderator: May 2, 2017
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