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Finding values of RLC circuit given resonance frequency

  1. Apr 15, 2014 #1

    Maylis

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    1. The problem statement, all variables and given/known data
    A series RLC circuit is driven by an ac source with a phasor voltage Vs = 10∠30◦ V. If the circuit resonates at 103 rad/s and the average power absorbed by the resistor at resonance is 2.5 W, determine the values of R, L, and C, given that Q = 5.

    2. Relevant equations



    3. The attempt at a solution
    Hello,

    As I am solving this, I am substituting into the equation for the power of the resistor using some of the parameters given in the problem statement. However, when I finally solve for L, then I end up getting an imaginary number part, 0.2∠60. Do I just use the real part as my answer, or am I doing this incorrectly?
     
  2. jcsd
  3. Apr 15, 2014 #2

    Maylis

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    Here is my attempt

    ImageUploadedByPhysics Forums1397617891.477692.jpg
     
  4. Apr 16, 2014 #3

    gneill

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    Staff: Mentor

    The phasor angle attributed to the source voltage should be irrelevant; You can always define the source phasor to be the reference phasor for your calculations (unless other current or voltage phasors elsewhere in the circuit are also given so that the true reference phasor is something or somewhere else that you can't "get at" directly). So just take your source to be 10V @ 103 rad/sec.

    At resonance the net reactance seen by the source is what? What does that tell you about the phase angle between the voltage and current at resonance?
     
  5. Apr 16, 2014 #4

    NascentOxygen

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    Average power is (magnitude of current)2 * R
    where you use the RMS value of the current
    So current in this formula has no angle, and the inductance you calculate will not have an angle.
     
  6. Apr 17, 2014 #5

    Maylis

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    I'm not entirely sure if this is what you guys are trying to communicate to me, so here is my interpretation of what you guys are telling me in my next attempt

    ImageUploadedByPhysics Forums1397719614.429544.jpg
     
  7. Apr 17, 2014 #6

    NascentOxygen

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    Your method looks better, though I haven't checked your arithmetic.

    You should give a few words' explanation why you reduced ZL + ZC + R to just R.
     
  8. Apr 20, 2014 #7

    rude man

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    So w_0 is 10^3 rad/s, not 103 rad/s?

    Anyway, start with determining R, which is already wrong.
    Then L.
    Then C.

    Don't use current at all.
     
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