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RLC Circuit- Find average power in circuit

  1. Apr 9, 2010 #1
    1. The problem statement, all variables and given/known data
    When the power factor of RLC circuit is equal to one, the frequency of the voltage source is 3 x 10^3 Hz. The rms value of the voltage source is 139 Volts and at a frequency of 3 x 10^3 Hz, the rms current in the circuit is 37.1 amps. If the inductive reactance at 3 x 10^3 Hz is 47 Ohms, what is the average power of the circuit in Watts at 0.78 times the resonant frequency of the circuit?

    2. Relevant equations

    Pav = Vrms Irms cos (|)
    Vrms= V/sqrt 2
    Irms= I/sqrt 2
    V= XL I
    V= Xc I
    XL= 2 pi f L
    Xc= 1/ 2 pi C
    Res freq= 1/2pi 1/ sqrt (LC)

    3. The attempt at a solution
    I'm going in circles with this problem. Given the RMS value of the voltage and current, I tried to find the max voltage and current, and then plug that into V=XL I and V= Xc I to find XL and Xc, but I am probably wrong.

    I guess I need to use the XL and Xc for each at the given frequency, to find both L and C to find the resonance frequency, multiply that number by .78, and then plug everything back into something?

    Can someone please help me sort out this problem? Thanks
  2. jcsd
  3. Apr 10, 2010 #2
    Can someone please help me out and get me started in the right direction please?
  4. Apr 17, 2010 #3
    If the power factor cos([tex]\varphi[/tex]) = 1, then the phase angle between the Vmax and Imax vectors in the phasor diagram must be [tex]\varphi[/tex] = 0. This means that Vmax vector has no y component, which means XL = XC. Since we know the inductive reactance and the resonant frequency, we can find the inductance and capacitance of the circuit. Also, at the resonant frequency, the impedance z = sqrt( R^2 + (XL -XC)^2 ) = sqrt( R^2 ) = R, so you can use Vrms and Irms to find R ( Vrms = Irms*z = Irms*R ). Then, you can find the reactances and impedance at the new frequency, draw the phasor/impedance diagram, find the new phase angle [tex]\varphi[/tex] between V and I ( [tex]\varphi[/tex] = tan^(-1)( (XL -XC) / R), and use those to calculate Pav.
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