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Heat dissipated in an RLC circuit

  1. Dec 3, 2012 #1
    1. The problem statement, all variables and given/known data
    A 4 Ω resistor, 14 mH inductor, and 99 µF
    capacitor are connected in series to a 65 V
    (rms) source having variable frequency.
    Find the heat dissipated in the circuit during one period if the operating frequency is
    twice the resonance frequency.
    Answer in units of J


    2. Relevant equations
    Vrms * R * ω^2/(Rω^2 + L^2(ω^2 -ω(0)^2)^2) = avg power


    3. The attempt at a solution
    I integrated the average power from 0 to ∏√(LC) because that was the time for one period. Then I got 8447.31 J. This is a massive number, which I'm sure is wrong. But I don't really know what I'm doing wrong.
     
  2. jcsd
  3. Dec 3, 2012 #2

    gneill

    User Avatar

    Staff: Mentor

    Your Relevant Equation yields the real component of the complex current (RMS complex current, since you're starting with Vrms). Multiply it by R to find the average power (or, perhaps you meant to have R2 in the numerator to begin with...)

    A full cycle is ##2\pi## radians, so that T = ##2\pi/\omega##.
     
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