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How to calculate power from angular frequency of LRC circuit

  1. Apr 3, 2012 #1
    1. The problem statement, all variables and given/known data
    A voltage Δv = (120 V) sin ωt (in SI units) is applied across a series combination of a 2.13 H inductor, a 12.8 μF capacitor, and a 15.0 Ω resistor.

    a) Determine the angular frequency, ω0 at which the power delivered to the resistor is a maximum. = 192
    b) Calculate the power at that frequency.
    c) Determine the two angular frequencies ω1 and ω2 at which the power delivered is one-half the maximum value. [The Q of the circuit is approximately ω0/(ω2 - ω1).] Enter the smaller one first.

    2. Relevant equations
    Not sure
    P = Irms^2 * R
    P = IV

    z = sqrt(R + (wL - 1/(wC)))
    z = V/I

    3. The attempt at a solution
    I got part a as 192, but I'm not sure where to go with part b. I calculated z to equal 15.0685 but how do I calculate I? Do i have to use z=V/I, but then what value do I use for V? Would it just be 120V? I'm not sure where to take this, so any help would be great. Thanks
     
  2. jcsd
  3. Apr 4, 2012 #2

    gneill

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    Staff: Mentor

    At resonance (ω = ωo) what is the magnitude of the imaginary component of the impedance? Hint: at resonance, |XL| = |XC|.
     
  4. Apr 4, 2012 #3
    So the imaginary component would just be 0 and z=R? But what do I use for V?
     
  5. Apr 4, 2012 #4

    gneill

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    Staff: Mentor

    At resonance, yes. So, given that the impedance at resonance is purely real (and equal to R), what is the power dissipated?
     
  6. Apr 4, 2012 #5
    Zero power is dissipated right?
     
  7. Apr 4, 2012 #6

    gneill

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    Staff: Mentor

    Nope. The supply voltage V still sees the resistor R (since Z = R at resonance).
     
  8. Apr 4, 2012 #7
    Ok, but won't I = V/R and then P=V*I? but i'm not getting the correct answer, unless im not supposed to use 120 for V
     
  9. Apr 4, 2012 #8

    gneill

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    Staff: Mentor

    What value did you get for the power? Do you know what the correct value should be?

    It could be that the 120V is a peak value rather than rms.
     
  10. Apr 4, 2012 #9
    Yep, wasnt rms. Thanks
     
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