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Calculating the average power supplied by a source

  1. Dec 20, 2016 #1
    1. For the circuit shown in (Figure 1) , where V= 2.8 cos(2 t+ 0.3 ) , R= 8 Ω and C= 4×10−2 F , find the average power supplied by the source, Ps and the average power absorbed by the resistor PR .


    2. p (t) = v(t)i(t) = VmIm cos (ωt + θv) cos (ωt + θi)
    PR = (1/2)(V2m/R)


    3. From the expression given, I've managed to isolate the value of omega and Vm. But I'm confused as to how to find the power if we're not given an expression for the current.

    Ac-Power-a.jpg
     
  2. jcsd
  3. Dec 20, 2016 #2

    vela

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    You're supposed to derive one from your knowledge of ##V_m## and the circuit.
     
  4. Dec 20, 2016 #3

    cnh1995

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    I think you are complicating the problem. This is a series RC circuit excited with an ac source. You know the resistance and capacitance. What is the capacitive reactance? What is the total impedance of the circuit?
     
  5. Dec 20, 2016 #4
    So I found the reactance to be equal to -12.5j S and the total impedance to be 8-12.5j Ω. Am I right in saying that I can then use the Y = 1/Z = I/V relation to find the current?
     
  6. Dec 20, 2016 #5

    cnh1995

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    Yes.
    Yes. You can also use the magnitude of impedance and voltage to calculate the magnitude of current, and then calculate the power consumed by the resistor.
     
  7. Dec 21, 2016 #6
    Thanks so much. Got the answer in the end. You were a terrific aid.
     
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