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Maximum Energy Stored in a Capacitor in an AC circuit

  1. Nov 21, 2012 #1

    TMO

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    1. The problem statement, all variables and given/known data

    A circuit is constructed with an AC generator, a resistor, capacitor and inductor as shown. The generator voltage varies in time as ε = Va - Vb = m*sin(ωt), where m = 24.0 V and ω = 187.0 radians/second. At this frequency,the circuit is in resonance with the maximum value of the current I = 0.5 A. The capacitance C = 130.0μF. L = 0.2199751 H.

    2. Relevant equations

    Energy capacity of a capacitor = ½CV2
    Energy capacity of an inductor = ½LV2

    3. The attempt at a solution

    I tried to calculate the energy in terms of plugging in the peak voltage into the energy equation. However, this doesn't yield the correct answer. So I tried combining the energy capacity of both the conductor an the inductor, but this didn't work either. I'm not sure where to proceed.
     
  2. jcsd
  3. Nov 21, 2012 #2

    gneill

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    Staff: Mentor

    "as shown" doesn't help much without a picture...

    And how are we to interpret Va and Vb?
     
  4. Nov 23, 2012 #3

    TMO

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    My apologies. The picture referenced is here:

    https://www.smartphysics.com/Content/Media/Images/EM/20/h20_AC1.png [Broken]
     
    Last edited by a moderator: May 6, 2017
  5. Nov 23, 2012 #4

    gneill

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    Staff: Mentor

    Okay, so it's a series circuit in resonance. What do you you know about the current in a series circuit? And, since you're given the frequency of operation, what can you say about the impedances of L and C? (or reactances, if you haven't covered impedances yet).
     
  6. Nov 23, 2012 #5

    TMO

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    Because the circuit is in resonance, I = εmax/R*sin(ωt). The impedance is only equal to the resistance.
     
  7. Nov 24, 2012 #6

    gneill

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    Staff: Mentor

    Right. Note that you are given the value of Imax. If you then have the individual impedances of the components you can determine the potentials across them. What's the impedance of the capacitor? What's the impedance of the inductor?
     
  8. Nov 24, 2012 #7

    TMO

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    I see the solution. Vc = IXc. Thanks.
     
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