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Finding the inductance of an circuit knowing the energy stored

  1. Oct 7, 2012 #1
    If the total energy stored in the circuit below is 190 mJ, what is the value of L?
    IS = 2 A
    R1 = 250 Ω : R2 = 38 Ω
    C = 41 µF
    Give your answer to the nearest whole number, in mH (I have attached the diagram)

    I first try to find the equivalent impedence knowing that the impedence of an inductor is jωL and the impedence of a capacitor is -j/(ωC)

    I try to do this so as I can find Vs and hence using the formula:
    E = (CV^2 + LI^2)/2
    I would be able to find the value of L

    However I have too many unknowns to be able to find the equivalent impedance, so how do i go about this question? Any help would be greatly appreciated I am really stuck. Thanks!
     

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  2. jcsd
  3. Oct 7, 2012 #2
    Notice how your current is unchanging. Your circuit is at a steady state.

    Using this fact you can simplify your circuit. Recall that at a steady state, capacitors act like open circuits, and inductors act as wires. Since you have a known current entering the circuit, you can use Kirchoffs Current Law to determine the current through the inductor at a steady state.
     
  4. Oct 7, 2012 #3
    Thanks for your help! Sorry to be a bit slow, but I still can't obtain the correct answer.
    As I am looking at it with the inductor replaced by a wire, and the capacitor replaced with an open circuit I am left with a simple circuit with the two resistors in parallel.

    I then go to find the current going through R2 such that:

    Ix = (R1/(R1 + R2))*Is

    I then use the formula E = (LI^2)/2

    To find the value of L

    Can anyone please explain the mistake I have made, thanks.!
     
  5. Oct 7, 2012 #4
    I think you're forgetting that the capacitor stores energy as well.
     
  6. Oct 7, 2012 #5
    Sorry lazy mistake.

    In that case I get this:

    E = (CV^2 + LI^2)/2
    Therefore:

    L = (2E - CV^2)/I^2

    I(through inductor) = (R/(R1 + R2))*Is

    V = (R1*R2/(R1+R2))*Is

    Doing this I still am left with an incorrect answer

    Where am I going wrong?
     
  7. Oct 7, 2012 #6
    Thanks for your help! corrected my mistakes was just a calculator error. cheers!!
     
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