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Homework Help: My try

  1. Feb 11, 2004 #1
    as far as i know about inductors i think it'll make an harmonic type of move...
    but it seems to make no sense
    can anyone help?
  2. jcsd
  3. Feb 12, 2004 #2

    Tom Mattson

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    Since you weren't very explicit as to what kind of circuit you are talking about, let's keep it simple: An LC circuit with a fully charged capacitor at t=0.

    Now let the capacitor discharge through the inductor. What happens?

    The voltage drop across the capacitor is EC=-q/C, and that across the inductor is EL=-L(di/dt)=-L(d2i/dt2). I will let q" (q-double-prime) denote the second time derivative of q from now on.

    Kirchhoff's voltage law says that the sum of the voltages around a closed loop in a circuit must be zero. This is just the conservation of energy in disguse. So, we have:




    The solution to this equation, with q(0)=Q and i(0)=q'(0)=0, is


    where ω=(1/LC)1/2.

    As you can see, the oscillatory behavior of q(t) is due to the combined influences of the element laws and the conservation of energy.
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