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LC Circuit

  1. Apr 6, 2010 #1
    1. The problem statement, all variables and given/known data

    In an oscillating LC circuit, L = 2.93 mH and C = 3.21 μF. At t = 0 the charge on the capacitor is zero and the current is 2.14 A. What is the maximum charge (in C) that will appear on the capacitor?

    2. Relevant equations

    I know that for an LC Circuit, the charge q at a given time t is:
    q = Q cos(wt + phi)

    3. The attempt at a solution

    At t = 0, q = 0;
    Thus,
    0 = Q cos(phi),
    which implies Q = 0.

    So the maximum charge is 0.

    However this is not right.
    Any help please?
     
  2. jcsd
  3. Apr 6, 2010 #2

    vela

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    The other possibility (the correct one) is that cos(phi)=0.

    Try differentiating q(t) and use the other information given in the problem.
     
  4. Apr 6, 2010 #3
    Okay, so

    i = dq/dt = -wq sin(wt + phi)

    Plugging in,
    since w = 1 / sqrt(LC)
    2.14 A = Q (-1 / sqrt(2.93 mH * 3.21 microF)) sin(phi)

    However I'm not sure what phi is. In fact, I'm not quite sure specifically what phi is. I know it is the phase difference. But in this case, the phase difference between what?

    Thanks so much.
     
  5. Apr 6, 2010 #4

    vela

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    The phase phi simply tells you where in the cycle you're starting.

    With the information you're given, you can solve for phi. First, you know cos(phi)=0, so phi=pi/2 or -pi/2. From your equation for the current, you can figure out which of the two possibilities is the correct one.
     
  6. Apr 6, 2010 #5
    Okay. I understand that one. Now here's the next part;

    (b) At what earliest time t > 0 is the rate at which energy is stored in the capacitor greatest?

    So, I know that U = q^2 / 2C
    So U = (Q^2)(sin^2(wt)) / (2C)

    deriving this (to find the "rate at which energy is stored"), we get

    dU/dt = (Q^2)(w)(sin(wt))(cos(wt)) / C

    The maximum occurs when sin(wt)cos(wt) is at a max, which is when wt = pi/4

    So, wt = pi/4 implies that the time when the rate at which energy is stored in the capacitor is greatest is
    t = (pi/4)(1/w)
    plugging in values, I get
    t = 7.61686 E-5 seconds

    However, this is incorrect.
    See my flaw anywhere?
    Thanks!
     
  7. Apr 6, 2010 #6

    vela

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    Other than perhaps the number of significant figures, it looks right to me.
     
  8. Apr 6, 2010 #7
    Going back to before, why is it that we know cos(phi) = 0?
     
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