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Homework Help: RC Circuit Oscillation

  1. Nov 7, 2009 #1
    1. The problem statement, all variables and given/known data
    An oscillating LC circuit has a current amplitude of 7.20 mA, a potential amplitude of 250 mV, and a capacitance of 240 nF.

    (a) What is the period of oscillation?

    (e) What is the maximum rate at which the inductor gains energy?

    2. Relevant equations
    Possibly: Energy stored in an inductor = 1/2 * L * I^2
    i = -wQsin(wt+ø)

    3. The attempt at a solution
    Energy per unit of time is Watts.

    If I find the equation for energy stored in an inductor, I can differenceate that with respect to time and find its maximum value.

    I thought that this would be:
    dE/dt = P = -L(w^3)(Q^2)sin(wt)cos(wt)

    And isn't the maximum value for this just

    (1/2)L(w^3)(Q^2) ?

    And isn't that just

    0.9 mW ?

    I've done this problem wrong several times so far, so is this one right?
    Last edited: Nov 7, 2009
  2. jcsd
  3. Nov 7, 2009 #2
    U = ((Q^2)/2C) cos(^2)(wt+ø) is the equation for the energy contained in the capacitor,
    not for the potential across it.
  4. Nov 7, 2009 #3

    Andrew Mason

    User Avatar
    Science Advisor
    Homework Helper

    How are you determining Q? I get Q = VC = .25 *2.4e(-7) = 6e(-8) C.

    [tex]Q = VC = \int_0^{\pi/2} dQ = \int_0^{\pi/2} idt = \int_0^{\pi/2} i_{max}\sin{\omega t}dt [/tex]


    [tex]Q = VC = i_{max}/\omega[/tex]

  5. Nov 7, 2009 #4
    Oh, I see. I misunderstood the equation for U I had written, and therefore got a bad Q. Thanks to both.
  6. Nov 7, 2009 #5
    But now I have another question for this problem, and I've edited the first post for it.
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