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Math Help - Physics-Type Dif EQ

  1. #1
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    Physics-Type Dif EQ

    Given that L = 1 henry, R = 100 ohms, C = 0.0004 farad, E(t) = 30 volts, q(0) = 0 coulombs, i(0) = 2 amperes:

    1.) Determine the charge on the capacitor and also the current in the above L-R-C circuit.

    2.) Determine what the maximum charge is on the capacitor.
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  2. #2
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    Not too many physics people here I see. Don't know why they make us learn this junk in a math course when it's not even really math!
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  3. #3
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    It's a differential equation so it is entirely a math problem. That doesnt mean that it cant be applicable in physics or a physics problem.

    The voltage drop across a linear resistor is IR.
    The voltage drop across a capacitor is Q/C.
    The voltage drop across an inductor is L \frac {dI}{dt}

    By Kirchoff's Law:
     L \frac{dI}{dt} + RI + \frac {1}{C}Q = E(t)

     I = \frac{dQ}{dt}
     \therefore
     LQ'' + RQ' + \frac{1}{C}Q = E(t), ~~ Q(t_0) = Q_0, ~~ Q'(t_0) = I(t_0) = I_0
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