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Math Help - Capacitor charge over time

  1. #1
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    Capacitor charge over time

    An electric current, I(t), flowing out of a capacitor, decays according to [1], where t is time. Find the charge, Q(t), remaining in the capacitor at time t. The initial charge is Q_0 and Q(t) is related to I(t) by [2]
    1: I(t) = I_{0}e^{-t}
    2: Q'(t) = -I(t)

    Work so far is
    Q(t) = \int Q'(t)dt = -\int I(t)dt = -I_{0}\int e^{-t}dt = I_{0}e^{-t} + C = I_{0}e^{-t} + Q_0
    Though the solution seems to be
    Q(t)=I_{0}e^{-t}+Q_{0}-I_{0}

    What am I missing?
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  2. #2
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    Re: Capacitor charge over time

    Q(t) = I_0e^{-t} + C

    Q(0) = I_0 + C

    C = Q(0) - I_0 = Q_0 - I_0
    Thanks from sgcb
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