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Thread: 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 $\displaystyle Q_0$ and Q(t) is related to I(t) by [2]
    1: $\displaystyle I(t) = I_{0}e^{-t}$
    2: $\displaystyle Q'(t) = -I(t)$

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

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

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

    $\displaystyle Q(0) = I_0 + C$

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