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charge Q coulombs at time t seconds is given by the differential equation RdQ/dt+Q/C=0, where c is the capacitance in farafd and R the resistance in ohms.solve the equation for Q given that Q=Qo where t=0

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  1. R dQ/dt + Q/C = 0
    R dQ/dt = -Q/C
    dQ/dt = -Q/(RC)
    dQ/Q = -1/(RC) dt
    lnQ = -1/(RC) t + k
    at t=0, we know that Q=Qo, so
    lnQo = k
    so,

    lnQ = -1/(RC) + lnQo
    ln(Q/Qo) = -1/(RC) t
    Q/Qo = e^(-t/RC)
    Q = Qo e^(-t/RC)

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