The charge Q on the positive plate of a discharging capacitor as a function of t

Question

The charge Q on the positive plate of a discharging capacitor as a function of time is given by an exponential relation: Q = Q_0^e^-1/tau. What is the charge on the plate at t = 0? (Express your answer in terms of Q_0.) (b) What is the charge on the plate at t = tau? (Express your answer in terms of Q_o.) (c) What do you need to do to linearize the equation? (d) What quantity would you plot on the y-axis of a linear graph against t, based on your answer to (c)? (c) What quantities will be represented by the slope and the y-intoccpt of the line of such a plot?

Explanation / Answer

(a) Q = Qoe-t/T
At t= 0
Q =Qo
(b) at t = T
Q = Qoe-T/T = Qoe-1 = 0.3678Qo
(c) Q/Qo = e-t/T
Take log both side
ln(Q/Qo) = -t/T
ln(Qo/Q) = t/T
Hence now this is in the form of linear eqation
(d) On Y axis we will plot ln (Qo/Q)
(e) Slope will give the value of time constant
and the Y intercept will give the value of ln(Qo/Q)

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