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 = Q0 e-t/t.

(a) (2 points) What is the charge on the plate at t = 0? (Express your answer in terms of Q0.)

(b) (2 points) What is the charge on the plate at t = t?(Express your answer in terms of Q0.)

(c) (2 points) What do you need to do to linearize the equation?

(d) (2 points) What quantity would you plot on the y-axis of a linear graph against t, based on your answer to (c)?

(e) (2 points) What quantities will be represented by the slope and the y-intercept of the line of such a plot?

Explanation / Answer

a) t = 0, Q = q0

b) t = tau

Q = q0 e^(-1)

c)
ln(q) = ln(q0) - t/tau

d) ln(Q)

e) slope = -1/tau

intercept = ln(q0)

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