Consider a capacitor C being discharged through a resistor R as shown in figure

Question

Consider a capacitor C being discharged through a resistor R as shown in figure a. The initial potential difference across the capacitor is 24.0 V, the capacitance is 4.00 10-6 F, and the resistance is 2.50 ?.
(a) How long does it take for the charge on the capacitor to drop to one-fourth of its initial value?


(b) Compute the initial charge and time constant.
Q =
? =

(c) How long does it take to discharge all but the last quantum of charge, 1.6 10-19 C? (Assume an exponential decrease during the entire discharge process.)

Explanation / Answer

q=q0exp(-t/CR)

q0/4=q0exp(-t/4*10-16 *2.5)

exp(t/10-15 )=4

t/10-15 =log4=1.38

t=1.38*10-15 s

b)q0=VC=24*4*10-16 =96*10-16 C

time constant=CR=10-15 s

c)1.6*10-19=96*10-16 exp(-t/ 10-15)

exp(t/10-15 )=96*10-16 /1.6*10-19 =60*103

t=log60000*10-15 =11.00*10-15 s

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