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11. Consider a capacitor C being discharged through a resistor R as in Figure be

ID: 1580765 • Letter: 1

Question

11. Consider a capacitor C being discharged through a resistor R as in Figure below. (a) How long does it e for the charge on the capacitor to drop to one-fourth of its initial value? (b) Compute the initial charge and time constant. (c) How long does it take to discharge all but the last quantum of charge, 1.60 x 10 C, if the Household circuits are a practical application of some of the ideas presented in this apter. In a typical installation, the utility company distributes electric power to individual houses with a pair of wires, or power lines. Electrical devices in a initial potential difference across the capacitor is 12.0 V, the capacitance is 3.50 F, and the resistance is 2.00? (Assume an exponential decrease during the entire discharge process.)

Explanation / Answer

a)

In a RC Circuit charge as a function of time for discharging is given by

Q=Qoe-t/T

=>Qo/4=Qoe-t/T

-t/T =Ln(1/4)

t=1.386T

t=1.386*7*10-6=9.7*10-6s

b)

Initial charge

Qo=CV=(3.5*10-6)*12=4.2*10-5C

Time constant

T=RC =2*(3.5*10-6)=7*10-6s

c)

Now

=>1.6*10-19=(4.2*10-5)e-t/7*10^-6

t=2.324*10-4 s