A 1.36 F capacitor is charged through a 124 resistor and then discharged through

Question

A 1.36 F capacitor is charged through a 124 resistor and then discharged through the same resistor by short-circuiting the battery.

A.) While the capacitor is being charged, find the time for the charge on its plates to reach 1/e of its maximum value.

B.) While the capacitor is being charged, find the current in the circuit at the time when the charge on its plates has reached 1/e of its maximum value.

C.) During the discharge of the capacitor, find the time for the charge on its plates to decrease to 1/e of its initial value.

D.) Find the time for the current in the circuit to decrease to 1/e  of its initial value.

Explanation / Answer

while charging,

the charge grows as q = Qmax*(1-e^(t/RC))

and current changes as i = Imax*e^-(t/RC)

A)

q = Qmax/e

1/e = (1-e^-(t/(124*1.36*10^-6)))

time t = 7.73*10^-5 s

(B)

when t = 7.73*10^-5 s

i = Imax*e^-(( 7.73*10^-5)/(124*1.36*10^-6))

i = Imax*0.632

-------------------

while discharging,

the charge decays as q = Qmax*(e^(t/RC))

and current changes as i = Imax*e^-(t/RC)

C)

q = Qmax/e

1/e = e^-(t/(124*1.36*10^-6))

time t = 1.68*10^-4 s

(D)

i = Imax/e

1/e = e^-(t/(124*1.36*10^-6))

t = 1.68*10^-4 s

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