A 1.60 F capacitor is charged through a 129 resistor and then discharged through

Question

A 1.60 F capacitor is charged through a 129 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

RC charging and discharging

A 1.60 F capacitor is charged through a 129 resistor

A ) Charging

Q = Qo (1 - e-t/RC)

RC = 129*1.60*10-6

Now   Qo/e = Qo(1 - e-t/RC)

   t = 94.67 seconds

B)

Current I = dq/dt = 1/RC *e-t/RC    = 4844.96*0.63 = 3062.6 A

C)

Qo/e = Qo e-t/RC   

or   t = 206.4 seconds

D) Io/e = Ioe-t/RC   

t = 206.4 seconds

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