A 1.44 F capacitor is charged through a 127 resistor and then discharged through
ID: 1398872 • Letter: A
Question
A 1.44 F capacitor is charged through a 127 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 1e 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 1e of its maximum value.
C)During the discharge of the capacitor, find the time for the charge on its plates to decrease to 1e of its initial value.
Explanation / Answer
A) tme constant of the ckt, T = R*C
= 127*1.44*10^-6
= 1.83*10^-4 s
Q = Qmax*(1 - e^(-t/T))
Qmax/e = Qmax*(1 - e^(-t/T))
1/e = 1 - e^(-t/T)
e^(-t/T) = 1 - 1/e
t = -T*ln(1 - 1/e)
= -1.83*10^-4*ln(1 - 1/e)
= 8.4*10^-5 s
B)
the current in the circuit at the time when the charge on its plates has reached 1/e of its maximum value = T
= 1.83*10^-4 s
C) the time for the charge on its plates to decrease to 1/e of its initial value = T
= 1.83*10^-4 s
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