A 1.51 F capacitor is charged through a 129 resistor and then discharged through
ID: 1656515 • Letter: A
Question
A 1.51 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 current in the circuit at the time when the charge on its plates has reached 1/e of its maximum value.
B) During the discharge of the capacitor, find the time for the charge on its plates to decrease to 1/e of its initial value.
C) Find the time for the current in the circuit to decrease to 1/e of its initial value.
Explanation / Answer
Given capacitor C = 1.51 micro F
resistor, R = 129 ohm
a. capacitance charging equation is given by
I = Io*e^(-t/RC)
and q = qo*(1 - e^(-t/RC))
now, q/qo = 1/e
so e^-1 = 1 - e^(-t/RC))
1 - 1/e = e^(-t/RC) = e^(-t/1.51*10^-6*129) = e^(-5133.733*t)
ln(1 - 1/e) = -5133.733 t
t = 8.8345*10^-5 s
now, Io is not known
so I/Io = 1 - 1/e = 0.632
I = 0.632Io
where Io is current at t = 0
b. discharge equation of capacitor
q = qo*e^(-t/RC)
q/qo = 1/e
e^-1 = e^(-t/RC)
t = RC = 1.9479*10^-4 s
c. discharge equation for current
i = io*e^(-t/RC)
i/io = 1/e
so, t = RC = 1.9479*10^-4 s
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