solve the following RC questions A souF is connected in series to a 60n resistor

Question

solve the following RC questions

A souF is connected in series to a 60n resistor. Initially the capacitor is not charged. Artime os they are connected in series to a 12V battery. a. What is the voltage across the capacitor after 2.5ms? b. what is the maximum charge on the capacitor as t oo? The resistor is c. The capacitor is completely charged and the battery disconnected. connected in series with the charged capacitor. How long does it take for 65% of the capacitor's charge to discharge through the resistor?

Explanation / Answer

time constant is T = R*C = 60*50*10^-6 = 3*10^-3 sec

a) voltage across capacitor at t sec is

v = V*(1-e^(-t/T))

given that V = 12 V

t = 2.5 ms = 2.5*10^-3 sec

T = 3 ms

then

v = 12*(1-e^(-2.5/3))

v = 6.78 volt

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b) maximum charge is Q = C*V = 50*10^-6*12 = 600*10^-6 C = 600 uC

C) while discharging

q = Qe^(-t/T)

0.65*Q = Q*e^(-t/(3*10^-3))

0.65 = e^(-t/(3*10^-3))

t = 1.29*10^-3 sec = 1.29 milli sec

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