A 8.0-μF uncharged capacitor is connected in series with a 6.0-kΩ resistor,an ideal 20-V dc source,and an open switch.If the switch is closed at time t = 0.0 s,what is the charge on the capacitor at t = 9.0 ms?
A)0 C
B)37% of the minimum charge
C)17% of the maximum charge
D)68% of the minimum charge
E)96% of the maximum charge

Question

Quizplus · Accepted Answer

First, we need to find the time constant:
τ = RC = (6.0 x 10^3 Ω)(8.0 x 10^-6 F) = 0.048 s
Then, we can use the formula for the charge on a capacitor in an RC circuit with a DC source:
Q(t) = Qmax(1 - e^(-t/τ))
At t = 9.0 ms = 0.009 s, we have:
Q(t) = Qmax(1 - e^(-0.009/0.048)) = 0.17Qmax
Therefore, the answer is (C), which says that the charge on the capacitor at t = 9.0 ms is 17% of the maximum charge.

A 80-μF Uncharged Capacitor Is Connected in Series with a 6