A 4.0 μF capacitor is connected in series with a 2.0 kΩ resistor across a 20-V DC source and an open switch. If the switch is closed at t = 0 s, what is the charge on the capacitor at t = 9 ms?
A) 0 C
B) 37% of the minimum charge
C) 68% of the maximum charge
D) 68% of the minimum charge
E) 96% of the maximum charge

Question

Quizplus · Accepted Answer

After the switch is closed, the capacitor/resistor circuit begins to charge up. The time constant (τ) for this circuit is given by τ = RC, where R is the resistance and C is the capacitance. In this case, τ = (2.0 kΩ)(4.0 μF) = 8.0 ms.
At t = 5τ, the capacitor should be charged to approximately 99.3% of its maximum charge (which is Q = CV, where V is the voltage of the source). Therefore, at t = 9 ms, the capacitor should be charged to approximately 68% of its maximum charge, which is answer choice C.

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