A 20-$\mu$F capacitor is charged to 200 V and is then connected across a 1000-$\Omega$ resistor.The amount of charge on the capacitor after 10 ms is approximately
A)14 mC
B)2.4 mC
C)0.80 mC
D)1.6 mC
E)3.2 mC

Question

Quizplus · Accepted Answer

The charge on the capacitor after a time $t$ can be calculated using the formula $Q = Q_0 e^{-\frac{t}{RC}}$, where $Q_0$ is the initial charge, $R$ is the resistance, $C$ is the capacitance, and $t$ is the time. The initial charge $Q_0 = CV = 20 \times 10^{-6} F \times 200 V = 4 \times 10^{-3} C = 4 mC$. With $R = 1000 \Omega$ and $C = 20 \times 10^{-6} F$, the time constant $\tau = RC = 1000 \times 20 \times 10^{-6} = 0.02 s = 20 ms$. After $10 ms$, $Q = 4 mC \times e^{-\frac{10 ms}{20 ms}} = 4 mC \times e^{-0.5} \approx 2.4 mC$.

A 20- μ\muμ F Capacitor Is Charged to 200 V and Is Then

A 20- $\mu$ F Capacitor Is Charged to 200 V and Is Then