How long does it take to charge a 50-µF capacitor to 90% of its maximum value through a 100-Ω resistor?
A)11.5 ms
B)87 s
C)2.3 µs
D)89 ns
E)1.2 s

Question

Quizplus · Accepted Answer

The time to charge a capacitor to a certain percentage of its maximum value can be calculated using the formula $t = -\tau \ln(1 - \frac{V}{V_{max}})$, where $\tau = RC$ is the time constant of the circuit. For a 50-µF capacitor and a 100-Ω resistor, $\tau = 50 \times 10^{-6} F \times 100 \Omega = 5 \times 10^{-3} s = 5 ms$. To charge to 90% of its maximum value, $t = -5 ms \ln(1 - 0.9) = 5 ms \ln(10) \approx 11.5 ms$.

How Long Does It Take to Charge a 50-µF Capacitor