A certain capacitor, in series with a 720- $\Omega$ resistor, is being charged.At the end of 10 ms its charge is half the final value.The capacitance is about:
A)9.6 $\mu$F
B)14 $\mu$F
C)20 $\mu$F
D)7.2 F
E)10 F

Question

A certain capacitor, in series with a 720- $\Omega$  resistor, is being charged.At the end of 10 ms its charge is half the final value.The capacitance is about:
A)9.6 $\mu$F
B)14 $\mu$F
C)20 $\mu$F
D)7.2 F
E)10 F

Quizplus · Accepted Answer

The time constant of the RC circuit is given by $RC$, which is equal to $720 	ext{ }\Omega \cdot C$. Since it takes 10 ms for the charge to reach half of the final value, we can use the time constant to find the ratio of the charge at 10 ms to the final charge:
$$\frac{Q(10	ext{ ms})}{Q_f}=\frac{1}{2}=e^{-10	ext{ ms}/(RC)}$$
Solving for $C$, we get:
$$C=\frac{10	ext{ ms}}{720	ext{ }\Omega \ln 2} \approx 20	ext{ }\mu	ext{F}$$
Therefore, the answer is choice C: 20 $\mu$F.

A Certain Capacitor, in Series with a 720- Ω\OmegaΩ Resistor, Is Being Charged

A Certain Capacitor, in Series with a 720- $\Omega$ Resistor, Is Being Charged