A capacitor of capacitance C and a resistor of resistance R are connected in series.At time t = 0 the combination is connected across a battery of negligible internal resistance.When is the current through the resistor equal to half of its maximum value?
A)0.500 RC
B)0.693 RC
C)0.707 RC
D)0.721 RC

Question

Quizplus · Accepted Answer

The current through the circuit is given by $I=I_{max}e^{-t/(RC)}$, where $I_{max}$ is the maximum current that occurs at $t=0$. We want to find when $I=I_{max}/2$, which means:
\begin{align*}
\frac{I_{max}}{2} &= I_{max}e^{-t/(RC)} \
\frac{1}{2} &= e^{-t/(RC)} \
\ln\left(\frac{1}{2}ight) &= -\frac{t}{RC} \
t &= RC\ln(2) \approx 0.693 RC
\end{align*}Thus, the answer is B.

A Capacitor of Capacitance C and a Resistor of Resistance