Question

At time t=0-, the circuit is in steady state condition. At time t=0+, the switch
is open. Find the voltage vc(t). At what time, the current through the capacitor will be
zero? What is the maximum voltage across the capacitor?

Answer 1

The moment switch is opened, voltage variation takes place across the capacitor as follows-

$V_c(t) = V_0(1-e^{-\frac{t}{RC}})$

Here, $\frac{1}{RC}$ is the time constant.

On putting limit of (t) tends to zero in the above equation, we get-

$$V_c(t\to \infin) = lim_{t\to\infin}(V_0(1-e^{-\frac{t}{RC}}))$$

= $V_0$

Therefore, after long time, the maximum capacitor voltage will be $V_0$

Since the capacitor is charged with polarity opposite to that of the battery, the current in the circuit will be zero after a very long time. Ideally, it will never be zero, but practically, it will take few seconds to few minutes depending upon the capacitance of the capacitor.