For the given input voltage waveform $V_{\text{in}}(t)$,the output voltage waveform $V_0(t)$ across the capacitor is correctly depicted by:

$A$ charged capacitor is allowed to discharge through a resistor by closing the key at the instant $t = 0$. At the instant $t = (\ln 4) \, \mu s$,the reading of the ammeter falls to half the initial value. The resistance of the ammeter is equal to

In the circuit shown below,the key is pressed at time $t=0$. Which of the following statement$(s)$ is(are) true?
$(A)$ The voltmeter displays $-5 \ V$ as soon as the key is pressed,and displays $+5 \ V$ after a long time.
$(B)$ The voltmeter will display $0 \ V$ at time $t=\ln 2 \ s$.
$(C)$ The current in the ammeter becomes $1/e$ of the initial value after $1 \ s$.
$(D)$ The current in the ammeter becomes zero after a long time.

The charge across the capacitor in two different $RC$ circuits $1$ and $2$ are plotted as shown in the figure. Choose the correct statement$(s)$ related to the two circuits.

At time $t=0$,a battery of $10 \ V$ is connected across points $A$ and $B$ in the given circuit. If the capacitors have no charge initially,at what time (in seconds) does the voltage across them become $4 \ V$? [Take $\ln 5=1.6, \ln 3=1.1$]

$A$ capacitor is charged to a potential difference of $100\, V$ and then connected across a resistor. The potential difference across the capacitor decays exponentially with time. After $1\, s$,the potential difference across the capacitor plates is $80\, V$. What is the fractional loss of the stored energy?