In the transient circuit shown,the time constant of the circuit is:

$A$ capacitor of capacity $C$ is charged to a steady potential difference $V$ and connected in series with an open key and a pure resistor $R$. At time $t = 0$,the key is closed. If $I$ is the current at time $t$,a plot of $\log I$ against $t$ is as shown in $(1)$ in the graph. Later,one of the parameters,i.e.,$V, R,$ or $C$,is changed while keeping the other two constant,and the graph $(2)$ is recorded. Then:

$A$ capacitor of capacity $0.1 \mu F$ connected in series to a resistor of $10 M \Omega$ is charged to a certain potential and then made to discharge through the resistor. The time in which the potential will take to fall to half its original value is (Given, $\log _{10} 2=0.3010$ ) (in $\,s$)

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

The capacitor $C$ is initially without charge. $X$ is now joined to $Y$ for a long time,during which $H_1$ heat is produced in the resistance $R$. The $X-Y$ connection is removed and $X$ is now joined to $Z$ for a long time,during which heat $H_2$ is produced in $R$.

$A$ $2\ \mu F$ capacitor and an $R$ resistor are connected in series to a $200\ V$ $DC$ supply. $A$ neon bulb is connected across the capacitor,which glows at $120\ V$. Calculate the value of $R$ so that the bulb glows for $5\ s$ after the switch is closed. (Given: $\log_{10} 2.5 = 0.4$)