$A$ $2\ \mu F$ 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: $\log_{10} 2.5 = 0.4$)

Find $I_1$ and $I_2$ at steady state.

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 figure shows an experimental plot for discharging of a capacitor in an $R-C$ circuit. The time constant $\tau$ of this circuit lies between

$A$ resistance $R$ and a capacitance $C$ are connected in series to a battery of negligible internal resistance through a key. The key is closed at $t = 0$. If after $t \, s$ the voltage across the capacitance is seven times the voltage across $R$,the value of $t$ is:

$A$ capacitor is discharging through a resistor $R$. Consider in time $t_{1}$,the energy stored in the capacitor reduces to half of its initial value and in time $t_{2}$,the charge stored reduces to one-eighth of its initial value. The ratio $t_{1} / t_{2}$ will be ................