An initially uncharged capacitor $C$ is being charged by a battery of emf $E$ through a resistance $R$. Up to the instant when the capacitor is charged to a potential $E/2$, the ratio of the work done by the battery to the heat dissipated by the resistor is given by

$A$ 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 ................

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

$A$ capacitor is a perfect insulator for

$A$ capacitor of capacitance $C = 10 \, \mu F$ is connected to a battery of emf $\varepsilon = 2 \, V$ through a resistor $R$. It is observed that it takes $t = 50 \, ms$ for the charge on the capacitor to reach $q = 12.6 \, \mu C$. Calculate the resistance $R$ of the circuit in $k \Omega$. (Take $1/e \approx 0.37$)

In the circuit shown in the diagram,the capacitances of the capacitors $C_1$,$C_2$,and $C_3$ are $4\ \mu F$,$6\ \mu F$,and $12\ \mu F$ respectively. The switch $S$ remains closed for a long time. When the switch $S$ is opened,which of the following statements will be correct about the current flowing through the battery $B$?