$A$ capacitor of capacitance $C = 1 \, \mu F$ is suddenly connected to a battery of $100 \, V$ through a resistance $R = 100 \, \Omega$. The time taken for the capacitor to be charged to $50 \, V$ is $.... \times 10^{-4} \, s$. (Take $\ln 2 = 0.69$)

$A$ 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:

$A$ $2500 \,\mu F$ capacitor is charged through a $1 \,k\Omega$ resistor by a $12 \,V$ d.c. source. The voltage across the capacitor after $5 \,s$ is ..... $V$.

The following circuit consists of a $5 \,\mu F$ capacitor,having a charge of $50 \,\mu C$ as shown. The switch is closed at $t=0$. The value of the current in the $2 \,M \Omega$ resistor at $t=0$ is ........... $\mu A$.

The capacitance of $C_1$ and $C_2$ shown in the diagram is $C$. $C_1$ is initially uncharged and $C_2$ is given a charge $2C\varepsilon$ as shown. Which of the following graph represents charge on plate $B$ of capacitor $C_2$ as a function of time?

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