$A$ $4\,\mu F$ capacitor is charged to $400\,V$ and then its plates are joined through a resistance of $1\,k\Omega$. The heat produced in the resistance is ............... $J$.

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 connected to a $20\, V$ battery through a resistance of $10\, \Omega$. It is found that the potential difference across the capacitor rises to $2\, V$ in $1\, \mu s$. The capacitance of the capacitor is $....\, \mu F$. Given: $\ln(10/9) = 0.105$.

In the $R-C$ circuit shown in the figure, the total energy of $3.6 \times 10^{-3} \ J$ is dissipated in the $10 \ \Omega$ resistor when the switch $S$ is closed. The initial charge on the capacitor is ..... $\mu C$.

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

Two identical capacitors $A$ and $B$ are charged to the same potential $V$ and are connected in two circuits at $t = 0,$ as shown in the figure. The charge on the capacitors at time $t = CR$ are respectively: