$A$ $4\,\mu F$ 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 ............... $J$.

$A$ $4 \mu F$ capacitor and a resistance of $2.5 \, M\Omega$ are in series with a $12 \, V$ battery. Find the time after which the potential difference across the capacitor is $3$ times the potential difference across the resistor. (Given $\ln(2) = 0.693$)

$A$ circuit element is placed in a closed box. At time $t=0$,a constant current generator supplying a current of $1\, A$ is connected across the box. The potential difference across the box varies according to the graph shown in the figure. The element in the box is:

After the switch shown in Figure $A$ is closed,there is a current $i$ through the resistance $R$. Figure $B$ indicates current variation curves $a, b, c,$ and $d$ for four sets of values of $R$ and capacitance $C$:
$(i)$ $R_0$ and $C_0$
$(ii)$ $2R_0$ and $C_0$
$(iii)$ $R_0$ and $2C_0$
$(iv)$ $2R_0$ and $2C_0$
Which set goes with which curve?

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

$A$ capacitor of $4\, \mu F$ is connected to a $15\, V$ supply through a $1\, M\Omega$ resistance. The time taken by the capacitor to charge up to $63.2\%$ of its final charge will be......$s$.