$512$ identical drops of mercury are charged to a potential of $2 \ V$ each. The drops are joined to form a single drop. The potential of this drop is ......... $V.$

The charge (in $\mu C$) on any one of the $2\,\mu F$ capacitors and the $1\,\mu F$ capacitor will be given respectively as:

In the circuit shown,the cell is ideal,with $emf$ $=$ $15$ $V$. Each resistance is of $3$ $\Omega$. The potential difference across the capacitor is.....$V$.

$A$ capacitor of capacity $C$ is connected to a battery of potential $V$ in parallel. The distance between its plates is reduced to half at once,while the battery remains connected. Then,the energy supplied by the battery to charge the capacitor to potential $V$ again is:

Calculate the amount of heat liberated in the circuit after closing the switch $S$.

Sixty-four conducting drops,each of radius $0.02 \ m$ and each carrying a charge of $5 \ \mu C$,are combined to form a bigger drop. The ratio of the surface charge density of the bigger drop to that of the smaller drop will be ............