$512$ 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 ......... $V.$

What is the effective capacitance between points $X$ and $Y$ in the given circuit? (All capacitors are in $\mu F$)

Each plate of a parallel plate capacitor has a charge $q$ on it. The capacitor is now connected to a battery. Now,

When a potential difference of $10^{3} \, V$ is applied between $A$ and $B$, a charge of $0.75 \, mC$ is stored in the circuit. The value of $C$ is (in $\mu F$):

Three capacitors $C_1, C_2$ and $C_3$ are connected as shown in the figure to a battery of $V$ volt. If the capacitor $C_3$ breaks down electrically,the change in total charge on the combination of capacitors is

$A$ parallel-plate capacitor is connected to a cell. Its positive plate $A$ and its negative plate $B$ have charges $+Q$ and $-Q$ respectively. $A$ third plate $C$, identical to $A$ and $B$, with charge $+Q$, is now introduced midway between $A$ and $B$, parallel to them. Which of the following are correct?