$A$ capacitor of capacitance $C$ is connected to a battery of $V$ volts. Now,the distance between the plates of the capacitor is halved while keeping the charge constant,and it is again charged to $V$ volts. What is the energy supplied by the battery?

Seven capacitors each of capacitance $2 \mu F$ are to be connected in a configuration to obtain an effective capacitance $\left(\frac{10}{11}\right) \mu F$. The combination is

The potential differences that must be applied across the parallel and series combination of $3$ identical capacitors are such that the energy stored in them becomes the same. The ratio of the potential difference in the parallel combination to the series combination is:

$A$ capacitor of capacitance $5\,\mu F$ is connected as shown in the figure. The internal resistance of the cell is $0.5\,\Omega$. The amount of charge on the capacitor plate is......$\mu C$.

Two capacitors of equal capacitance $(C_1 = C_2)$ are shown in the figure. Initially,while the switch $S$ is open,one of the capacitors is uncharged and the other carries charge $Q_0$. The energy stored in the charged capacitor is $U_0$. After the switch is closed,the capacitors $C_1$ and $C_2$ carry charges $Q_1$ and $Q_2$,respectively; the voltages across the capacitors are $V_1$ and $V_2$; and the energies stored in the capacitors are $U_1$ and $U_2$. Which of the following statements is $INCORRECT$?

$27$ identical drops of mercury are charged simultaneously with the same potential of $10 \ V$. Assuming the drops to be spherical,if all the charged drops are made to combine to form one large drop,then its potential will be . . . . . . volt.