$A$ charged capacitor is disconnected from the battery and if the distance between the two plates of the capacitor is increased then . . . . . . .

The ratio of potential difference that must be applied across parallel and series combination of two capacitors $C_1$ and $C_2$ with their capacitance in the ratio $1: 2$ so that energy stored in these two cases becomes same is

Five capacitors together with their capacitances are shown in the adjoining figure. The potential difference between the points $A$ and $B$ is $60\, V$. The equivalent capacitance between the points $A$ and $B$ and the charge on the $5\, \mu F$ capacitor will be respectively:

$A$ conducting sphere of radius $a$ has charge $Q$ on it. It is enclosed by a neutral conducting concentric spherical shell having inner radius $2a$ and outer radius $3a$. Find the electrostatic energy of the system.

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 $INCORRECT$?

$A$ parallel plate capacitor of capacitance $C$ is connected to a battery and is charged to a potential difference $V$. Another capacitor of capacitance $2C$ is connected to another battery and is charged to a potential difference $2V$. The charging batteries are now disconnected and the capacitors are connected in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is