$A$ parallel plate capacitor has capacitance $C$. If the charges on the plates are $Q$ and $-3Q$,find the potential difference between the plates.

The figure shows a diagonal symmetric arrangement of capacitors and a battery. The potentials of the points $B$ and $D$ are:

Three capacitors of capacitances $25 \mu F, 30 \mu F$ and $45 \mu F$ are connected in parallel to a supply of $100 \ V$. Energy stored in the above combination is $E$. When these capacitors are connected in series to the same supply,the stored energy is $\frac{9}{x} E$. The value of $x$ is . . . . . . .

What is the net force on a small electric dipole placed inside a parallel plate capacitor at steady state,if the plates are separated by $1 \ cm$? The circuit diagram is provided.

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

$A$ spherical conductor of radius $2\,m$ is charged to a potential of $120\,V$. It is now placed inside another hollow spherical conductor of radius $6\,m$. Calculate the potential to which the bigger sphere would be raised.