Two identical parallel plate capacitors $A$ and $B$ are connected to a battery of $V$ volts with the switch $5$ closed. The switch is now opened and the free space between the plates of the capacitors is filled with a dielectric of dielectric constant $K$. Find the ratio of the total electrostatic energy stored in both capacitors before and after the introduction of the dielectric.

The insulated plates of a parallel plate capacitor has a charge density $\sigma$. Show that the wark done in changing the distance from $d_1$ to $d_2$ is

$U=\frac{{\sigma }^{2}A}{2{\epsilon }_0\kappa }\left(d_2-d_1\right)$.

The capacitors $C_1, C_2$, having plates of area $A$ each, are connected in series, as shown. Compare the capacitance of this combination with the capacitor $C_3$, again having plates of area $A$ each, but 'make up' as shown in figure below.

Three identical parallel plate (air) capacitors $C_1, C_2, C_3$ have capacitances $C$ each. The space between their plates is now filled with dielectrics as shown. If all the three capacitors, still have equal capacitances, obtain the relation between the dielectric constants $k_1, k_2, k_3$ and $k_4$.

Between the plates of a parallel-plate capacitor of area $A$, a copper plate sits on a dielectric slab of $k=2$, as shown in figure below. Find the equivalent capacitance of this arrangement.

What is the capacitance of arrangement of $4$ plates of area $A$ at distance d in air in Figure below?

What is the capacitance of arrangement of $4$ plates of area $A$ at distance $d$ in air in Figure below?