Four parallel large plates separated by equal distance $d$ are arranged as shown in the figure. The area of the plates is $S$. Find the potential difference between plates $B$ and $C$, if plate $B$ is given a charge $Q$.

Two dielectric slabs of relative permittivities ${\epsilon }_{r_1}=2$ and ${\epsilon }_{r_2}=3$ thickness $d$ and $2d$ are filled in between the grounded parallel plates each of area $A$. If a battery of emf $\mathrm{\epsilon }$ is connected to the middle conducting plate, find the
(a) the capacitance of the system,
(b) the charge flowing through the battery,
(c) induced charges on the plates,
(d) energy stored in the system.

In the given figure the area of each plate is $A.$ The conducting plates are connected to a battery of emf $V$ volts. Find charges $q_1$ to $q_6.$

A number of capacitors, each of equal capacitance $C,$ are arranged as shown in the figure. The equivalent capacitance between $A$ and $B$ is

Three plates $A, B$ and $C$ each of area $50 \mathrm{c}{\mathrm{m}}^2$ have separation $3 \text{mm}$ between $A$ and $B$ and $3 \mathrm{m}\mathrm{m}$ between $B$ and $C$. The energy stored when the plates are fully charged is