Figure shows an arrangement of identical metal plates placed parallel to each other. The diagram also shows the variation of potential between the plates. Using the details given in the diagram, find the equivalent capacitance connected across the battery (separation between the consecutive plates is equal to $l$ and the cross-sectional area of each plate is $A$).

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

The capacitance of an infinite circuit formed by the repetition of the same link consisting of two identical capacitors, each with capacitance $C$ (figure), is