Find the resultant capacitance between the points $X$ and $Y$ of the combination of capacitors shown in Figure.

The outer cylinders of two cylindrical capacitors of capacitance $2.2 \mu F$ each are kept in contact and the inner cylinders are connected through a wire. A battery of emf $10 V$ is connected, as shown in Figure. Find the charge supplied by the battery to the inner cylinders.

In Figure below, ${\mathrm{C}}_1=1\mathrm{ }\mathrm{\mu F},\mathrm{ }{\mathrm{C}}_2=2\mathrm{ }\mathrm{\mu F}$ and ${\mathrm{C}}_3=3\mathrm{ }\mathrm{\mu F}$. Find the equivalent capacitance between points $A$ and $B$.
 

Four capacitors of equal capacitances are connected in series with a battery of  $10\mathrm{ }\mathrm{V},$ as shown in Figure. The middle point $B$ is connected to the earth. What will be the potentials of the points $A$ and $C$?

Determine the potential difference across the plates of each capacitor of the network shown in Fig. Take $E_2>E_1$. 

Find the potential difference between the points $A$ and $B$ of the arrangement shown in Fig. 

Determine the potential difference $V_A-V_B$ between points $A$ and $B$ of the circuit shown in Figure below. Under what condition is it equal to zero?

A variable capacitor has $n$ plates and the distance $r$ between two successive plates is $d$. Determine its capacitance.

A network of four capacitors each of $12\mathrm{ }\mathrm{\mu F}$ capacitance is connected to a $500\mathrm{ }\mathrm{V}$ supply as shown in Figure. Determine equivalent capacitance of the network.