Find the equivalent capacitance of the combinations shown in the figure between the indicated points.

A finite ladder circuit is constructed by connecting several sections of $6 \mathrm{\mu F}, 8\mathrm{\mu F}$ capacitor combinations as shown in the figure. Circuit is terminated by a capacitor of capacitance $C$. Find the value of $C$, such that the equivalent capacitance of the ladder between the points $A$ and $B$  becomes independent of the number of sections in between?

The capacitance of a parallel plate capacitor with plate area $A$ and separation is $d$, is $C$. The space between the plates is filled with two wedges of dielectric constant $K_1$ and $K_2$ respectively (figure). Find the capacitance of the resulting capacitor.

A conducting sphere $S_1$ of radius $r$ is attached to an insulating handle. Another conducting sphere $S_2$ of radius R is mounted on an insulating stand. $S_2$ is initially uncharged. $S_1$ is given a charge $Q$, brought into contact with $S_2$ and removed. $S_1$ is then recharged such that the charge on it is again $Q$ & it is again brought into contact with $S_2$ & removed. This procedure is repeated $n$ times

(a) Find the electrostatic energy of $S_2$ after n such contacts with $S_1$ .

(b) What is the limiting value of this energy as $n\to \infty$?

Two capacitors of capacitances $2C \& C$ are connected in series with an inductor of inductance L. Initially capacitors have charges such that $V_B-V_A=4V_0\mathit{ }\&\mathit{ }{V}_{\mathit{C}}-V_D=V_0.$ Initial current in the circuit is zero. Find The maximum current that will flow in the circuit and the potential difference across each capacitor at that instant.