A battery of $10 \mathrm{V}$ is Connected to a capacitor of capacity $0.1 \mathrm{F}$. The battery is now removed and this capacitor is connected to a second uncharged capacitor. If the charge distributes equally on these two capacitors, find the total energy stored in the two capacitors. Further, compare this energy with the initial energy stored in the first capacitor.

Two medium od dielectric constant $K_1$ and $K_2$ are introduced according to given figure. If $\frac{K_1}{K_2}=3$ then calculate ratio of capacity of part $A$ and part $B$ and net capacity of system. (Area of each plate is $A$)

$X$ and $Y$ are two parallel plate capacitors having the same area of plates and same separation between the plates. $X$ has air between the plates and $Y$ contains a dielectric medium ${\epsilon }_r=5$.

(i) Calculate the potential difference between the plates of $X$ and $Y$.

(ii) What is the ratio of electrostatic energy stored in $X$ and $Y$?

The two identical parallel plates are given charges as shown in figure. If the plate area of either face of each plate is $A$ and separation between plate is $d$, then find the amount of heat liberate after closing the switch.

In the following circuit, the resultant capacitance between $A$ and $B$ is $1 \mathrm{\mu F}$. Find the value of $C$.

Five identical conducting plates $1,2,3,4$ and $5$ are fixed parallel to and equidistant from each other (see figure). Plates $2$ and  $5$ are connected by a conductor while $1$ and $3$ are joined by another conductor. The junction of $1$ and $3$ and the plate $4$ are connected to a source of constant e.m.f. $V_0$. Find

(i) the effective capacity of the system between the terminals of the source

(ii) the charges on plates $3$ and $5$.

Given: $d=$distance between any $2$ successive plates and $A=$area of either face of each plate.

When the switch $S$ in the figure is thrown to the left, the plates of capacitors $C_1$ acquire a potential difference $V$. Initially the capacitors $C_2$ and $C_3$ are uncharged. The switch is now thrown to the right. What are the final charges $q_1,q_2$ and $q_3$ on the corresponding capacitors.