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.

A capacitor consists of two air spaced concentric cylinders. The outer radius $b$ is fixed, and the inner is of radius $a$. If breakdown of air occurs at field strength than $Eb$ show that the inner cylinder should have 

(i) radius $a=\frac{b}{e}$ if the potential of the inner cylinder is to be maximum.

(ii) radius $a=\frac{b}{\sqrt{e}}$ if the energy per unit length of the system is to be maximum.