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.

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.

The lower plate of a parallel plate capacitor lies on an insulating plane. The upper plate is suspended from one end of a balance. The two plates are joined together by a thin wire and subsequently disconnected. The balance is achieved. A voltage $5000\mathrm{V}$ is applied between the plates, what additional weight should be placed to maintain the balance? The separation between the plates $d=5 \mathrm{mm}$ and the area of each plate $A=100 {\mathrm{cm}}^2$.

Find the charge which flows from point $A$ to $B$, when switch is closed.

Three capacitors of $2\mathrm{\mu F},3\mathrm{\mu F}$ and $5\mu F$ are individually charged with batteries of emf's $5\mathrm{V},20\mathrm{V}$ and $10 \mathrm{V}$ respectively. After disconnecting from the voltage sources, these capacitors are connected as shown in figure with their positive polarity plates are connected to $A$ and negative polarity s earthed. Now a battery of $20\mathrm{V}$ and an uncharged capacitor of $4\mathrm{\mu F}$ capacitance are connected to the junction $A$ as shown with a switch $S$. When switch is closed, find (i) the potential of the junction $A$. (ii) final charges on all four capacitors.