An air capacitor, a capacitor with a dielectric and a capacitor with a conducting slab (thickness one half the separation between the plates of parallel plate air capacitor are introduced in both cases) has capatity C₁, C₂ and C₃ respectively then :

The value of a capacitor formed by thin metallic foil is 2 µF. The foil is attached to both sides of a paper having a thickness of 0.015 mm. The dielectric constant of the paper is 2.5 and its breadth is 40 mm. The length of the foil used is :

Seven capacitors each of capacitance $2 \mathrm{\mu F}$ are to be connected to have a total capacity of $\frac{10}{11} \mathrm{\mu F}$. Which will be the combination shown?

An infinite number of identical capacitors each of capacitance $1 \mathrm{\mu F}$ are connected as in the adjoining figure. Then the equivalent capacitance between $A$ and $B$ is:

$N$ identical capacitors are joined in parallel and the combination is charged to a potential $V$. Now if they are separated and then joined in series then the energy of combination will

A capacitance of value $4 \mathrm{\mu F}$ charged to $50 \mathrm{V}$ is connected with another capacitance of value $2 \mathrm{\mu F}$ charged to $100 \mathrm{V}$, in such a way that plates of similar charges are connected together. The total energy in multiples of ${10}^{-2} \mathrm{J}$ before joining and after joining will be:

A $3 \mathrm{\mu F}$ capacitor is charged to a potential of $300 \mathrm{V}$ and $2 \mathrm{\mu F}$ capacitor is charged to $200 \mathrm{V}$. The capacitors are then connected in parallel with plates of opposite polarities join together. What amount of charge will flow, when the plates are so connected?

Two parallel plate capacitors whose capacities are$C$ and $2C$ respectively, are joined in parallel. These are charged by $V$ potential difference. If the battery is now removed and a dielectric of dielectric constant $K$ is filled in between the plates of the capacitor $C$, then, what will be the potential difference across each capacitor?

In the given circuit if point $C$ is connected to the earth and a potential of $+2000 \mathrm{V}$ is given to point $A$, then potential at $B$ is: