What is capacitor ? And explain capacitance. Give its $\mathrm{SI}$ unit.

A capacitor is a system of two conductors separated by an insulator which is shown in figure. Definition : "Arrangement in which two good conductors of arbitrary shape and volume are arranged close to one another, but separated from each other is called capacitor."

Suppose the conductors have charges $Q_{1}$ and $Q_{2}$ and potentials $V_{1}$ and $V_{2}$. The potential difference is $\mathrm{V}=\mathrm{V}_{1}-\mathrm{V}_{2}$.

Single conductor can be used as a capacitor by assuming the other at infinity.

The conductors may be charged by connecting them to the two terminals of a battery.

$\mathrm{Q}$ is called the charge of the capacitor, though this infact is the charge (magnitude) on one of the conductors.

The total charge of the capacitor is zero.

The electric field $\vec{E}$ in the capacitor is from $+Q$ charge to $-Q$ charge it is proportional to the charge $Q$.

$\therefore \mathrm{E} \propto \mathrm{Q}$

The potential difference $\mathrm{V}$ is the work done per unit positive charge in taking a small test charge from the conductor 2 to 1 against the field. Hence, $V$ is also proportional to the charge $Q$. $\therefore \mathrm{V} \propto \mathrm{Q}$

Hence, ratio $\frac{Q}{V}$ is constant.

$\therefore \quad C=\frac{Q}{V}$

$\ldots$ $(1)$

$\mathrm{C}$ is the capacitance of capacitor.

Definition of Capacitance : The ratio of the amount of charge on the plate of parallel capacitor and the potential difference between two plates is known as capacitance of capacitor.

Hence, capacitance is independent of $Q$ or $V$.