What is a parallel plate capacitor? Derive an expression for the capacitance of a parallel plate capacitor?

Explanation

Parallel Plate Capacitor : When the two plates of the capacitor are plane and parallel to each other, then it is called parallel plate capacitor.
Capacitance of a Parallel Plate Capacitor: A parallel plate capacitor consists of two plane conducting metallic plates P and Q parallel to each other,
Let d = distance between the plates P and Q of a capacitor. Let plate P is given the positive charge + q and plate Q is given negative charge - q.
`+sigma` and `-sigma` be the surface charge densities of plates P and Q respectively.
Electric field in-between the plates is given by:
`E = sigma/epsilon_(0)`......(i)

where `epsilon_(0)` is the absolute permittivity of the free space because in this case the medium between the plates is considered to be vacuum or air.
But magnitude of electric field, `E=V/d`
(E is uniform and `bot` to the plates)
where V is potential difference between the plates of the capacitor.
or, `V =Ed = (sigmad)/epsilon_(0)` [Using eqn. (i)]
`therefore` Surface charge density `sigma =q/A`
where A = Area of each plate of the capacitor.
`V = (qd)/(epsilon_(0)A)`
But, `C =q/V`
`C =q/(qd//epsilon_(0)A)`
`C = (epsilon_(0)A)/d`
which is the required expression for tlje capacity of a parallel plate capacitor.