Briefly explain the principle of a capacitor. Derive an expression for the capacitance of a parallel plate capacitor, whose plates are separated by a dielectric medium.

Explanation

Principle of a Capacitor: A capacitor works on the principle that the capacitance of a conductor increases appreciable when an earthed conductor is brought near it. Thus, a capacitor has two plates separated by a distance having equal and opposite charges.
Parallel Plate Capacitor: Consider a parallel plate capacitor having two plane metallic plates A and B, placed parallel to each other as shown in the figure. The plates carry equal and opposite charges + Q and – Q respectively.
In general, the electric field between the plates due to charges +Q and –Q remains uniform, but at the edges, the electric field lines deviate outward. If the separation between the plates is much smaller than the size of plates, the electric field strength between the plates may be assumed uniform.

Suppose A be the area of each plate, ‘d’ the separation between the plates, K the dielectric constant of medium between the plates. If is the magnitude of charge density of plates, then `sigma=(Q)/(A)`
The electric field strength between the plates
`E=(sigma)/(Kepsi_(0)),` where `epsi_(0)=` permittivity of free space . . . (i) The potential difference between the plates, `V_(AB)=Ed=(sigmad)/(Kepsi_(0))` . . (ii)
Putting the value of `sigma`, we get `V_(AB)=((Q//A)d)/(Kepsi_(0))=(Qd)/(Kepsi_(0)A)`
`therefore`Capacitance of capacitor, `C=(Q)/(V_(AB))=(Q)/((Qd//(Kepsi_(0)A))) or C=(Kepsi_(0)A)/(d)` . .. (iii)
This is a general expression for capacitance of parallel plate capacitor. Obviously, the capacitance is directly proportional to the dielectric constant of medium between the plates.
For air capacitor `(K=1)`, capacitance `C=(epsi_(0)A)/(d)`. this is expression for the capacitance of a parallel plate air capacitor. Obviously, the capacitance of parallel plate (air) capacitor is
(i) Directly proportional to the area of each plate.
(ii) Inversely proportional to the distance between the places. (iii) Independent of metal plates.