Compare the capacitance of a parallel plate capacitor with and without the dielectric medium.

Explanation

A parallel plate capacitor consists of two large plane parallel conducting plates separated by a small distance . Let A be the area of each plate and d be the distance between them. The two plates have charges (Q) and -(Q) while the surface charge densities are `(sigma)` and -`(sigma)` respectively. Electric field in the outer region of I and II.
`E=sigma/(2epsilon_0)-sigma/(2epsilon_0)=0`
In the region between the plates (1) and(2)
`E=sigma/(2epsilon_0)+sigma/(2epsilon_0)=sigma/epsilon_0`
`E=sigma/epsilon_0=Q/(Aepsilon_0)`...(1) where `sigma=Q/A`
As the electric field E is equal to the potential gradient , for uniform electric field.
`E=v/d`
v=Ed ....(2)
Substituting (2) in equation (1) ,
`V=Q/(Aepsilon_0)d`
The capacitance C of the parallel plate capacitor is
`C=Q/V=Q/(Q//Aepsilon_0xxd)=Q/Qxx(Aepsilon_0)/d`
`C=(Aepsilon_0)/d`