Question

A dielectric slab of dielectric constant K and thickness t is introduced between the two plates of a capacitor of plate-separation d (>t) and common area A. The capacitance of this system is given as:

`C = (∈_o"A")/((d-t)+(t/k))`

How does the capacitance C modify in each of the following cases?

1. The dielectric slab covers half the distance of separation between the two plates.
2. The whole space between the plates is filled with the dielectric.

Answer 1

(a) Using t = `d/2`

Substituting in the given formula and calculating,

C = `(∈_oA)/([(d-d/2)+d/(2K)])`

C = `(2∈_o "AK")/([d(K+1)])`

(b) The whole space between the plates is filled with the dielectric implies, t = d, so C = `(K∈_o"A")/d`