Question

1 A parallel plate capacitor, when there is
vacuum between the plates, has
capacitance Co, what will be its capacitance,
when
(i) thickness between the plate is doubled?
(ii) a sheet of thickness t of a dielectric of
relative permittivity K is introduced
between the plates?​

Answer 1

Given:

A parallel plate capacitor, when there is a vacuum between the plates, has

capacitance $\displaysyle \mathbf {c_0}$.

To find :

The capacitance of a parallel plate capacitor when

(i) thickness between the plate is doubled?

(ii) a sheet of thickness t of a dielectric of relative permittivity K is introduced

between the plates?​

Explanation:

1)

The capacitance of the parallel plate capacitor is given by

C = $\displaystyle \varepsilon _0$ $\displaystyle \frac{A}{d}$

where

A = area of two plates

d = thickness between two plates

Hense capacitance is inversely proportional to thickness.

C∝ $\displaystyle \frac{1}{d}$.

when thickness between the plate is doubled, capacitance decreases by$\displaystyle \mathbf { \frac{1}{4} }\ times.$

2)

A dielectric permittivity k is introduced between two plates when there is a medium between two plates like air, water.

∴ $\displaystyle \varepsilon = \varepsilon _0 \times k$

where $\varepsilon_0$ is the vaccum permittivity.

∴ $\displaystyle \mathbf {C=\mathbf \varepsilon \frac{A}{d} }$