An air parallel plate capacitor has capacity C. The capacity and distance between plates are doubled when immersed in a liquid then dielectric constant of the liquid is:

Question

An air parallel plate capacitor has capacity C. The capacity and distance between plates are doubled when immersed in a liquid then dielectric constant of the liquid is: (A) 1 (B) 2 (C) 3 (D) 4

Tardigrade Admin · Accepted Answer

The capacitance of parallel plate air capacitor

C = \frac{ε _{o} A}{d} ... (i)

where

A

is the area of each plate and

d

is the distance between the plates.
In a medium of dielectric constant

K

and with given condition

C = \frac{K ε _{0} A ^{'}}{d ^{'}}

Given,

A^{'} = A, d^{'} = 2 d, C^{'} = 2 C

∴ 2 C = \frac{K ε _{o} A}{2 d} ... (ii)

Equating Eqs. (i) and (ii), we get

K = 4

Q. An air parallel plate capacitor has capacity C. The capacity and distance between plates are doubled when immersed in a liquid then dielectric constant of the liquid is:

1

2

3

4

Q. An air parallel plate capacitor has capacity $C$ . The capacity and distance between plates are doubled when immersed in a liquid then dielectric constant of the liquid is: