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

Answer 1

Answer: (D)

The capacitance of parallel plate air capacitor $C=\frac{\varepsilon_{o} A}{d}\,\,\,...(i)$
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
$C=\frac{K \varepsilon_{0} A'}{d'}$
Given, $A'=A, d'=2 d, C'=2 C$
$\therefore 2 C=\frac{K \varepsilon_{o} A}{2 d} \,\,\,...(ii)$
Equating Eqs. (i) and (ii), we get $K=4$