Question

The initial capacitance of a parallel plate capacitor with air as a medium is $C_0$. After introducing a conducting sheet of thickness $\frac{d}{6}$, where $d$ is the separation between the metal plates, the capacitance becomes $C$. Then $\frac{C}{C_0}$ is

• A. $\frac{5}{6}$
• B. $\frac{6}{5}$
• C. $\frac{8}{7}$
• D. $\frac{9}{5}$

Answer 1

The correct option is B $\frac{6}{5}$

Capacitance without dielectric is given by
$C_0=\frac{{ϵ}_{0}A}{d}$

Given:
Thickness of dielectric, $t=\frac{d}{6}$

Dielectric constant of a conductor is, $K=\infty$

Hence, new capacitance of capacitor become

$C=\frac{{ϵ}_{0}A}{d-t+\frac{t}{K}}=\frac{{ϵ}_{0}A}{d-\frac{d}{6}+\frac{t}{\infty }}$

$\Rightarrow C=\frac{6{ϵ}_{0}A}{5d}=\frac{6}{5}{C}_0$

$\Rightarrow \frac{C}{C_0}=\frac{6}{5}$

Hence, option $\left(b\right)$ is correct.