Question

If in one case an asbestos sheet of thickness $t(<d)$ is introduced between the plates of a parallel plate capacitor and in other case an aluminium slab of same thickness is introduced, then

• A. Capacitance is more when the medium is asbestos as compared to aluminium.
• B. Capacitance is the same for both the media.
• C. Capacitance is more when the medium is aluminium as compared to asbestos.
• D. Insufficient information

Answer 1

The correct option is C Capacitance is more when the medium is aluminium as compared to asbestos.

As we know that capacitance of partially filled dielectric slab of thickness $t$ and dielectric constant $K$ is given by

$C=\frac{{ϵ}_{0}A}{d-t+\frac{t}{K}}$

So, when the dielectric medium is asbestos $(K>1)$

$C_1=\frac{{ϵ}_{0}A}{d-t+\frac{t}{K}}$

And, when the dielectric medium is aluminium $(K=\infty )$, since field inside the metal(aluminium) is zero.

$C_2=\frac{{ϵ}_{0}A}{d-t}$

Clearly, the denominator of $C_1$ is greater than $C_2$, which implicates that $C_2>C_1$

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

Key concept- $1.)$ Capacitance with partial dielectric is given by $C=\frac{{ϵ}_{0}A}{d-t+\frac{t}{K}}$ $2.)$ Aluminium is a metal.