Question

The capacity of a parallel plate condenser without any dielectric is C. If the distance between the plates is doubled and the space between the plates is filled with a substance of dielectric constant $3$, the capacity of the condenser becomes:

• A. $\frac{3}{4}C$
• B. $\frac{9}{2}C$
• C. $\frac{2}{3}c$
• D. $\frac{3}{2}C$

Answer 1

Answer: (D)

$\frac{3}{2}C$

The capacitance of a parallel plate capacitor is given by

$C=\frac{{\epsilon }_o{\epsilon }_{r}A}{d}$,

where $A$ is the area of the plate and $d$ is the distance between them.

In the first case, there was no dielectric medium, i.e., ${\epsilon }_r=1$.

So we have $C=\frac{{\epsilon }_{o}A}{d}$

In the second case, the distance is doubled, i.e., $2d$ and a substance of dielectric constant $3$ is inserted between the plates.

Hence capacitance will change to

$C^{\prime }=\frac{3{\epsilon }_{o}A}{2d}$

So, $\frac{C^{\prime }}{C}=\frac{3}{2}$

$⟹C^{\prime }=\frac{3}{2}C$