Question

A parallel plate capacitor with air between the plates has a capacitance of 2pF. The capacitance if the distance between the plates is reduced by half, and the space between them is filled with a substance of dielectric constant 6 is

• A. 24pF
• B. 12pF
• C. 6pF
• D. 18pF

Answer 1

Answer: (A)

We know,

$C=\frac{Ak{\epsilon }_0}{d}$

Given,

For $k=1,$

$C=\frac{A{\epsilon }_0}{d}=2$

For k=6, and $d\to \frac{d}{2}$

$C=\frac{A\times 6{\epsilon }_0}{\frac{d}{2}}$

$C=\frac{12A{\epsilon }_0}{d}=12C=24pF$

Option $\text{B}$ is the correct answer