Question

If the distance between parallel plates of a Capacitor is halved and dielectric constant is Doubled then the capacitance will:

• A. remain the same
• B. increase 4 times
• C. increase 2 times
• D. decrease 2 times

Answer 1

Answer: (B)

In order to obtain high capacitance, plats of large area should be taken and kept close to each other.
The capacitance of a parallel plate capacitor of plate area $A$ and the distance $d$, between the plated is given by
$C=\frac{K{\epsilon }_{o}A}{d}$
Given, $d_1=d,$
$d_2=\frac{d}{2},$
$K_1=K,$
$K_2=2K$
$\therefore \frac{C_1}{C_2}=\frac{K_1}{d_1}\times \frac{d_2}{K_2}$
$=\frac{K}{d}\times \frac{d}{2\times 2K}$
$\frac{C_1}{C_2}=\frac{1}{4}$
$\Rightarrow C_2=4C_1$
Hence, capacitance increases four times.