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 \varepsilon_{o} A}{d} $
Given, $d_{1}=d, $
$d_{2}=\frac{d}{2}, $
$K_{1}=K, $
$K_{2}=2 \,K $
$\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 2 K} $
$\frac{C_{1}}{C_{2}}=\frac{1}{4}$
$\Rightarrow C_{2}=4 C_{1}$
Hence, capacitance increases four times.