First slide

Capacitance

Question

The capacity of a parallel plate condenser is C. If a dielectric of relative permittivity K and thickness equal to one-fourth of the plate separation is placed between the plates, then its capacity becomes C'. The value of C'/C will be

Easy

A

$\frac{4 K}{3 K + 1}$
B

$\frac{5 K}{4 K + 1}$
C

$\frac{2 K}{K + 1}$
D

$\frac{K}{2 (K + 1)}$

Solution

$C = \frac{ε_{0} A}{d}$
and $C^{'} = \frac{ε_{0} A}{d - \frac{d}{4} (1 - \frac{1}{K})} = \frac{4 ε_{0} A}{3 d + (d / K)}$
$= \frac{4 ε_{0} AK}{d (3 K + 1)} = \frac{4 KC}{(3 K + 1)}$

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