CBSE Class 12 · 2024 · CapacitanceMultiple Choice

An air-filled capacitor with plate area

A

and plate separation

d

has capacitance

C_{0}

. A slab of dielectric constant

K

, area

A

and thickness

\frac{d}{5}

is inserted between the plates. The capacitance becomes

Answer: (C)

Solution

This is a series combination of an air gap

\frac{4 d}{5}

and a dielectric gap

\frac{d}{5}

\frac{1}{C} = \frac{4 d /5}{ε _{0} A} + \frac{d /5}{K ε _{0} A} = \frac{d}{5 ε _{0} A} (4 + \frac{1}{K}) = \frac{d ( 4 K + 1 )}{5 K ε _{0} A} .

C = \frac{5 K}{4 K + 1} \cdot \frac{ε _{0} A}{d} = [\frac{5 K}{4 K + 1}] C_{0}

— option (C).

CBSE Class 12 Board · 2024 · Single correct option