Question

A parallel plate capacitor has the space between its plates filled by two slabs of thickness (d/2) each and dielectric  constant K₁ and K₂ If d is the plate separation of the capacitor, then capacity of the capacitor is………

(A) [(2d∈₀) / A] [(K₁ + K₂) / (K₁K₂)]

(B) [(2A∈₀) / d] [(K₁K₂) / (K₁ + K₂)]

(C) [(2Ad∈₀) / d] [(K₁ + K₂) / (K₁K₂)]

(D) [(2A∈₀) / d] (K₁ + K₂)

Answer 1

The correct option (B) [(2A∈₀)/d] [(K₁K₂)/(K₁ + K₂)]

Explanation:

After introducing dielectric of constants K₁ & K₂ capacitor acts as it consists of two capacitors each having plate of area A & separation (d/2) connected in series combination

(1/C₂) = [{1/(A∈₀K₁)} / (d/2)] + [{1/(A∈₀K₂)}/(d/2)]

∴ (1/C₂) = [1/(A∈₀/d)] [(1/2K₁) + (1/2K₂)]

∴ (1/C₂) = [1/{(2A∈₀)/d}] [(1/K₁) + (1/K₂)]

∴ C₂ = [(2A∈₀)/d] × [1/{(1/K₁) + (1/K₂)}]

= [(2A∈₀)/d] [(K₁K₂)/(K₁ + K₂)]