JEE Main2014PhysicsCapacitanceActual
The gap between the plates of a parallel plate capacitor of area A and distance between plates d , is filled with a dielectric whose relative permittivity varies linearly from ϵ 1 at one plate to ϵ 2 at the other. The capacitance of the capacitor is
Options
- Aϵ 0 ∈ 2 - ∈ 1 A d ln ∈ 2 / ∈ 1
- Bϵ 0 ∈ 2 + ∈ 1 A 2 d
- Cϵ 0 ∈ 1 + ∈ 2 A d
- Dϵ 0 A d ln ∈ 2 / ∈ 1
Correct answer
A. ϵ 0 ∈ 2 - ∈ 1 A d ln ∈ 2 / ∈ 1
Step-by-step solution
1 d C = d x ϵ 0 ϵ A = d x ϵ 0 ϵ 1 + ϵ 2 - ϵ 1 d x A 1 C = ∫ 1 d C = 1 ∈ 0 A ∫ 0 x d x ∈ 1 + ∈ 2 - ∈ 1 d = ln ∈ 2 / ∈ 1 d ∈ 0 A ∈ 2 - ∈ 1 C = ∈ 0 A ∈ 2 - ∈ 1 ln ∈ 2 / ∈ 1 · d