Question

The circular plates A and B of a parallel plate air capacitor have a diameter of 0.1m and are 2 × 10^–3m apart. The plates C and D of a similar capacitor have a diameter of 0.12 m and are 3 × 10^–3 m apart. Plate A is earthed. Plates B and D are connected together. Plate C is connected to the positive pole of a 120V battery whose negative is earthed, The energy stored in the system is 

(A) 0.1224μJ 

(B) 0.2224μJ 

(C) 0.4224μJ 

(D) 0.3224μJ

Answer 1

The correct option (A) 0.1224μJ   

Explanation:

capacitance of capacitor AB, C₁ = (A∈₀/d₁)

capacitance of capacitor CD, C₂ = [(A₂∈₀)/d₂]

combined capacitance : C = [(C₁C₂)/(C₁ + C₂)] = [(A₁A₂∈₀) / (A₁d₁ + A₂d₁)]

∴ C = [(π∈₀r₁²r₂²)/(r₁²d₂ + r₂²d₁)]

= π∈₀[{(5 × 10^–2)² (6 × 10^–2)²}/{(5 × 10^–2)² × 3 × 10^–3 + (6 × 10^–2)² × 2 × 10^–3}]

= (30/49)π∈₀

Energy stored = U = (1/2)CV²

= (1/2) [(30/49)π∈₀] (120)²

= 0.1224 × 10^–6

= 0.12μJ