Three parallel plate air capacitors are connected in parallel. Each capacitor has plate area A/3 and separation between the plates is d, 2d and 3d respectively. The equivalent capacity of the combination is ( ₀ -permittivity of free space)

Step-by-step solution

The capacitance of a parallel plate capacitor is given by C = ₀ A' d' For the three capacitors, the capacitances are: C₁ = ₀ (A/3) d = ₀ A 3d C₂ = ₀ (A/3) 2d = ₀ A 6d C₃ = ₀ (A/3) 3d = ₀ A 9d Since the capacitors are connected in parallel, the equivalent capacitance is the sum of individual capacitances: C_ eq = C₁ + C₂ + C₃ C_ eq = ₀ A 3d + ₀ A 6d + ₀ A 9d C_ eq = ₀ A d ( 1 3 + 1 6 + 1 9 ) C_ eq = ₀ A d ( 6 + 3 + 2 18 ) = 11 ₀ A 18d Answer: 11 ₀ A 18d