In a parallel plate capacitor the separation between plates is 3 x . This separation is filled by two layers of dielectrics, in which one layer has thickness x and dielectric constant 3 k , the other layer is of thickness 2 x and dielectric constant 5 k . If the plates of the capacitor are connected to a battery, then the ratio of potential difference across the dielectric layers is

Step-by-step solution

Key Idea Capacitance of a parallel plate capacitor is give by relation, C= _r ₀ A d where, _r= dielectric constant, A= area of parallel plate and d= distance between the plate. Here, d₀=3 x, d₁=x, ₁=3 k, d₂=2 x and ₂=5 k The capacitor is shown in the figure below, Now, C₁=3 k ₀ A x and C₂=5 k ₀ A 2 x Since, m in series combination of capacitor, stored charge in each capacitor is same. So, V₁= Q C₁ and V₂= Q C₂ V₁= x 3 k ₀ A and V₂= 2 x 5 k ₀ A The ratio, V₁ V₂ = x 3 k ₀ A 2 x 5 k ₀ A = 5 3 2 = 5 6 Hence, option (d)