A parallel plate capacitor with air as the dielectric has capacitance C . A slab of dielectric constant K and having the same thickness as the separation between the plates is introduced so as to fill one-fourth of the capacitor as shown in the figure. The new capacitance will be

Step-by-step solution

The condenser with air as the dielectric has capacitance C₁= ₀ d ( 3 A 4 )= 3 ₀ A 4 d Similarly, the condenser with K as the dielectric constant has capacitance C₂= ₀ K d ( A 4 )= ₀ A K 4 d Since, C₁ and C₂ are in parallel C_ net =C₁+C₂= 3 ₀ A 4 d + ₀ A K 4 d = ₀ A d [ 3 4 + K 4 ]= C 4 (K+3)