A parallel plate air capacitor has a capacitance C . When it is half filled as show in figure with a dielectric constant K = 5 , the percentage increase in the capacitance is _______.

Step-by-step solution

Initial capacitance of the air capacitor is given by: C = ₀ A d When the capacitor is half-filled with a dielectric of thickness d/2 , it can be considered as two capacitors connected in series. Capacitance of the dielectric-filled part: C₁ = K ₀ A d/2 = 2K ₀ A d = 2KC Capacitance of the air-filled part: C₂ = ₀ A d/2 = 2 ₀ A d = 2C The equivalent capacitance C_ eq of the series combination is: C_ eq = C₁ C₂ C₁ + C₂ = (2KC)(2C) 2KC + 2C = 2K K+1 C Substituting K = 5 : C_ eq = 2(5) 5+1 C = 10 6 C = 5 3 C The increase