MHT CET202520 Apr 2025Evening ShiftPhysicsCapacitanceActual
A parallel plate air capacitor has capacitance C_p . It is equally filled with parallel layers of materials of dielectric constants K ₁ and K ₂ . Now its capacity becomes C_K . The ratio C_P to C_K is
Options
- AK ₁+ K ₂
- BK ₁+ K ₂ ~K ₁ ~K ₂
- CK₁+K₂ 2 K₁ K₂
- D2 ~K ₁ ~K ₂ ~K ₁+ K ₂
Correct answer
C. K₁+K₂ 2 K₁ K₂
Step-by-step solution
Capacitance of parallel plate air capacitor The capacitance of an air capacitor with plate area A and plate separation d is C_p = ₀ A d . Capacitance with dielectric layers When filled with two dielectric layers of equal thickness d/2 and dielectric constants K₁ and K₂ , the configuration forms two capacitors in series. The individual capacitances are C₁ = 2K₁ ₀ A d and C₂ = 2K₂ ₀ A d . The equivalent capacitance satisfies 1 C_K = 1 C₁ + 1 C₂ = d 2 ₀ A ( 1 K₁ + 1 K₂ ) , yielding C_K = 2 ₀ A d ( K₁ K₂ K₁ + K₂ ) . Ra