A parallel plate air capacitor has capacitance CP. It is equally filled with parallel layers of materials of dielectric constants K₁ and K₂. Now its capacity becomes CK. The ratio CP to CK is (a) K₁ + K₂ (b) (K₁+K₂)/(K₁K₂) (c) (K₁+K₂)/(2K₁K₂) (d) (2K₁K₂)/(K₁+K₂)

Answer: (c). Layers parallel to the plates, each of thickness d/2, act in series. Each layer: C₁ = 2K₁CP, C₂ = 2K₂CP. CK = (C₁C₂)/(C₁ + C₂) = (2K₁K₂CP)/(K₁ + K₂). So (CP)/(CK) = (K₁ + K₂)/(2K₁K₂), answer (c).

A parallel plate air capacitor has capacitance CP. It is equally… | MHT CET 2025 (20 Apr, Shift 2)

Q29MHT CET 2025 · 20 APR · SHIFT 2Easy

Dielectrics

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

Show answer and solution

Answer: (c)

Layers parallel to the plates, each of thickness $\frac{d}{2}$ , act in series.
Each layer: $C_1 = 2K_1C_P$ , $C_2 = 2K_2C_P$ .
$C_K = \frac{C_1C_2}{C_1 + C_2} = \frac{2K_1K_2C_P}{K_1 + K_2}$ .
So $\frac{C_P}{C_K} = \frac{K_1 + K_2}{2K_1K_2}$ , answer (c).

Report a mistake

Dielectrics question from MHT CET 2025 (20 Apr, Shift 2)

More questions on Dielectrics