The space between the plates of a parallel plate capacitor of capacitance C (without any dielectric) is now filled with three dielectric slabs of dielectric constants K₁ = 2, K₂ = 3 and K₃ = 5 (as shown in figure). If new capacitance is n/3C then the value of n is ______. Numerical answer type. Work it out, then open the answer.

Answer: 8. Top layer ( K₁, area A, thickness d/2): C₁ = 2K₁ C = 4C. Bottom layer: K₂ and K₃ in parallel, each area A/2, thickness d/2: K₂ C + K₃ C = 8C. Top and bottom in series: C' = (4C × 8C)/(12C) = 8/3C So n = 8.

The space between the plates of a parallel plate capacitor of… | JEE Main 2026 (23 Jan, Shift 1)

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Dielectrics

The space between the plates of a parallel plate capacitor of capacitance C (without any dielectric) is now filled with three dielectric slabs of dielectric constants $K_1 = 2, K_2 = 3$ and $K_3 = 5$ (as shown in figure). If new capacitance is $\frac{n}{3}C$ then the value of $n$ is ______.

Numerical answer type. Work it out, then open the answer.

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Answer: 8

Top layer ( $K_1$ , area $A$ , thickness $d/2$ ): $C_1 = 2K_1 C = 4C$ .
Bottom layer: $K_2$ and $K_3$ in parallel, each area $A/2$ , thickness $d/2$ : $K_2 C + K_3 C = 8C$ .
Top and bottom in series: $C' = \frac{4C \times 8C}{12C} = \frac{8}{3}C$
So $n = 8$ .

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