A parallel plate capacitor is filled equally(half) with two… | JEE Main 2025 (3 Apr, Shift 1)

Q35JEE Main 2025 · 3 APR · SHIFT 1Medium

Dielectrics

A parallel plate capacitor is filled equally(half) with two dielectrics of dielectric constants $\varepsilon_1$ and $\varepsilon_2$ , as shown in figures. The distance between the plates is $d$ and area of each plate is $A$ . If capacitance in first configuration and second configuration are $C_1$ and $C_2$ respectively, then $\frac{C_1}{C_2}$ is: First Configuration

Second Configuration

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Answer: (c)

First configuration: layers stacked between the plates, series: $C_1=\frac{\epsilon_0A}{d}\cdot\frac{2\varepsilon_1\varepsilon_2}{\varepsilon_1+\varepsilon_2}$
Second configuration: side by side, parallel: $C_2=\frac{\epsilon_0A}{d}\cdot\frac{\varepsilon_1+\varepsilon_2}{2}$
$\frac{C_1}{C_2}=\frac{4\varepsilon_1\varepsilon_2}{(\varepsilon_1+\varepsilon_2)^2}$ . So the answer is (c).

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