The distance between two plates of a capacitor is d and its capacitance is C₁, when air is the medium between the plates. If a metal sheet of thickness 2d/3 and of the same area as plate is introduced between the plates, the capacitance of the capacitor becomes C₂. The ratio (C₂)/(C₁) is (a) 1: 1 (b) 3: 1 (c) 2: 1 (d) 4: 1

Answer: (b). A metal sheet of thickness t reduces the effective gap to d - t: C₂ = (ε₀ A)/(d - t). d - 2d/3 = d/3, so C₂ = 3C₁. So C₂: C₁ = 3:1, answer (b).

The distance between two plates of a capacitor is d and its… | JEE Main 2023 (10 Apr, Shift 2)

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Dielectrics

The distance between two plates of a capacitor is $d$ and its capacitance is $C_1$ , when air is the medium between the plates. If a metal sheet of thickness $\frac{2d}{3}$ and of the same area as plate is introduced between the plates, the capacitance of the capacitor becomes $C_2$ . The ratio $\frac{C_2}{C_1}$ is

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Answer: (b)

A metal sheet of thickness $t$ reduces the effective gap to $d - t$ : $C_2 = \frac{\varepsilon_0 A}{d - t}$ .
$d - \frac{2d}{3} = \frac{d}{3}$ , so $C_2 = 3C_1$ .
So $C_2 : C_1 = 3:1$ , answer (b).

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