A parallel plate air capacitor has capacity ' C ' and distance of separation between plates is ' d '. If a conducting sheet of thickness 2d/3 is inserted in between the plates, the capacitance becomes C₁. The ratio of C₁/C is (a) 2:1 (b) 4:1 (c) 3:1 (d) 5:1

Answer: (c). A conducting sheet of thickness t acts like K → ∞: C₁ = (ε₀ A)/(d - t). d - t = d - 2d/3 = d/3, so C₁ = 3C. So C₁: C = 3:1, answer (c).

A parallel plate air capacitor has capacity ' C ' and distance of… | MHT CET 2025 (23 Apr, Shift 1)

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Dielectrics

A parallel plate air capacitor has capacity ' $C$ ' and distance of separation between plates is ' $d$ '. If a conducting sheet of thickness $\frac{2d}{3}$ is inserted in between the plates, the capacitance becomes $C_1$ . The ratio of $\frac{C_1}{C}$ is

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Answer: (c)

A conducting sheet of thickness $t$ acts like $K \to \infty$ : $C_1 = \frac{\epsilon_0 A}{d - t}$ .
$d - t = d - \frac{2d}{3} = \frac{d}{3}$ , so $C_1 = 3C$ .
So $C_1 : C = 3:1$ , answer (c).

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