The distance between two plates of a capacitor is and its capacitance is , when air is the medium between the plates. If a metal sheet of thickness and of the same area as the plates is introduced between the plates, the capacitance of the capacitor bec

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Solution

Q.
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 $\frac{2 d}{3}$ and of the same area as the plates is introduced between the plates, the capacitance of the capacitor becomes $C_{2}$ . The ratio $\frac{C_{2}}{C_{1}}$ is [2023]

1 2 : 1

2 4 : 1

3 3 : 1

4 1 : 1

Ans.
(3)

$K_{metal sheet} = \infty, t = \frac{2 d}{3}$

$C_{1} = \frac{ε_{0} A}{d}$

$C_{2} = \frac{ε_{0} A}{d - t + \frac{t}{k}} = \frac{ε_{0} A}{d - \frac{2 d}{3} + 0} = 3 C_{1}$

$\frac{C_{2}}{C_{1}} = 3$

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