A parallel plate capacitor has capacitance C, when there is vacuum within the parallel plates. A sheet having thickness of the separation between the plates and relative permittivity K is introduced between the plates. The new capacitance

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Solution

Q.
A parallel plate capacitor has capacitance C, when there is vacuum within the parallel plates. A sheet having thickness ${(1 / 3)}^{rd}$ of the separation between the plates and relative permittivity K is introduced between the plates. The new capacitance of the system is : [2026]

1 $\frac{C K}{2 + K}$

2 $\frac{3 C K^{2}}{{(2 K + 1)}^{2}}$

3 $\frac{3 K C}{2 K + 1}$

4 $\frac{4 K C}{3 K - 1}$

Ans.
(3)

$C_{1} = \frac{3 A ε_{0}}{2 d}$ $C_{2} = \frac{3 A ε_{0} \times K}{d}$

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

$C_{eq} = \frac{C_{1} C_{2}}{C_{1} + C_{2}} = \frac{\frac{3}{2} C \times 3 K C}{\frac{3}{2} C + 3 K C}$

$C_{eq} = \frac{\frac{9}{2} K C^{2}}{\frac{3}{2} C (2 K + 1)} = \frac{3 K C}{2 K + 1}$

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