A parallel plate capacitor with plate separation 5 mm is charged by a battery. On introducing a mica sheet of 2 mm and maintaining the connections

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Solution

Q.
A parallel plate capacitor with plate separation 5 mm is charged by a battery. On introducing a mica sheet of 2 mm and maintaining the connections of the plates with the terminals of the battery, it is found that it draws 25% more charge from the battery. The dielectric constant of mica is __________. [2026]

1 2.0

2 1.5

3 1.0

4 2.5

Ans.
(1)

[IMAGE 199]

$c_{eq} = \frac{C_{1} C_{2}}{C_{1} + C_{2}} = \frac{\frac{ε_{0} A}{3} \times \frac{K ε_{0} A}{2}}{\frac{ε_{0} A}{3} + \frac{K ε_{0} A}{2}}$

$c_{eq} = \frac{{(ε_{0} A)}^{2} (\frac{K}{6})}{ε_{0} A (\frac{2 + 3 K}{6})} \Rightarrow C_{eq} = \frac{K ε_{0} A}{2 + 3 K}$

$1.25 \times \frac{ε_{0} A}{5} = \frac{K ε_{0} A}{2 + 3 K} \Rightarrow 0.25 (2 + 3 K) = K$

$2 + 3 K = 4 K \Rightarrow K = 2$

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