A parallel plate capacitor with plate separation 5mm is charged up by a battery. It is found that on introducing a dielectric sheet of thickness 2 mm, while keeping the battery connections intact, the capacitor draws 25% more charge from the battery than

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Solution

Q.
A parallel plate capacitor with plate separation 5mm is charged up by a battery. It is found that on introducing a dielectric sheet of thickness 2 mm, while keeping the battery connections intact, the capacitor draws 25% more charge from the battery than before. The dielectric constant of the sheet is __________. [2024]

Ans.
(2) Without dielectric $Q = \frac{A \in_{0}}{d} V$

with dielectric

$Q = \frac{A \in_{0} V}{d - t + \frac{t}{K}}$

Given $\frac{A \in_{0} V}{d - t + \frac{t}{K}} = (1.25) \frac{A \in_{0} V}{d}$

$\Rightarrow 1.25 (3 + \frac{2}{K}) = 5 \Rightarrow K = 2$

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