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JEE Main 2024 (31 Jan, Shift 1) · Dielectrics

Dielectrics question from JEE Main 2024 (31 Jan, Shift 1)

Q41JEE Main 2024 · 31 JAN · SHIFT 1Medium

Dielectrics

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

Numerical answer type. Work it out, then open the answer.

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Answer: 2

Battery connected, $Q\propto C$ , so $C'=1.25C$ .
$C'=\frac{\epsilon_0A}{d-t+\frac{t}{K}}$ with $d=5$ mm, $t=2$ mm.
$\frac{5}{3+\frac{2}{K}}=1.25 \Rightarrow 3+\frac{2}{K}=4$
$K=2$

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