A parallel plate capacitor with plate separation $5$ $\mathrm{mm}$ is charged up by a battery. It is found that on introducing a dielectric sheet of thickness $2 \mathrm{~mm}$, while keeping the battery connections intact, the capacitor draws $25 \%$ more charge from the battery than before. The dielectric constant of the sheet is_____.
JEE MAIN 2024, Diffcult
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Without dielectric
$\mathrm{Q}=\frac{\mathrm{A} \in_0}{\mathrm{~d}} \mathrm{~V}$
with dielectric
Q=$\frac{A \in_0 V}{d-t+\frac{t}{K}}$
given
$\frac{\mathrm{A} \in_0 \mathrm{~V}}{\mathrm{~d}-\mathrm{t}+\frac{\mathrm{t}}{\mathrm{K}}}=(1.25) \frac{\mathrm{A} \in_0 \mathrm{~V}}{\mathrm{~d}}$
$\Rightarrow 1.25\left(3+\frac{2}{\mathrm{~K}}\right)=5$
$\Rightarrow \mathrm{K}=2$
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