JEE MAIN - Physics (2024 - 31st January Morning Shift - No. 23)
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 _________.
Answer
2
Explanation
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
$$\begin{aligned} & \frac{\mathrm{A} \in_0 \mathrm{~V}}{\mathrm{~d}-\mathrm{t}+\frac{\mathrm{t}}{\mathrm{K}}}=(1.25) \frac{\mathrm{A} \in_0 \mathrm{~V}}{\mathrm{~d}} \\ & \Rightarrow 1.25\left(3+\frac{2}{\mathrm{~K}}\right)=5 \\ & \Rightarrow \mathrm{K}=2 \end{aligned}$$
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