A parallel plate capacitor with plate separation 5 mm 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
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Solution
Sol. Without dielectric
$$
Q=\frac{A \epsilon_0}{d} V
$$
with dielectric
$$
Q=\frac{A \epsilon_0 V}{d-t+\frac{t}{K}}
$$
given
$$
\begin{aligned}
& \frac{A \in_0 V}{d-t+\frac{t}{K}}=(1.25) \frac{A \in_0 V}{d} \\
& \Rightarrow 1.25\left(3+\frac{2}{K}\right)=5 \\
& \Rightarrow K=2
\end{aligned}
$$
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