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 (integer)
2
Solution
<p>Without dielectric</p>
<p>$\mathrm{Q}=\frac{\mathrm{A} \in_0}{\mathrm{~d}} \mathrm{~V}$</p>
<p>with dielectric</p>
<p>$Q=\frac{A \in_0 V}{d-t+\frac{t}{K}}$</p>
<p>given</p>
<p>$$\begin{aligned}
& \frac{\mathrm{A} \in_0 \mathrm{~V}}{\mathrm{~d}-\mathrm{t}+\frac{\mathrm{t}}{\mathrm{K}}}=(1.25) \frac{\mathrm{A} \in_0 \mathrm{~V}}{\mathrm{~d}} \\
& \Rightarrow 1.25\left(3+\frac{2}{\mathrm{~K}}\right)=5 \\
& \Rightarrow \mathrm{K}=2
\end{aligned}$$</p>
About this question
Subject: Physics · Chapter: Electrostatics · Topic: Dielectrics
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