Question 366: Electrostats & Capacitance

Question

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 _________.

Accepted Answer

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
$$\begin{aligned}
& \frac{\mathrm{A} \in_0 \mathrm{~V}}{\mathrm{~d}-\mathrm{t}+\frac{\mathrm{t}}{\mathrm{K}}}=(1.25) \frac{\mathrm{A} \in_0 \mathrm{~V}}{\mathrm{~d}} \
& \Rightarrow 1.25\left(3+\frac{2}{\mathrm{~K}}ight)=5 \
& \Rightarrow \mathrm{K}=2
\end{aligned}$$

Electrostats & Capacitance

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