Capacitance Question 8
Question 8 - 2024 (31 Jan Shift 1)
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
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Answer: (2)
Solution:
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
$$ \begin{aligned} & \frac{\mathrm{A} \in_{0} \mathrm{~V}}{\mathrm{~d}-\mathrm{t}+\frac{\mathrm{t}}{\mathrm{K}}}=(1.25) \frac{\mathrm{A} \in_{0} \mathrm{~V}}{\mathrm{~d}} \ & \Rightarrow 1.25\left(3+\frac{2}{\mathrm{~K}}\right)=5 \ & \Rightarrow \mathrm{K}=2 \end{aligned} $$
