Capacitance Question 8
Question 8 - 2024 (31 Jan Shift 1)
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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Answer: (2)
Solution:
Without dielectric
$Q=\frac{A \in _0}{d} V$
with dielectric
$Q=\frac{A \in _0 V}{d-t+\frac{t}{K}}$
given
$$ \begin{aligned} & \frac{A \in _0 V}{d-t+\frac{t}{K}}=(1.25) \frac{A \in _0 V}{d} \\ & \Rightarrow 1.25\left(3+\frac{2}{K}\right)=5 \\ & \Rightarrow K=2 \end{aligned} $$
