Q 12-02-080JEE MainJEE Main 2024 (31 Jan, Shift 1)Medium
A parallel plate capacitor with plate separation $5\ \text{mm}$ is charged up by a battery. It is found that on introducing a dielectric sheet of thickness $2\ \text{mm}$, while keeping the battery connections intact, the capacitor draws $25\%$ more charge from the battery than before. The dielectric constant of the sheet is ______.
Numerical value type. Enter your answer.
Answer: 2
With the battery connected, $Q \propto C$, so $C' = 1.25\,C$:
$$\frac{d}{d - t + t/K} = 1.25 \Rightarrow \frac{5}{3 + 2/K} = 1.25 \Rightarrow 3 + \frac2K = 4 \Rightarrow K = 2$$
Solution by Sreeraj P, M.Sc Physics