Q 12-02-042JEE MainJEE Main 2026 (2 Apr, Shift 1)Medium
A parallel plate air capacitor has a capacitance $C$. When it is half filled as shown in figure with a dielectric constant $K=5$, the percentage increase in the capacitance is ______.
Answer: (B) $66.67$
The slab fills half the gap (thickness $d/2$) over the whole plate area, so the air layer and the dielectric layer are in series:
$$C'=\frac{\epsilon_0A}{\frac d2+\frac{d}{2K}}=\frac{\epsilon_0A}{d}\cdot\frac{2K}{K+1}=C\times\frac{10}{6}=\frac53C$$
Percentage increase $=\left(\tfrac53-1\right)\times100=66.67\%$
Solution by Sreeraj P, M.Sc Physics