Q 12-02-116JEE MainJEE Main 2022 (26 Jun, Shift 2)Medium
A parallel plate capacitor with plate area $A$ and plate separation $d = 2\ \text{m}$ has a capacitance of $4\ \mu\text{F}$. The new capacitance of the system if half of the space between them is filled with a dielectric material of dielectric constant $K = 3$ (as shown in figure) will be
Answer: (C) $6\ \mu\text{F}$
The air gap $d/2$ and the dielectric layer $d/2$ are in series:
$$C' = \frac{\varepsilon_0A}{\frac d2 + \frac{d}{2K}} = \frac{\varepsilon_0A}{d}\cdot\frac{1}{\frac12 + \frac16} = \frac32C_0 = \frac32\times4 = 6\ \mu\text{F}$$
Solution by Sreeraj P, M.Sc Physics