Q 12-02-121JEE MainJEE Main 2022 (26 Jul, Shift 1)Medium
A composite parallel plate capacitor is made up of two different dielectric materials with different thicknesses ($t_1$ and $t_2$) as shown in figure. The two different dielectric materials are separated by a conducting foil $F$. The voltage of the conducting foil is ______ V.
Numerical value type. Enter your answer.
Answer: 60
The two layers act as capacitors in series: $C_1\propto\dfrac{3}{0.5} = 6$ and $C_2\propto\dfrac41 = 4$ (same area).
Voltages divide inversely as capacitance: $V_1 = 100\times\dfrac{4}{10} = 40\ \text{V}$ and $V_2 = 100\times\dfrac{6}{10} = 60\ \text{V}$.
Measured from the plate on the $\varepsilon_{r2}$ side (the negative, $0\ \text{V}$ plate), the foil is at $60\ \text{V}$.
Solution by Sreeraj P, M.Sc Physics