A composite parallel plate capacitor is made up of two different… | JEE Main 2022 (26 Jul, Shift 1)

Q66JEE Main 2022 · 26 JUL · SHIFT 1Medium

Dielectrics

A composite parallel plate capacitor is made up of two different dielectric materials with different thickness $(t_1$ and $t_2)$ as shown in figure. The two different dielectric materials are separated by a conducting foil $\text{F}$ . The voltage of the conducting foil is ____________ V.

Numerical answer type. Work it out, then open the answer.

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Answer: 60

The foil splits it into two capacitors in series, $C\propto\frac{\varepsilon_r}{t}$ .
$C_1\propto\frac{3}{0.5}=6$ , $C_2\propto\frac{4}{1}=4$ ; series charge is the same, so $V\propto\frac{1}{C}$ .
$V_1=100\times\frac{4}{10}=40\text{ V}$ , $V_2=60\text{ V}$
Taking the negative (lower) plate at 0 V, foil potential $=V_2=60\text{ V}$

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