CBSE 2026 · Region 5 · Set 1 · Q22 · 3 marks
Two parallel plate capacitors X and Y are connected in series to a $\displaystyle 6$ V battery. They have the same plate area and same plate separation but capacitor X has air between its plates, whereas capacitor Y contains a material of dielectric constant $\displaystyle 4$ .(a)Calculate the capacitances of X and Y, if the equivalent capacitance of the combination of X and Y is $\displaystyle 4 \mu \mathrm{~F}$.(b)Calculate the potential difference across the plates of X and Y.
Two parallel plate capacitors X and Y are connected in series to a $\displaystyle 6$ V battery. They have the same plate area and same plate separation but capacitor X has air between its plates, whereas capacitor Y contains a material of dielectric constant $\displaystyle 4$ .
(a)
Calculate the capacitances of X and Y, if the equivalent capacitance of the combination of X and Y is $\displaystyle 4 \mu \mathrm{~F}$.
(b)
Calculate the potential difference across the plates of X and Y.
Marking-scheme solution
(a)
Calculating the capacitance of $\displaystyle \mathrm{X} \& \mathrm{Y}$.
(b)
Calculating the potential difference across plates of X & Y
(a)
$\displaystyle \mathrm{C}_{\mathrm{X}}=\mathrm{C}, \mathrm{C}_{\mathrm{Y}}=\mathrm{KC}=4 \mathrm{C}$
\[\begin{aligned}
& \frac{1}{\mathrm{C}_{e q}}=\frac{1}{\mathrm{C}_{\mathrm{X}}}+\frac{1}{\mathrm{C}_{\mathrm{Y}}} \\
& \mathrm{C}_{e q}=\frac{\mathrm{C}_{\mathrm{X}} \mathrm{C}_{\mathrm{Y}}}{\mathrm{C}_{\mathrm{X}}+\mathrm{C}_{\mathrm{Y}}} \\
& 4=\frac{\mathrm{C} \cdot 4 \mathrm{C}}{\mathrm{C}+4 \mathrm{C}}
\end{aligned}
\]
$\displaystyle \mathrm{C}=5 \mu \mathrm{~F}$
\[\begin{aligned}
& \mathrm{C}_{\mathrm{X}}=5 \mu \mathrm{~F} \\
& \mathrm{C}_{\mathrm{Y}}=20 \mu \mathrm{~F}
\end{aligned}
\]
(b)
Total charge $\displaystyle \mathrm{Q}=\mathrm{C}_{\mathrm{eq}} \mathrm{V}$
\[\begin{aligned}
& =4 \times 10^{-6} \times 6 \\
& =24 \times 10^{-6} \mathrm{C}
\end{aligned}
\]
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CBSE Class 12 Physics past-paper question from the 2026board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.