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Physics · 2025 · 3 marks
CBSE 2025 · Region 5 · Set 1 · Q23
A parallel plate capacitor has plate area A and plate separation d. Half of the space between the plates is filled with a material of dielectric…
A parallel plate capacitor has plate area A and plate separation d. Half of the space between the plates is filled with a material of dielectric constant K in two ways as shown in the figure.
\[\kappa \frac{\mathrm{d}}{2} \rightarrow \]
(a)
(b)
Find the values of the capacitance of the capacitors in the two cases.
Marking-scheme solution
(a)
$\displaystyle \frac{1}{C}=\frac{1}{K\left(\dfrac{\varepsilon_{0} A}{d / 2}\right)}+\frac{1}{\dfrac{\varepsilon_{0} A}{d / 2}}$
$\displaystyle \frac{1}{C}=\frac{d}{2 K \varepsilon_{0} A}+\frac{d}{2 \varepsilon_{0} A}$
$\displaystyle =\left(\frac{1}{K}+1\right) \frac{d}{2 \varepsilon_{0} A}$
$\displaystyle C=\left(\frac{2 K}{K+1}\right) \frac{\varepsilon_{0} A}{d}$
(b)
$\displaystyle C=\frac{\varepsilon_{0} A K}{2 d}+\frac{\varepsilon_{0} A}{2 d}$
$\displaystyle =\left(\frac{K+1}{2}\right) \frac{\varepsilon_{0} A}{d}$
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CBSE Class 12 Physics past-paper question from the 2025 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.