CBSE 2025 · Region 5 · Set 3 · Q22 · 3 marks
(a)"There is a limit to the amount of charge that can be stored on a given capacitor." Explain.(b)A capacitor is charged by a battery to a potential difference V. It is disconnected from the battery and connected across another identical uncharged capacitor. Calculate the ratio of total energy stored in the combination to the initial energy stored in the capacitor.
(a)
"There is a limit to the amount of charge that can be stored on a given capacitor." Explain.
(b)
A capacitor is charged by a battery to a potential difference V. It is disconnected from the battery and connected across another identical uncharged capacitor. Calculate the ratio of total energy stored in the combination to the initial energy stored in the capacitor.
Marking-scheme solution
(a)
When a conductor holds a large amount of charge its potential is also high. If the electric field becomes high enough, the atoms or molecules of the surrounding medium get ionized. A breakdown occurs in the medium and the charge on the conductor gets neutralized or leaks away.
(b)
The common potential after the connection of two capacitors:
Given $\displaystyle V_{1}=V$, $\displaystyle V_{2}=0$; $\displaystyle C_{1}=C_{2}=C$
$\displaystyle V^{\prime}=\frac{C V}{2 C}=\frac{V}{2}$
$\displaystyle U_{i}=\frac{1}{2} C V^{2}$
$\displaystyle U_{f}=\frac{1}{2} C^{\prime} V^{\prime 2}$
$\displaystyle =\frac{1}{2} \times 2 C \times\left(\frac{V}{2}\right)^{2}$
$\displaystyle =\frac{1}{4} C V^{2}$
$\displaystyle \frac{U_{f}}{U_{i}}=\frac{1}{2}$
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CBSE Class 12 Physics past-paper question from the 2025board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.