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A capacitor C₁ is charged to a potential difference V. The charging battery is then removed and the capacitor is connected to an uncharged capacitor C₂. The potential difference across the combination is
- VC₁ / (C₁ + C₂)
- V [C₁ / (C₁ + C₂)]
- V [1 + C₁ / C₂]
- VC₂ / (C₁ + C₂)
Correct answer: V [C₁ / (C₁ + C₂)]
Solution
When the charged capacitor C₁ is connected to the uncharged capacitor C₂, charge is conserved. The total charge before connection is Q = C₁V. After connection, the total capacitance becomes (C₁ + C₂), and the potential difference across the combination is V' = Q / (C₁ + C₂) = V [C₁ / (C₁ + C₂)].
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