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A series combination of n₁ capacitors, each of value C₁, is charged by a source of potential difference V. When another parallel combination of n₂ capacitors, each of value C₂, is charged by a source of potential difference V', it has the same (total) energy stored in it, as the first combination has. The value of C₂ in terms of C₁ is then:

1. 2C₁/n₁n₂
2. 16n₂C₁/n₁
3. 2n₂C₁/n₁
4. 16C₁/n₁n₂

Correct answer: 2C₁/n₁n₂

Solution

The energy stored in a capacitor is given by U = (1/2)CV². For the series combination of n₁ capacitors, the equivalent capacitance is C₁/n₁, and for the parallel combination of n₂ capacitors, the equivalent capacitance is n₂C₂. Equating the energies and solving for C₂ in terms of C₁ gives C₂ = 2C₁ / (n₁n₂).

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