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In the circuit shown in the figure, \(C_1 = C\), \(C_2 = 2C\), \(C_3 = 3C\), and \(C_4 = 4C\). Match the following: Column I A) Maximum potential difference B) Minimum potential difference C) Maximum potential energy D) Minimum potential energy Column II P) across \(C_1\) Q) across \(C_2\) R) across \(C_3\) S) across \(C_4\)

1. A → P ; B → R,S ; C → P ; D → R
2. A → Q ; B → Q,S ; C → P ; D → R
3. A → P,R ; B → S ; C → Q ; D → R,S
4. A → S ; B → P,S ; C → P ; D → R

Correct answer: A → S ; B → P,S ; C → P ; D → R

Solution

In a series combination, all capacitors carry the same charge, so the potential difference across each is inversely proportional to its capacitance. Hence the largest capacitance has the minimum voltage and the smallest capacitance has the maximum voltage; energy also follows the inverse-capacitance trend for fixed charge.

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