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Two wires of the same metal have same length, but their cross-sections are in the ratio 3:1. They are joined in series. The resistance of thicker wire is 10Ω. The total resistance of the combination will be

1. 10Ω
2. 20Ω
3. 40Ω
4. 100Ω

Correct answer: 20Ω

Solution

The resistance of a wire is inversely proportional to its cross-sectional area. Since the cross-sectional areas are in the ratio 3:1, the resistance of the thinner wire will be 3 times that of the thicker wire. Thus, the resistance of the thinner wire is 30Ω. In series, the total resistance is the sum of individual resistances: 10Ω + 30Ω = 40Ω.

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