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A resistance wire connected in the left gap of a metre bridge balances a 1 Ω resistance in the right gap at a point which divides the bridge wire in the ratio 3 : 2. If the length of the resistance wire is 1.5 m, then the length of 1 Ω of the resistance wire is

1. 1.0 × 10⁻² m
2. 7.5 × 10⁻³ m
3. 1.5 × 10⁻² m
4. 1.0 × 10⁻³ m

Correct answer: 7.5 × 10⁻³ m

Solution

The metre bridge balance condition gives the ratio of resistances as the ratio of the lengths of the bridge wire. Since the ratio is 3:2, the resistance of the wire in the left gap is 1.5 Ω. The total length of the wire is 1.5 m, so the length of 1 Ω of the resistance wire is (1.5 m / 1.5 Ω) = 7.5 × 10⁻³ m.

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