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In a metre-bridge, the balancing length from the left end when standard resistance of 1 Ω is in right gap is found to be 20 cm. The value of unknown resistance is

1. 0.25 Ω
2. 0.4 Ω
3. 0.5 Ω
4. 4 Ω

Correct answer: 0.5 Ω

Solution

In a metre-bridge, the balancing condition is given by the ratio of resistances being equal to the ratio of the lengths. Here, the balancing length is 20 cm, so the other length is 100 - 20 = 80 cm. Using the formula R1/R2 = L1/L2, where R1 is the unknown resistance and R2 is 1 Ω, we get R1 = (L1/L2) * R2 = (20/80) * 1 = 0.25 Ω.

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