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A material 'B' has twice the specific resistance of 'A'. A circular wire made of 'B' has twice the diameter of a wire made of 'A'. then for the two wires to have the same resistance, the ratio lB/lA is

1. 1
2. 1/2
3. 1/4
4. 2

Correct answer: 2

Solution

The resistance of a wire is directly proportional to its length and resistivity, and inversely proportional to its cross-sectional area. Since material 'B' has twice the resistivity of 'A' and its diameter is twice that of 'A', its cross-sectional area is four times larger. To maintain equal resistance, the length of wire 'B' must be twice that of wire 'A', resulting in a ratio of lB/lA = 2.

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