A metal wire of length l and diameter d has a resistance R. What would be the resistance of another wire of the same metal and of same length but having double the diameter ?
- A.R
- B.R/4
- C.R/2
- D.2R
Correct answer
Explanation
The correct answer is B, R/4. Resistance varies inversely with the area of cross-section, and doubling the diameter makes the area four times larger.
The resistance of a wire is R = ρl/A, where ρ is the resistivity of the metal, l the length and A the cross-sectional area. Since A = πd²/4, the area depends on the square of the diameter. With the same metal and the same length, a wire of diameter 2d has area four times as large, so its resistance falls to one-fourth, R/4.
A is wrong because the resistance would stay R only if the area did not change.
C is wrong because R/2 would follow if resistance depended on the diameter itself, not on its square.
D is wrong because a thicker wire offers less resistance, not more; 2R would need a longer or thinner wire.
Exam tip: R ∝ l and R ∝ 1/d²; double the diameter gives one-fourth the resistance.
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