Two uniform wires made of the same material, having the same length, and maintained at the same temperature are compared. Which factor will cause one wire to have greater electrical resistance than the other?
Smaller cross-sectional area
The electrical resistance of a uniform conductor is given by R = ρL / A, where ρ is the resistivity of the material, L is the length and A is the cross-sectional area.
When both wires are made of the same material, have the same length and are at the same temperature, ρ and L are identical, so the resistance depends only on the cross-sectional area A.
Since R is inversely proportional to A, a wire with a smaller cross-sectional area offers a higher resistance; voltage and current do not change the resistance itself, which is a property of the conductor.
Hence, the correct answer is Smaller cross-sectional area.
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