We are given three copper wires of different lengths and different areas of cross-section. Which one of the following would have highest resistivity?
- A.Copper wire of 50 cm length and 1 mm diameter
- B.Copper wire of 25 cm length and 0.5 mm diameter
- C.Copper wire of 10 cm length and 2.0 mm diameter
- D.All the wires would have same resistivity
Correct answer
Explanation
The correct answer is D, All the wires would have same resistivity. Resistivity is a property of the material and its temperature, not of the wire's shape, so every copper wire has the same resistivity.
The resistance of a wire is R = ρL/A, where L is its length, A its area of cross-section and ρ its resistivity. Resistance changes with length and thickness, but ρ is fixed for a given material at a given temperature. For copper at room temperature it is about 1.7 × 10⁻⁸ ohm metre, which is why copper is a favourite for electric wiring. Among these wires, the one 25 cm long and 0.5 mm thick would have the highest resistance, but the resistivity of all three is identical.
A is wrong because its length and diameter affect resistance, not resistivity. B is wrong because a thinner wire has more resistance, yet the same resistivity. C is wrong because a short, thick wire has low resistance but still the resistivity of copper.
Exam tip: Resistance depends on length, area, material and temperature; resistivity depends only on material and temperature. SI unit of resistivity: ohm metre.
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