Which one among the following statements regarding the electrical resistivity of a conducting wire is correct?
- A.The resistivity of the conductor increases if the length of the wire is increased.
- B.The resistivity of the conductor decreases if the length of the wire is increased.
- C.The resistivity of the conductor remains the same if the length of the wire is changed.
- D.The resistivity of the conductor increases if the cross-sectional area of the wire is increased.
Correct answer
Explanation
The correct answer is C. Resistivity is a property of the material itself, so it stays the same when the length of the wire is changed.
The resistance of a wire is given by R = ρL/A, where L is the length, A the area of cross-section and ρ the resistivity. Stretching or cutting the wire changes R, because L and A change, but ρ depends only on the material and its temperature. Copper has a low resistivity, nichrome a high one, whatever the shape of the wire. Its SI unit is the ohm-metre.
A is wrong: a longer wire has more resistance, not more resistivity.
B is wrong: length has no effect on resistivity in either direction.
D is wrong: a thicker wire has less resistance, while its resistivity is unchanged.
Exam tip: resistance depends on length, area, material and temperature; resistivity only on material and temperature.
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