Compare the resistivities of a metallic material at absolute zero temperature and at room temperature.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → At room temperature, the resistivity is greater.
The resistivity of a material is \( \rho=m/(ne^{2}\tau) \). As the temperature rises, the electrons move faster and collide more often, so the average time between collisions \( \tau \) decreases.
Option (1) At room temperature, the resistivity is greater. — Correct. In a metal, the number of free electrons per unit volume hardly changes with temperature. So the shorter \( \tau \) at higher temperature makes the resistivity increase with temperature. Room temperature is far above absolute zero, so the resistivity there is greater.
Option (2) At absolute zero temperature, the resistivity is greater. — Incorrect. Lowering the temperature makes collisions less frequent, so the resistivity of a metal falls as it is cooled and is least near absolute zero.
Option (3) The resistivities are the same at both the temperatures. — Incorrect. The temperature coefficient of resistivity of a metal is positive. So its resistivity rises as the temperature rises.
Option (4) The behaviour of the resistivities cannot be predicted. — Incorrect. The relation \( \rho=m/(ne^{2}\tau) \), with \( n \) nearly constant and \( \tau \) falling with temperature, predicts the behaviour of a metal.
NCERT (2026-27):
Temperature Dependence of Resistivity – “In a metal, n is not dependent on temperature to any appreciable extent and thus the decrease in the value of τ with rise in temperature causes ρ to increase as we have observed.”