You are given a copper wire. What is the effect of a rise in temperature on the conductivity of the wire?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → The conductivity of the copper wire decreases.
The conductivity is the reciprocal of the resistivity, \( \sigma=1/\rho \), so whatever raises the resistivity of copper lowers its conductivity.
Option (1) The conductivity of the copper wire increases. — Incorrect. Copper is a metal, and the resistivity of a metal rises with temperature, so its conductivity cannot rise.
Option (2) The conductivity of the copper wire decreases. — Correct. As the temperature rises the electrons move faster and collide more often, so the average time between collisions \( \tau \) decreases. In a metal the number of free electrons per unit volume hardly changes, so the resistivity increases and the conductivity \( 1/\rho \) decreases.
Option (3) As the temperature rises, the conductance rises. — Incorrect. The conductance is \( 1/R \). The resistance \( R=\rho l/A \) of the wire grows with its resistivity. So the conductance also falls as the wire warms up.
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.”
Ohm’s Law – “The above relation for magnitudes E and j can indeed be cast in a vector form. … Thus, the last equation can be written as,
\( \mathbf{E}=\mathbf{j}\rho \qquad (3.12) \)
or,
\( \mathbf{j}=\sigma\mathbf{E} \qquad (3.13) \)
where σ ≡ 1/ρ is called the conductivity.”