Which of the following are correct statements?A. The resistivity of a…

The correct answer is Option (4) → A, B and D only

The resistivity is \( \rho = m/(ne^{2}\tau) \), where n is the number of free electrons per unit volume and \( \tau \) is the average time between collisions. Its temperature dependence comes from how n and \( \tau \) change.

(A) The resistivity of a material is found to be dependent on the temperature — Correct. Different materials show different dependences, but none is independent of temperature.

(B) In metals number of free electrons per unit volume is not dependent on temperature. — Correct. In a metal n is essentially fixed by the atoms, so it does not change appreciably with temperature.

(C) Resistivity of semiconductors increases with increasing temperature — Incorrect. In a semiconductor n increases rapidly with temperature, which more than offsets the fall in \( \tau \), so the resistivity decreases.

(D) Resistivity of metal increases with increase in temperature — Correct. n stays constant while \( \tau \) falls because of more frequent collisions, so \( \rho \) rises.

NCERT (2026-27):
Temperature Dependence of Resistivity – “The resistivity of a material is found to be dependent on the temperature. … The average time of collisions τ, thus decreases with temperature. 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. For insulators and semiconductors, however, n increases with temperature. This increase more than compensates any decrease in τ in Eq.(3.23) so that for such materials, ρ decreases with temperature.”