Which of the following statements are correct?(A) Metals obey Ohm's l…

The correct answer is Option (1) → (A), (B) and (D) only

In a metal the resistivity is\( \rho = m/(n e^{2}\tau) \), where \( n \) is the number of free electrons per unit volume and \( \tau \) the relaxation time.

(A) Metals obey Ohm's law at constant temperature. — Correct. At a fixed temperature the current is proportional to the voltage, so \( V/I \) is constant.

(B) The resistivity of the metals depends on temperature. — Correct. It rises with temperature, \( \rho = \rho_0[1 + \alpha(T - T_0)] \), because the electrons collide more often and \( \tau \) decreases.

(C) The conductivity of the metals is independent of temperature. — Incorrect. Conductivity is \( \sigma = 1/\rho \), so it falls as the resistivity rises.

(D) The number of electrons per unit volume in a metal is independent of temperature. — Correct. The free electrons come from the atoms and their number density does not change appreciably with temperature; the change in \( \rho \) comes from \( \tau \).

Statements (A), (B) and (D) are correct, which is Option (1).

NCERT (2026-27):
Temperature Dependence of Resistivity – “… \( \rho \) thus depends inversely both on the number \( n \) of free electrons per unit volume and on the average time \( \tau \) between collisions. As we increase temperature, average speed of the electrons, which act as the carriers of current, increases resulting in more frequent collisions. The average time of collisions \( \tau \), 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 \( \tau \) with rise in temperature causes \( \rho \) to increase as we have observed.”