A resistor connected to a battery is heated due to the current. The q…

The correct answer is Option (2) → number of free electrons

For a metallic conductor, a rise in temperature makes the ions vibrate more strongly, so the electrons collide more often and the relaxation time falls. The resistivity therefore increases, while the number of free electrons, fixed by the atoms of the metal, does not change.

Option (1) drift speed of the charge carriers — Incorrect. The larger resistance lowers the current \( I = n e A v_d \); with \( n \), \( e \) and \( A \) unchanged, the drift speed falls.

Option (2) number of free electrons — Correct. Each atom of the metal gives a fixed number of free electrons, so the number of free electrons stays the same on heating.

Option (3) conductance — Incorrect. The resistance increases, so the conductance \( 1/R \) decreases.

Option (4) resistivity — Incorrect. The resistivity of a metal increases with temperature, \( \rho_T = \rho_0[1 + \alpha(T - T_0)] \).

Note: A similar question was also asked in CUET (UG) 2026 on 18-05-2026 (Slot 2).

NCERT (2026-27):
Temperature Dependence of Resistivity – “… 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.”