A piece of copper and another of germanium are cooled from room temperature to 100 K. The resistance of:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → copper decreases and germanium increases
The resistance of a conductor depends on how the temperature changes the number of free charge carriers and their collisions.
Copper (a metal): the number of free electrons is almost fixed, but at a lower temperature the lattice ions vibrate less and the electrons collide less often. The resistivity follows \( \rho_T = \rho_0[1 + \alpha(T - T_0)] \) with \( \alpha \gt 0 \), so on cooling the resistance decreases.
Germanium (a semiconductor): its carriers come from thermal excitation across the small band gap. At a lower temperature fewer electron-hole pairs are generated, so the number of carriers falls a great deal, and this outweighs any change in collisions. The resistance increases on cooling (its temperature coefficient is negative).
NCERT (2026-27):
Resistivity of Various Materials – “… In between the two are the semiconductors. These, however, have resistivities characteristically decreasing with a rise in temperature.”
Temperature Dependence of Resistivity – “… Over a limited range of temperatures, that is not too large, the resistivity of a metallic conductor is approximately given by,
\( \displaystyle \rho_T = \rho_0[1 + \alpha(T - T_0)] \qquad (3.26) \)
… For metals, α is positive.”