A piece of copper and a piece of germanium are cooled from room temperature 20 °C down to 80 K. The resistance of
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → copper decreases and that of germanium increases.
Copper is a metal and germanium is a semiconductor, and their resistances change with temperature in opposite ways.
In copper the number of free electrons is fixed. On cooling, the ions vibrate less, the electrons collide less often, and the resistance decreases (positive temperature coefficient).
In germanium the current depends on carriers freed by thermal energy. On cooling, far fewer electron-hole pairs are produced, so the resistance increases (negative temperature coefficient).
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 \( \tau \) with rise in temperature causes \( \rho \) to increase as we have observed. For insulators and semiconductors, however, \( n \) increases with temperature. This increase more than compensates any decrease in \( \tau \) in Eq.(3.23) so that for such materials, \( \rho \) decreases with temperature.”