In which one of the following substances does the resistance decrease…

The correct answer is Option (1) → Germanium

For a wire of fixed size, \( R=\rho l/A \). So the resistance changes with temperature in the same way as the resistivity. The small change in the size of the wire on heating can be ignored.

Option (1) Germanium — Correct. Germanium is a semiconductor. In a semiconductor, the number of free charge carriers per unit volume rises with temperature. This rise has a larger effect than the more frequent collisions. So its resistivity decreases as the temperature rises.

Option (2) Constantan — Incorrect. Constantan is an alloy. Its resistivity changes very little with temperature, so it is used in standard resistors.

Option (3) Copper — Incorrect. Copper is a metal. Its number of free electrons per unit volume hardly changes with temperature, but the collisions become more frequent. So its resistance increases on heating.

Option (4) Silver — Incorrect. Silver is also a metal. Its temperature coefficient of resistivity is positive, so its resistivity and its resistance rise as the temperature rises.

NCERT (2026-27):
Temperature Dependence of Resistivity – “Unlike metals, the resistivities of semiconductors decrease with increasing temperatures.”

Points to Ponder – “Homogeneous conductors like silver or semiconductors like pure germanium or germanium containing impurities obey Ohm’s law within some range of electric field values.”