Complete the following statement with the most appropriate option.
The resistivity of conductors ____ and that of semiconductors ____ with an increase in temperature.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → increases, decreases
The resistivity is \( \rho=m/(ne^{2}\tau) \), so it depends on the number of free charge carriers per unit volume \( n \) and on the average time between collisions \( \tau \). A rise in temperature shortens \( \tau \) in every material, but it changes \( n \) only in semiconductors and insulators.
Option (1) decreases, increases — Incorrect. A conductor’s resistivity rises with temperature and a semiconductor’s falls. This pair gives them the other way round.
Option (2) decreases, decreases — Incorrect. In a metal \( n \) hardly changes while \( \tau \) falls, so the resistivity of a conductor rises.
Option (3) increases, increases — Incorrect. In a semiconductor, more charge carriers are set free as the temperature rises. This rise in \( n \) has a larger effect than the fall in \( \tau \), so its resistivity falls.
Option (4) increases, decreases — Correct. For a conductor, \( \tau \) falls while \( n \) stays nearly constant, so \( \rho \) increases. For a semiconductor, the rise in \( n \) has a larger effect than the fall in \( \tau \), so \( \rho \) decreases.
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 τ with rise in temperature causes ρ to increase as we have observed.”
Temperature Dependence of Resistivity – “For insulators and semiconductors, however, n increases with temperature. This increase more than compensates any decrease in τ … so that for such materials, ρ decreases with temperature.”