Identify the graph from the following showing the temperature dependence of resistivity for a typical semiconductor?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3)
The resistivity is \( \rho = \frac{m}{ne^{2}\tau} \). In a semiconductor the number density n of charge carriers rises rapidly with temperature, which more than makes up for the decrease in the collision time \( \tau \). So the resistivity decreases as the temperature rises: the curve falls steeply at low temperature and then flattens out.
Why the other options are incorrect
Option (1) — Incorrect. Resistivity rising linearly with temperature is the behaviour of a metallic conductor.
Option (2) — Incorrect. The resistivity does fall, but a straight line is not the typical curve: the fall is steep at low temperature and levels off at high temperature.
Option (4) — Incorrect. Here the resistivity increases with temperature, the opposite of a semiconductor.
NCERT (2026-27):
Temperature Dependence of Resistivity – “… Unlike metals, the resistivities of semiconductors decrease with increasing temperatures. A typical dependence is shown in Fig. 3.10.”
