Resistivity (\( \rho \)) vs temperature graphs of some materials are given below. The graph corresponds to a semiconductor is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3)
In a semiconductor, the number density of charge carriers \( n \) increases very rapidly as the temperature rises. This increase outweighs the small decrease in relaxation time \( \tau \), so the resistivity falls.
\( \displaystyle \rho = \frac{m}{n e^{2} \tau} \)
The resistivity therefore decreases steeply at first and then more and more slowly (roughly exponentially) as the temperature increases, which is the curve of Option (3).
Why the other options are incorrect
Option (1) — Incorrect. The resistivity rises with temperature, ever more steeply; a semiconductor's resistivity falls.
Option (2) — Incorrect. A straight line rising with temperature is the behaviour of a metal such as copper.
Option (4) — Incorrect. The resistivity falls, but along a straight line; for a semiconductor it falls steeply at first and then flattens out.
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.”
