Question

Which of the following graph represents the temperature (T) dependence of resistivity (\(ρ\)) of a semiconductor?

• A. A
• B. B
• C. C
• D. D

Hint:

In a semiconductor more carriers are freed as temperature rises, so resistivity falls in a curved, exponential way.

Answer 1

The Correct Option is B

Step 1: Use conductivity:
Conductivity $\sigma = ne\mu$ depends on carrier density $n$. In a semiconductor, $n$ increases exponentially with temperature.

Step 2: Resistivity:
Since $\rho = 1/\sigma$, resistivity decreases as T increases, and the decrease is steep at first, then slows down.

Step 3: Match:
A decreasing, convex curve is graph B. The two rising graphs (A and D) show metal-like behaviour. The straight falling line C does not follow an exponential law.

Final Answer:
The graph is B. \[ \boxed{\text{B}} \]