Question

When the temperature of a semiconductor is increased, its resistance and electric conductivity respectively

• A. increases and decreases
• B. decreases and decreases
• C. increases and increases
• D. decreases and increases

Hint:

Always remember: Conductors have a positive temperature coefficient ($\text{Temp} \uparrow \; \rightarrow R \uparrow$), while semiconductors have a negative temperature coefficient ($\text{Temp} \uparrow \; \rightarrow R \downarrow$). Knowing this distinction saves time on conceptual classification questions.

Answer 1

The Correct Option is D

Step 1: Identify the material behaviour.
The question is about how heating a semiconductor changes its resistance and its conductivity. Semiconductors behave oppositely to metals, so we must reason carefully.
Step 2: Recall the band picture.
In a semiconductor the valence band is nearly full and the conduction band nearly empty, separated by a small energy gap. Conduction needs charge carriers in the conduction band.
Step 3: See what heat does.
Raising the temperature supplies thermal energy that breaks covalent bonds, pushing many electrons across the gap and leaving holes behind. The number of free carriers therefore grows rapidly with temperature.
Step 4: Effect on conductivity.
Conductivity $\sigma$ is proportional to the carrier concentration. More carriers means $\sigma$ increases as the semiconductor gets hotter.
Step 5: Effect on resistance.
Resistance is the inverse of conductivity, $R \propto \dfrac{1}{\sigma}$. Since $\sigma$ rises, $R$ must fall. This is the negative temperature coefficient of resistance characteristic of semiconductors.
Step 6: Combine the two findings.
On heating: resistance decreases and conductivity increases, which is option (4).
\[ \boxed{\text{Resistance decreases, conductivity increases}} \]