Question

Given below are two statements:
Statement I: The resistivity of a conductor is independent of its temperature
Statement II: The resistivity of a semiconductor decreases with increase in temperature
Select the correct option.

• A. Both Statement I and Statement II are false
• B. Both Statement I and Statement II are true
• C. Statement I is true but Statement II is false
• D. Statement I is false but Statement II is true

Hint:

Recall the graph of resistivity (\(\rho\)) vs temperature (T):
- For conductors: Graph shows a positive slope (linear or nearly linear at high T).
- For semiconductors/insulators: Graph shows an exponential decay (\( \rho = \rho_0 e^{E_g / k_B T} \)).

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The question evaluates theoretical knowledge regarding how temperature affects the electrical resistivity of different classes of materials (conductors and semiconductors).
Step 3: Detailed Explanation:
Analysis of Statement I:
Resistivity (\(\rho\)) of a conductor (metal) depends on temperature as:
\[ \rho_T = \rho_0 [1 + \alpha(T - T_0)] \]
where \(\alpha\) is the temperature coefficient. For conductors, \(\alpha\) is positive. As temperature increases, thermal vibrations of lattice ions increase, causing more frequent collisions with electrons. This increases resistance and resistivity. Therefore, Statement I is false.
Analysis of Statement II:
For semiconductors, the temperature coefficient of resistivity \(\alpha\) is negative. As temperature increases, more valence electrons gain enough thermal energy to jump into the conduction band, significantly increasing the charge carrier density (\(n\)). This effect outweighs the increase in lattice scattering. Consequently, the resistivity decreases. Therefore, Statement II is true.
Step 4: Final Answer:
Statement I is false but Statement II is true, which corresponds to option (4).