Question

As the temperature increases, the electrical resistance:

• A. Increases for both conductors and semiconductors
• B. Decreases for both conductors and semiconductors
• C. Increases for conductors but decreases for semiconductors
• D. Decreases for conductors but increases for semiconductors

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The electrical resistance of a material depends on the temperature because temperature affects both the number of free charge carriers and the frequency of collisions between those carriers and the atomic lattice.
Key Formula or Approach:
The variation of resistance with temperature is generally expressed as:
\[ R_T = R_0 (1 + \alpha \Delta T) \]
where \(\alpha\) is the temperature coefficient of resistance.
Step 2: Detailed Explanation:
1. For Conductors (Metals):
In metals, the number of free electrons is already very high and does not change significantly with temperature.
As temperature increases, the thermal energy causes the metal ions in the lattice to vibrate with greater amplitude.
This increases the frequency of collisions between the flowing electrons and the ions.
The relaxation time (\(\tau\)) decreases, which increases the resistance (\(R \propto \frac{1}{\tau}\)).
Conductors have a positive temperature coefficient (\(\alpha>0\)).

2. For Semiconductors:
Semiconductors have a small number of free charge carriers at room temperature.
As temperature increases, thermal energy breaks covalent bonds, significantly increasing the concentration (\(n\)) of free electrons and holes.
Although the collision frequency also increases, the effect of the massive increase in charge carrier density dominates.
The conductivity increases, meaning the resistance decreases.
Semiconductors have a negative temperature coefficient (\(\alpha<0\)).
Step 3: Final Answer:
Hence, as temperature increases, resistance increases for conductors and decreases for semiconductors.