By increasing the temperature , the specific resistance of a conductor and a semiconductor

Options

A. both conductor and semiconductor increases
B. both conductor
C. conductor increases and semiconductor decreases
D. conductor decreases and semiconductor increases

Answer

To solve the question regarding the effect of temperature on the specific resistance of a conductor and a semiconductor, we can break it down into a series of logical steps.

### Step-by-Step Solution:

1. **Understanding Resistivity and Conductivity**:
- Resistivity (\( \rho \)) is the measure of how strongly a material opposes the flow of electric current. It is related to conductivity (\( \sigma \)) by the equation:
\[ \rho = \frac{1}{\sigma} \]

2. **Effect of Temperature on Conductors**:
- In conductors, as the temperature increases, the atoms in the conductor vibrate more vigorously. This increased vibration leads to more frequent collisions between the conduction electrons and the vibrating atoms.
- The relaxation time (\( \tau \)), which is the average time between collisions, decreases with increasing temperature.
- As a result, the resistivity of the conductor increases. This can be expressed as:
\[ \rho_{conductor} \uparrow \text{ (increases with temperature)} \]

3. **Effect of Temperature on Semiconductors**:
- In semiconductors, increasing the temperature provides energy to the electrons, allowing more of them to jump from the valence band to the conduction band.
- This increase in the number of charge carriers (electrons) leads to an increase in conductivity (\( \sigma \)).
- Since resistivity is inversely related to conductivity, the resistivity of the semiconductor decreases with increasing temperature:
\[ \rho_{semiconductor} \downarrow \text{ (decreases with temperature)} \]

4. **Conclusion**:
- Therefore, by increasing the temperature:
- The specific resistance of a conductor increases.
- The specific resistance of a semiconductor decreases.
- Thus, the final answer is that the specific resistance of a conductor increases while that of a semiconductor decreases.

### Final Answer:
- The specific resistance of a conductor increases, and the specific resistance of a semiconductor decreases with increasing temperature.