With increase in temperature, the resistivity of a conductor

Options

A. Does not change
B. May increase or decrease
C. Decreases
D. Increases

Answer

To solve the question regarding the effect of temperature on the resistivity of a conductor, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Resistivity**:
- Resistivity (ρ) is a property of materials that quantifies how strongly they resist the flow of electric current. It is influenced by temperature, especially in conductors like metals.

2. **Effect of Temperature on Metal Conductivity**:
- In metals, electrical conductivity is primarily due to the movement of free electrons. As the temperature of a metal increases, the thermal energy of the metal ions also increases.

3. **Increased Vibrations of Metal Ions**:
- With an increase in temperature, the vibrations of the metal ions become more pronounced. This increased vibration leads to more frequent collisions between the free electrons and the vibrating metal ions.

4. **Impact on Resistance**:
- The increased collisions between electrons and vibrating ions result in an increase in resistance (R) of the conductor. According to the relationship \( R = \rho \frac{L}{A} \), where \( L \) is the length and \( A \) is the cross-sectional area, an increase in resistance implies an increase in resistivity (ρ).

5. **Conclusion**:
- Therefore, as the temperature increases, the resistivity of the conductor also increases. Thus, the correct answer to the question is that the resistivity of the conductor increases with an increase in temperature.

### Final Answer:
The resistivity of a conductor increases with an increase in temperature.