As the temperature of a metallic resistor is increased,the product of its resistivity and conductivity

Options

A. (a)increase
B. (b)decrease
C. (c ) remains constant
D. (d) may increase or decrease.

Answer

To solve the question regarding the relationship between resistivity, conductivity, and temperature for a metallic resistor, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definitions**:
- **Resistivity (ρ)**: A measure of how strongly a material opposes the flow of electric current. It is temperature-dependent for metallic conductors.
- **Conductivity (σ)**: A measure of how easily electricity flows through a material. It is also temperature-dependent and is defined as the inverse of resistivity: \( σ = \frac{1}{ρ} \).

2. **Relationship Between Resistivity and Conductivity**:
- The product of resistivity and conductivity can be expressed mathematically as:
\[ ρ \cdot σ = ρ \cdot \frac{1}{ρ} = 1 \]
- This indicates that the product of resistivity and conductivity is a constant value, regardless of temperature changes.

3. **Effect of Temperature on Resistivity and Conductivity**:
- For metallic conductors, as the temperature increases, resistivity generally increases. This is because the increased thermal energy causes more collisions between charge carriers, leading to higher resistance.
- Conversely, conductivity decreases with increasing temperature for metals, as it is inversely related to resistivity.

4. **Conclusion**:
- Since the product of resistivity and conductivity is always equal to 1, it does not change with temperature. Therefore, the correct answer to the question is that the product remains constant.

### Final Answer:
The product of resistivity and conductivity remains constant as the temperature of a metallic resistor is increased.