As the temperature of a conductor increases,its resistivity and conductivity change.the ratio of resistivity to conductivity

Options

A. (a)increase
B. (b)decrease
C. (c )remain constant
D. (d)may increase or decrease depending on the actual temperature.

Answer

To solve the problem, we need to understand the relationship between resistivity (ρ) and conductivity (σ) of a conductor as temperature changes.

### Step-by-Step Solution:

1. **Understanding the Definitions**:
- **Resistivity (ρ)**: It is a measure of how strongly a material opposes the flow of electric current. It is temperature-dependent.
- **Conductivity (σ)**: It is the measure of a material's ability to conduct electric current. It is the reciprocal of resistivity.

2. **Relationship Between Resistivity and Conductivity**:
- The relationship can be expressed as:
\[ \sigma = \frac{1}{\rho} \]
- This means that conductivity is inversely proportional to resistivity.

3. **Finding the Ratio of Resistivity to Conductivity**:
- We need to find the ratio \( \frac{\rho}{\sigma} \).
- Using the relationship from step 2, we can express this ratio as:
\[ \frac{\rho}{\sigma} = \frac{\rho}{\frac{1}{\rho}} = \rho^2 \]

4. **Effect of Temperature on Resistivity and Conductivity**:
- As the temperature of a conductor increases, its resistivity (ρ) generally increases. This is because the increased thermal energy causes more collisions between charge carriers and the lattice structure of the material.
- Consequently, since conductivity (σ) is inversely related to resistivity, as resistivity increases, conductivity decreases.

5. **Analyzing the Ratio**:
- Since \( \frac{\rho}{\sigma} = \rho^2 \), if resistivity increases with temperature, then \( \rho^2 \) will also increase.
- Therefore, the ratio \( \frac{\rho}{\sigma} \) will increase as the temperature increases.

### Conclusion:
As the temperature of a conductor increases, the ratio of resistivity to conductivity \( \frac{\rho}{\sigma} \) increases.