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 question regarding the relationship between resistivity and conductivity as the temperature of a conductor increases, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definitions**:
- **Resistivity (ρ)**: It is a property of the material that quantifies how strongly it resists the flow of electric current. It typically increases with temperature for conductors.
- **Conductivity (σ)**: It is the reciprocal of resistivity and indicates how easily electric current can flow through a material. It typically decreases with an increase in temperature for conductors.

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

3. **Ratio of Resistivity to Conductivity**:
- We need to find the ratio of resistivity to conductivity:
\[ \text{Ratio} = \frac{\rho}{\sigma} \]
- Substituting the relationship from step 2:
\[ \text{Ratio} = \frac{\rho}{\frac{1}{\rho}} = \rho^2 \]

4. **Effect of Temperature on the Ratio**:
- As the temperature increases, the resistivity (ρ) increases. Since the ratio is proportional to the square of resistivity (ρ²), we can conclude that:
\[ \text{Ratio} = \rho^2 \text{ increases as } \rho \text{ increases.} \]

5. **Conclusion**:
- Therefore, the ratio of resistivity to conductivity increases as the temperature of the conductor increases. The correct answer is option A: increases.