How does the ratio of resistivity to conductivity changes when temperature of a conductor is increased?

Options

A. Increases
B. Decreases
C. Remain constant
D. Cannot say anythings

Explanation

To solve the question of how the ratio of resistivity to conductivity changes when the temperature of a conductor is increased, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Conductivity and Resistivity**:
- Conductivity (σ) is defined as the ability of a material to conduct electric current, and it is given by the formula:
\[ \sigma = \frac{n e^2 \tau}{m} \]
where \( n \) is the charge carrier density, \( e \) is the charge of an electron, \( \tau \) is the relaxation time, and \( m \) is the mass of the charge carriers.
- Resistivity (ρ) is the reciprocal of conductivity:
\[ \rho = \frac{1}{\sigma} \]

2. **Effect of Temperature on Conductivity**:
- When the temperature of a conductor is increased, the kinetic energy of the electrons increases. This leads to more frequent collisions among the charge carriers.
- As a result of these more frequent collisions, the relaxation time (τ) decreases.

3. **Relating Relaxation Time to Conductivity**:
- Since conductivity is directly proportional to the relaxation time, if τ decreases, the conductivity σ will also decrease:
\[ \sigma \propto \tau \implies \text{If } \tau \text{ decreases, then } \sigma \text{ decreases.} \]

4. **Effect on Resistivity**:
- Since resistivity is the reciprocal of conductivity, if conductivity decreases, resistivity will increase:
\[ \rho \propto \frac{1}{\sigma} \implies \text{If } \sigma \text{ decreases, then } \rho \text{ increases.} \]

5. **Calculating the Ratio of Resistivity to Conductivity**:
- The ratio of resistivity to conductivity can be expressed as:
\[ R = \frac{\rho}{\sigma} \]
- Since we established that resistivity (ρ) increases and conductivity (σ) decreases with increasing temperature, we can analyze the ratio:
- If ρ increases and σ decreases, the overall ratio \( R \) will increase.

6. **Conclusion**:
- Therefore, when the temperature of a conductor is increased, the ratio of resistivity to conductivity (R) increases.

### Final Answer:
The ratio of resistivity to conductivity increases when the temperature of a conductor is increased.