The specific resistance of a conductor increases with:

Options

A. increases in temperature
B. increases in cross-sectional area
C. decreases in length
D. decreases in cross-sectional area

Explanation

To solve the question regarding how the specific resistance of a conductor changes, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Specific Resistance (Resistivity)**:
- Specific resistance (or resistivity) of a material is a measure of how strongly it resists the flow of electric current. It is denoted by the symbol \( \rho \).

2. **Recall the Formula for Resistance**:
- The resistance \( R \) of a conductor can be expressed by the formula:
\[ R = \frac{\rho L}{A} \]
where \( L \) is the length of the conductor, \( A \) is the cross-sectional area, and \( \rho \) is the specific resistance.

3. **Identify the Relationship Between Resistivity and Temperature**:
- The resistivity of a conductor is dependent on temperature. The relationship can be expressed as:
\[ \rho_T = \rho_0 (1 + \alpha (T - T_0)) \]
where:
- \( \rho_T \) is the resistivity at temperature \( T \),
- \( \rho_0 \) is the resistivity at a reference temperature \( T_0 \),
- \( \alpha \) is the temperature coefficient of resistivity,
- \( T \) is the temperature,
- \( T_0 \) is the reference temperature.

4. **Analyze the Effect of Temperature on Resistivity**:
- For most metallic conductors, the temperature coefficient \( \alpha \) is positive, meaning that as the temperature \( T \) increases, the term \( (1 + \alpha (T - T_0)) \) also increases.
- Therefore, as temperature increases, the specific resistance \( \rho_T \) also increases.

5. **Conclusion**:
- From the analysis, we can conclude that the specific resistance of a conductor increases with an increase in temperature. Thus, the correct answer is:
- **Option A**: The specific resistance of a conductor increases with temperature.