The electrical resistance of a conductor :

Options

A. varies directly to its area of cross-section
B. decreases with increase in its temperature
C. decreases with increase in its conductivity
D. is independent of its shape but depends only on its volume

Answer

To solve the question regarding the electrical resistance of a conductor, we will analyze the statements provided and determine their validity based on the properties of resistance.

### Step-by-Step Solution:

1. **Understanding Resistance**:
The resistance \( R \) of a conductor is given by the formula:
\[ R = \frac{\rho L}{A} \]
where:
- \( R \) is the resistance,
- \( \rho \) is the resistivity of the material,
- \( L \) is the length of the conductor,
- \( A \) is the area of cross-section.

2. **Analyzing Statement 1**:
- **Statement**: "It varies directly to its area of cross-section."
- **Analysis**: From the formula, we see that resistance is inversely proportional to the area \( A \). Therefore, if the area increases, the resistance decreases. This statement is **incorrect**.

3. **Analyzing Statement 2**:
- **Statement**: "It decreases with increase in its temperature."
- **Analysis**: For most conductors (like metals), resistance increases with an increase in temperature due to increased collisions among free electrons. This statement is also **incorrect**.

4. **Analyzing Statement 3**:
- **Statement**: "It decreases with increase in its conductivity."
- **Analysis**: Conductivity \( \sigma \) is defined as the inverse of resistivity \( \rho \) (i.e., \( \sigma = \frac{1}{\rho} \)). From the resistance formula, if conductivity increases, resistivity decreases, leading to a decrease in resistance. Thus, this statement is **correct**.

5. **Analyzing Statement 4**:
- **Statement**: "It is independent of its shape, but depends only on its volume."
- **Analysis**: Resistance does depend on the shape of the conductor because the area of cross-section is a function of the shape. Therefore, this statement is **incorrect**.

### Conclusion:
The only correct statement regarding the electrical resistance of a conductor is **Statement 3**: "It decreases with increase in its conductivity."