Resistivity of a conducting wire :

Options

A. varies with its length
B. varies with mass
C. varies with is cross-section
D. is independent of its demensions.

Answer

To solve the question regarding the resistivity of a conducting wire, we need to analyze the relationship between resistivity and the dimensions of the wire.

### Step-by-Step Solution:

1. **Understanding Resistivity**:
Resistivity (ρ) is a property of the material that indicates how strongly it resists the flow of electric current. It is defined as the resistance of a unit length of the material with a unit cross-sectional area.

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

3. **Rearranging the Formula**:
From the resistance formula, we can rearrange it to express resistivity:
\[ \rho = \frac{R \cdot A}{L} \]
This shows that resistivity is calculated based on resistance, area, and length.

4. **Analyzing Dependence**:
At first glance, it may seem that resistivity depends on both the area (A) and length (L) of the wire. However, resistivity is a material property and does not change with the dimensions of the wire.

5. **Conclusion**:
Since resistivity is a characteristic of the material itself and is independent of the wire's length and cross-sectional area, we can conclude that:
- **Resistivity is independent of its dimensions**.

6. **Final Answer**:
Therefore, the correct option is **D: is independent of its dimension**.