The resistivity of a wire

Options

A. Varies with its length
B. Varies with its mass
C. Varies with it cross section
D. Is independent of length, cross section and mass of the wire

Answer

To solve the question regarding the resistivity of a wire, we need to understand the factors that affect resistivity and how it differs from resistance. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the definition of resistivity
Resistivity (ρ) is a material property that quantifies how strongly a given material opposes the flow of electric current. It is defined as the resistance of a unit cube of the material.

### Step 2: Identify the factors affecting resistivity
Resistivity is primarily affected by:
- **Nature of the Material**: Different materials have different intrinsic resistivities. For example, copper has a lower resistivity compared to rubber.
- **Temperature**: As temperature increases, the resistivity of most conductors increases due to increased atomic vibrations, leading to more collisions between charge carriers.

### Step 3: Analyze the options given in the question
1. **Varies with its length**: This is incorrect. Resistivity does not depend on the length of the wire; it is a property of the material itself.
2. **Varies with its mass**: This is also incorrect. Resistivity does not vary with mass; it is independent of the amount of material.
3. **Varies with its cross-section**: This is incorrect as well. Resistivity is a property of the material and does not depend on the cross-sectional area of the wire.
4. **Independent of length, cross-section, and mass of the wire**: This statement is correct. Resistivity remains constant for a given material at a specific temperature, regardless of the wire's dimensions.

### Step 4: Conclusion
Based on the analysis, the correct answer is that resistivity is independent of length, cross-section, and mass of the wire. Therefore, option D is the correct answer.

### Final Answer:
**The resistivity of a wire is independent of its length, cross-section, and mass.**

---