In basic electricity and materials science, the resistivity of a conducting wire depends primarily on which of the following factors?

Introduction / Context:
In physics and electrical engineering, it is important to distinguish between resistance and resistivity. Resistance depends on dimensions such as length and cross-sectional area, while resistivity is a fundamental property of the material itself. This question tests whether you understand what resistivity depends on, which is a basic but frequently examined concept.

Given Data / Assumptions:

We are given:
- Several possible factors: length, cross-sectional area, material, shape, and colour of the wire.
- The question specifically refers to 'resistivity' and not simple resistance.

Concept / Approach:
The resistance R of a uniform conductor is given by:
R = ρ * (L / A)
where ρ (rho) is the resistivity of the material, L is the length and A is the cross-sectional area. From this formula, resistivity is a constant for a given material at a given temperature. It does not change with length or area; instead, those quantities affect the resistance. Therefore, resistivity depends only on the nature (material) of the conductor and on temperature, not on its dimensions or shape.

Step-by-Step Solution:
Step 1: Recall the formula R = ρ * (L / A).
Step 2: Recognize that ρ is a material-dependent constant for a particular temperature.
Step 3: Understand that changing length L or cross-sectional area A changes R, but ρ remains the same if the material and temperature remain unchanged.
Step 4: Identify that the material of the wire (e.g., copper, aluminium, nichrome) determines its resistivity.
Step 5: Therefore, choose 'Material of the wire' as the correct answer.

Verification / Alternative check:
Physics textbooks clearly list tables of resistivity values for different materials (metals, alloys, semiconductors, insulators). These values do not depend on how long or thick the wire is, confirming that resistivity is an intrinsic property of the material, not of its size or shape.

Why Other Options Are Wrong:
- Length of the wire: Affects resistance (R), not the intrinsic resistivity ρ.
- Area of cross-section of the wire: Also affects resistance but not ρ itself.
- Shape of the wire: Changing shape or bending does not change the material's intrinsic resistivity.
- Colour of the wire: Colour has no direct relation to electrical resistivity; it is irrelevant here.

Common Pitfalls:
A very common error is to confuse resistance and resistivity. Students who see formulae involving length and area may mistakenly think resistivity also depends on those. Always remember the distinction: resistivity (ρ) is a property of the material and temperature; resistance (R) is what depends on the geometry (L and A) and the material's resistivity. Clarifying this difference avoids many conceptual mistakes in electricity problems.

Final Answer:
Correct option: Material of the wire