Electrical resistivity of a given metallic wire depends upon

Options

A. its length.
B. its thickness.
C. its shape.
D. nature of the material.

Explanation

To solve the question regarding the factors on which the electrical resistivity of a given metallic wire depends, we can break it down into the following steps:

### Step 1: Understand the Concept of Electrical Resistivity
Electrical resistivity, often denoted by the symbol ρ (rho), is a fundamental property of materials that quantifies how strongly a given material opposes the flow of electric current. It is also referred to as specific resistance.

### Step 2: Identify the Formula for Resistance
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.

### Step 3: Analyze the Factors Affecting Resistance
From the formula, we can see that resistance depends on:
- Length (L) of the wire: Longer wires have higher resistance.
- Cross-sectional area (A) of the wire: Thicker wires have lower resistance.

### Step 4: Differentiate Between Resistivity and Resistance
While resistance depends on the dimensions (length and area) of the wire, resistivity (ρ) is a property that is intrinsic to the material itself. It does not change with the dimensions of the wire.

### Step 5: Identify the Factor that Affects Resistivity
The only factor that affects the electrical resistivity of a metallic wire is the nature of the material. This means that different materials (like copper, aluminum, silver, or iron) will have different resistivities.

### Conclusion
Thus, the electrical resistivity of a given metallic wire depends solely on the nature of the material.

### Final Answer
**The electrical resistivity of a given metallic wire depends on the nature of the material.**

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