A metallic wire having resistivity ρ is cut into four equal parts. The resistivity of each part is:

Correct option is C

The correct answer is (C) ρ.

The resistivity (ρ) of a material is an intrinsic property of the material and does not depend on its shape, size, or dimensions. When a metallic wire is cut into four equal parts:

1. Resistivity (ρ): It remains constant because it depends only on the material of the wire, not its length or cross-sectional area.
2. Resistance (R): Resistance is given by:

​$$R=ρ \frac{L}{A}$$​​

• When the wire is cut into four equal parts, the length of each part (L′) becomes one-fourth of the original length (L/4).
• Resistance for each part will reduce proportionally, but the resistivity (ρ) remains unchanged.

Key Concept:

• Resistivity (ρ): Depends only on the material and its temperature.
• Resistance (R): Depends on dimensions (length and cross-sectional area) and the resistivity.