**Explanation:**

When a wire is stretched to double its length, its resistance becomes 4 times, while the resistivity remains the same. To understand why this happens, let's break down the concept step by step.

**1. Resistance of a Wire:**
Resistance is a property of a material that opposes the flow of electric current. It is determined by the following factors:

- Length of the wire: The longer the wire, the higher the resistance.
- Cross-sectional area of the wire: The smaller the cross-sectional area, the higher the resistance.
- Resistivity of the material: A material with higher resistivity will have higher resistance.

**2. Relationship between Resistance, Length, Cross-sectional Area, and Resistivity:**
The resistance of a wire can be mathematically expressed using Ohm's Law:

Resistance (R) = (Resistivity (ρ) * Length (L)) / Cross-sectional Area (A)

This equation shows that resistance is directly proportional to the length of the wire and resistivity, and inversely proportional to the cross-sectional area of the wire.

**3. Effect of Stretching the Wire:**
When a wire is stretched to double its length:

- Length (L) is doubled.
- Cross-sectional area (A) remains the same.
- Resistivity (ρ) remains the same.

**4. Calculation of New Resistance:**
Using the equation from step 2, we can calculate the new resistance (R') of the stretched wire:

R' = (ρ * 2L) / A

Since ρ and A remain constant, the equation simplifies to:

R' = 2R

This means that the new resistance (R') is double the original resistance (R).

**5. Relationship between Resistance and Length:**
From step 4, we can observe that the resistance of a wire is directly proportional to its length. When the length is doubled, the resistance also doubles.

**6. Relationship between Resistance and Resistivity:**
From step 4, we can also observe that the resistance of a wire is independent of its resistivity. Stretching the wire does not change the resistivity of the material.

**Conclusion:**
When a wire is stretched to double its length, its resistance becomes 4 times the original resistance. This is because resistance is directly proportional to the length of the wire. However, the resistivity of the material remains the same, as it is an inherent property of the material.

Yes no change in resistivty being same material' s wire