If a wire is stretched to quadruple its length without changing its area, what will happen to its resistivity?

Correct option is C

Correct option: (c), It remains the same.

• ​Resistivity (ρ\rhoρ ) is a material property that depends on the nature of the material and does not change with the physical dimensions of the wire (such as length or cross-sectional area).
  
• In other words, resistivity is independent of the length or cross-sectional area of the wire. It only depends on the material itself (like copper, aluminum, etc.) and its temperature. So, if a wire is stretched to quadruple its length without changing its cross-sectional area, the resistivity will remain the same.
  

Information Booster: 

Resistivity ($\rho$) is defined as: 

$$R = p \times \frac{L}{A}$$ 

• ​R is the resistance,
  
• ρ is the resistivity,
  
• L is the length,
  
• A is the cross-sectional area.
  If the length of the wire is stretched to four times its original length ($L\to 4L$) and the area remains constant, then the resistivity (ρ\rhoρ) remains unchanged, because resistivity is only a function of the material and temperature.