If the cross-sectional area of a conductor is doubled, other factors remaining the same, the resistivity of the conductor will be: 

The Correct answer is same.

Key Points

• Resistivity is a material property that measures how strongly a material opposes the flow of electric current.
• The resistivity of a conductor is dependent only on the material's nature and is independent of its shape and size, such as its cross-sectional area or length.
• When the cross-sectional area of a conductor is doubled, the resistance is affected (resistance decreases), but the resistivity remains unchanged.
• This is because resistivity is defined as a constant for a specific material at a given temperature, regardless of changes in its dimensions.
• The formula for resistivity is ρ = R × (A / L), where ρ represents resistivity, R is resistance, A is the cross-sectional area, and L is the length of the conductor.
• From the formula, resistivity is independent of the conductor's dimensions; it is solely determined by the intrinsic properties of the material.
• Thus, doubling the cross-sectional area affects the resistance but does not alter the inherent resistivity of the conductor.

 Additional Information

• halved
  • Halving the resistivity would imply a change in the fundamental properties of the material, which does not happen by altering the conductor's dimensions.
  • Resistivity is constant for a specific material and is independent of changes in cross-sectional area.
• one fourth
  • The term one fourth might apply to changes in resistance when the cross-sectional area is quadrupled, but it does not affect resistivity, as resistivity depends solely on the material.
• doubled
  • Doubling resistivity would require a fundamental alteration of the material properties, which is not related to changes in physical dimensions like cross-sectional area.