A. as area of a cross section of the Conductor is inversely proportional to the resistance.hence the resistance will be doubled if area of a cross section of a wire is halted.

Explanation:

To analyze the changes in resistance and resistivity when a wire is stretched, we need to consider the relationship between these quantities and the physical properties of the wire.

(a) Change in Resistance:

Resistance (R) is given by the formula R = ρ * (L/A), where ρ is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area of the wire.

When the length of the wire is doubled, the new length becomes 2L. However, the area of the cross-section is halved, so the new area becomes A/2.

Using the formula for resistance, the new resistance (R') can be calculated as follows:

R' = ρ * (2L) / (A/2)
= 4ρL / A

Therefore, when the wire is stretched so that the length is doubled and the area of cross-section is half, the resistance of the wire increases by a factor of 4.

(b) Change in Resistivity:

Resistivity (ρ) is a characteristic property of a material and represents its inherent resistance to electric current. It is given by the formula ρ = R * (A/L).

When the length of the wire is doubled and the area of cross-section is halved, the new resistivity (ρ') can be calculated as follows:

ρ' = R' * (A/2) / (2L)
= (4ρL / A) * (A/2) / (2L)
= 2ρ/A

Therefore, when the wire is stretched as described, the resistivity of the wire remains unchanged. The resistivity is solely dependent on the material from which the wire is made and is not affected by changes in length or area.

Summary:

(a) When a wire of length L and resistance R is stretched so that the length is doubled and area of cross-section is half, the resistance of the wire increases by a factor of 4.

(b) The resistivity of the wire remains unchanged. It is solely dependent on the material from which the wire is made and is not affected by changes in length or area.