Final answer:
When a wire of fixed volume is stretched thus doubling its length, the resistance will quadruple due to the halving of its cross-sectional area. However, the resistivity will remain constant as it's a property of the material, not dependent on its dimensions.
Step-by-step explanation:
The subject of this question is Electrical Resistance and Resistivity in a wire, which are concepts in Physics. In Physics, the resistance, R, of a wire is given by the formula R = ρL/A, where ρ is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area. If the length of the wire is doubled without changing the total volume of the material, the cross-sectional area will be halved. Since the resistance is directly proportional to the length but inversely proportional to the area, doubling the length and halving the area will effectively quadruple the resistance.
However, resistivity is a property of the material itself and not dependent on its shape or size. Thus, the resistivity, ρ, will not change when the wire length is stretched.
Learn more about Resistance and Resistivity