In this question, we are given three copper wires with different lengths and different areas of cross-section, and we need to determine which wire has the highest resistivity.
Resistivity is a property of a material that determines its resistance to the flow of electric current. It is given by the formula ρ = R × A / L, where ρ represents resistivity, R represents resistance, A represents the cross-sectional area, and L represents the length of the wire.
In options 1, 2, and 3, the lengths and cross-sectional areas of the wires are different. According to the formula, the resistivity of a wire is directly proportional to its length and inversely proportional to its cross-sectional area. Therefore, the wire with the highest resistivity would have the longest length and the smallest cross-sectional area.
Option 4 states that all the wires would have the same resistivity. This is because resistivity is a property of the material, not the specific dimensions of the wire. Copper has a constant resistivity regardless of the length or cross-sectional area of the wire.
Therefore, the correct answer is option 4 - all the wires would have the same resistivity.