Final answer:
The resistance of a copper wire can be computed using its resistivity, length, and cross-sectional area derived from its diameter. Area is calculated with the wire's radius, in turn obtained from the diameter, and then the resistance is found using the formula for resistance.
Step-by-step explanation:
The resistance of a copper wire can be calculated using the formula R = ρ × (L/A), where ρ is the resistivity of the material (for copper, it's typically 1.68 × 10-8 Ω·m at 20°C), L is the length of the wire, and A is its cross-sectional area. Since the area is a function of diameter, we can find the area A of the wire using the formula A = π × (d/2)2, where d is the diameter of the wire. For a 1.5 mm diameter wire, the radius is 0.75 mm, or 0.75 × 10-3 m. Hence, A = π × (0.75 × 10-3 m)2. Once we have the area, we can substitute ρ, L, and A into the first formula to get the resistance of the 5.1-m length of copper wire.