Final answer:
To find the length of wire needed to create a 4.0Ω resistor with a given diameter and resistivity, use the resistance formula for a cylindrical conductor, and solve for the length, resulting in approximately 190 meters.
Step-by-step explanation:
The question involves finding the length of wire used to create a 4.0Ω resistor given the wire diameter (1.0 mm) and the resistivity (1.68×10⁻⁸ Ω·m). We use the formula for the resistance of a cylindrical conductor, R = ρL/A, where R is resistance, ρ is resistivity, L is length, and A is the cross-sectional area of the wire.
The area, A, can be calculated using the formula for the area of a circle, A = π(d/2)², where d is the diameter of the wire. Substituting the known values into the resistance formula and solving for L gives us the length of the wire that would create a 4.0Ω resistor.
Upon calculating using the given values, we find that the length of the wire is closest to option (D) 190 m.