Copper has resistivity 1.72 x 10^-8 ohm m. What is the resistance of 20.0 m of 12-gauge copper wire of diameter 2.053 mm?

1. Use R = rho L / A for a uniform cylinder. 2. The radius is half the diameter, r = 1.0265 x 10^-3 m. 3. A = pi r^2 = 3.310 x 10^-6 m^2. 4. Numerator: rho L = (1.72 x 10^-8 ohm m)(20.0 m) = 3.44 x 10^-7 ohm m^2. 5. R = (3.44 x 10^-7 ohm m^2) / (3.310 x 10^-6 m^2) = 0.104 ohm. 6. 0.052 ohm is what you get by using the full diameter as the radius, which doubles the area. 7. 1.04 ohm is a factor of ten out and would make ordinary house wiring waste noticeable power. _Source: OpenStax College Physics (CC BY 4.0), Ch 20 "Electric Current, Resistance, and Ohm's Law", section 20.3 Resistance and Resistivity_