A 14-gauge copper wire of diameter 1.628 mm has a drift speed of 1.00 mm/s. Using 8.342 x 10^28 free electrons per cubic metre, what current flows?

1. The radius is half the diameter: r = 0.814 x 10^-3 m. 2. A = pi r^2 = pi (0.814 x 10^-3 m)^2 = 2.082 x 10^-6 m^2. 3. Use I = n q A v_d with v_d = 1.00 mm/s = 1.00 x 10^-3 m/s. 4. n q = (8.342 x 10^28 /m^3)(1.60 x 10^-19 C) = 1.335 x 10^10 C/m^3. 5. I = (1.335 x 10^10 C/m^3)(2.082 x 10^-6 m^2)(1.00 x 10^-3 m/s) = 27.8 A. 6. 13.9 A halves the area by using the diameter instead of the radius before squaring. 7. 55.6 A doubles it the other way, and 8.90 A drops the pi from the area entirely. _Source: OpenStax College Physics (CC BY 4.0), Ch 20 "Electric Current, Resistance, and Ohm's Law", section Drift Velocity_