Residential building codes typically require the use of 12ga

Residential building codes typically require the use of 12-gauge copper wire (diameter 0.2053 cm) for wiring receptacles. Such circuits carry currents as large as 20 A. If a wire of smaller diameter (with a higher gauge number) carried that much current, the wire could rise to a high temperature and cause a fire. (a) Calculate the rate at which internal energy is produced in 2.50 m of 12-gauge copper wire carrying a current of 20.0 A. (b) Repeat the calculation for an aluminum wire.

Solution

Resistance, R = rho*l/A = 1.7*10^-8 * 2.5/pi*(0.2053/2)^2*10^-4 = 0.01284 ohm
P = I^2R = 5.138 W

New resistance, R = 0.021148
P = I^2 *R = 8.4592 W