Residential building codes typically require the use of 12-gauge copper wire (di

Question

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 2.10 m of 12-gauge copper wire carrying a current of 20.0 A.

Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. W
(b) Repeat the calculation for an aluminum wire.

Your response differs from the correct answer by more than 10%. Double check your calculations. WWould a 12-gauge aluminum wire be as safe as a copper wire?

Explanation / Answer

the copper wire carrying a current , I = 20.0 A.
the length of the copper wire is 2.10 m

the resistance in 12- Cu is 0.0052 ohms/m
the total resistance , R = 2.10*0.0052 = 0.01092 ohms

power P = I²R = 20²*0.01092 = 4.36 watts

the resistance in 12- Al is 0.00856 ohms/m
the total resistance , R = 2.10*0.00856 = 0.01797 ohms

power, P = I²R = 20²*0.01797 = 7.19 watts

therefore the Al wire dissipates more heat than Cu.

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