Question

Residential building codes typically require the use of 12-gauge copper wire (diameter 0.205 cm) for wiring receptacles. Such circuits carry currents as large as 20.0 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. (Table of resistivities)

Material	Resistivitya (Ω · m)	Temperature Coefficient of Resistivityb α [(°C)−1]
Silver	1.59 ✕ 10−8	3.8 ✕ 10−3
Copper	1.7 ✕ 10−8	3.9 ✕ 10−3
Gold	2.44 ✕ 10−8	3.4 ✕ 10−3
Aluminum	2.82 ✕ 10−8	3.9 ✕ 10−3
Tungsten	5.6 ✕ 10−8	4.5 ✕ 10−3
Iron	10.0 ✕ 10−8	5.0 ✕ 10−3
Platinum	11 ✕ 10−8	3.92 ✕ 10−3
Lead	22 ✕ 10−8	3.9 ✕ 10−3
Nichromec	1.00 ✕ 10−6	0.4 ✕ 10−3
Carbon	3.5 ✕ 10−5	−0.5 ✕ 10−3
Germanium	0.46	−48 ✕ 10−3
Silicond	2.3 ✕ 103	−75 ✕ 10−3
Glass	1010–1014
Hard rubber	≈1013
Sulfur	1015
Quartz (fused)	75 ✕ 1016

(a) Calculate the rate at which internal energy is produced in 2.40 m of 12-gauge copper wire carrying a current of 20.0 A.
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(b) Repeat the calculation for a 12-gauge aluminum wire.
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Explain whether a 12-gauge aluminum wire would be as safe as a copper wire.

Answer 1