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

Question

Residential building codes topically require the use of 12-gauge copper wire (diameter -2.05 mm, 1 mm = 0.001 m) for firing receptacles. Such circuits cam current as Urge as 20.0 A. If a wire of smaller diameter carried such current, the wire could become overheated and cause a fire. (a) Calculate the rate at which internal heat is produced in a 12-gauge copper (Cu) wire (I - 1.00 m, d = 1 mm) carrying 20.0 A. (b) What if? Repeat the calculation for a 12-gauge aluminum (Al)wire(I = 1.00 m, d = 1 mm). (c) Discuss whether a 12-gauge aluminum wire would be as safe as a copper wire. The resistivities of copper (Cu) and aluminum (Al); rho = 1.7 times 10^-8 Ohm m; rho_ = 2.82 times 10^-8 Ohm m.

Explanation / Answer

rate at which internal heat is produced is P = i^2*R

Given that i = 20 A

R = rho*l/A

rho is the resistivity of copper wire = 1.7*10^-8 ohm-m

l = 1 m

A = pi*(d/2)^2 = 3.142*(10^-3/2)^2 = 7.855*10^-7 m^2

then R = rho*l/A = 1.7*10^-8*1/(7.855*10^-7) = 0.0216 ohm

P= i^2*R = 20^2*0.0216 = 8.64 W

b) P = i^2*R

R = rho*l/A = (2.82*10^-8(1))/(7.855*10^-7) = 0.0359 ohm

P = i^2*R = 20^2*0.0359

P = 14.36 W

C) the wire in which lowest power losses occured is safe

the safest wire is copper -wire

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