Maximum allowable current in a 12-gauge aluminum wire

[yanyin]

Aluminum wiring has sometimes been used instead of copper for economy. According to the National Electrical Code, the maximum allowable current for 12-gauge copper wire with rubber insulation is 20A. What should be the maximum allowable current in a 12-gauge aluminum wire if the power per unit length delivered to the resistance in the aluminum write is the same as that delivered in the copper wire?
Please help me to figure out the steps. the answer is 15.5A.

 

[drmermaid]

Although I am late with an answer for the original author someone might benefit.
You need to calculate the respective Resistances for Copper and Aluminium using their resistivities. The problem also stated that the wire was 12 gauge- I found the xs Area to be 3.310 x 10^-6 m2 (looked this up on internet) and the Power used by each wire to be equal while the Imax for the copper wire was 20A.
Starting with Copper the resistivity is 1.7 x 10^-8 ohm/m.
Using the formula R/l= resistivity/ xs Area I found that R/l= 5.14 x 10^-3 ohm/m
The using V=IR I found V= 1.03 x 10^-1 V.
Calculate the Power using P=I2R or P=IV you get 2.056W.

Next work out the copper story by firstly finding the R/l= 2.82 x 10^-8 ohm.m/ 3.310 m2
and that works out to be 8.52 x 10^-3 ohm/m.
Using the Power value above substitute the value for R(aluminium) and Power (copper) in P=I2R and you get Imax for Aluminium = 15.53A.

It also agrees with the theory that the greater the resistance in a wire the lesser the Imax for the wire when comparing two different metal wires of the same gauge.

This is my FIRST POST ANSWER!

 

[MATLABdude]

...This is my FIRST POST ANSWER!

Unfortunately, I think it's 5 years too late for this fellow's NEC exam (or whatever it was for)!

 

[drmermaid]

It was in my physics homework so who knows who else wants to figure it out.