Nichrome wire resistance problem

[Jakefreese]

Homework Statement

Build a heater that runs on 120vac no more than 10 amps. How many watts, 1mm nichrome wire, how long will it have to be at 20deg C. What will the resistance be at 1200deg F. What is the new power at the new resistance.

Homework Equations

R=V/I P=E/I R=L/A

P(T)=p0(1+a(t-t0)

Nichrome resistance 100e^-8 at 20 deg C Temp coefficient .0004

The Attempt at a Solution

I have the wattage for the original, I have the resistance at 1200deg F for 1 meter of wire. I just can not seem to get the right number for the wire length at 20deg C I keep coming up with like 15mm long but it is not right, when you use that length value with the resistance for 1200deg it is soooo far off.

I also tried 1*10^6/1=12/x to find the length and that does not work either and I do not have the wire area if I do it that way. I have gotten myself sooo confused trying to figure out this one part!

 

[Delphi51]

Nichrome resistance 100e^-8 at 20 deg C Temp coefficient .0004

Was this given in the question? What units does it have?
My GUESS would be that it is the resistivity in ohm-meters and that you need to use a formula (entering the cross sectional area and length) to calculate the resistance.

Actually, you will calculate the resistance you require from the potential and current first, then enter that in the resistivity formula to find the length you need. If you don't have the resistivity formula, look up resistivity in Wikipedia.

 

[Jakefreese]

Yeah it was in ohm/meters. I Believe I have figured out where I had it screwed up.

It ended up being 9.42 meters of wire to keep under 10 amps, and resistance at 635deg C was 7620 ohms which ends up being 2 watts. The resistance and the temp coefficient were in the book. Thanks! I will be more clear on the next one!