# Design of a nichrome heating element - achieving predetermined power dissipation

I want to make a nichrome heating element with 1500 watts of heat being produced while running on 120v AC. This will be part of a air heater as a fan drives air over a circular coil of nichrome wire.

My first thoughts where that this would be very simple with Ohm's law. I'd simply divide 1500 watts by 120 volts to get 12.5 amps of current. Then knowing v and i and Ohm's Law i'd figure out r by 120v/12.5a = 9.6 ohms of resistance needed in the element.

But after reading more on the behavior of metals resistance as temperature increases also tends to increases the metals resistance, my first attempt seemed less valid as a way to truly determine how much heat this thing is really going to produce. According to this the 9.6 ohm element will make less heat than what what I thought.

The book I read, All About Circuits, describes the current through a metal conductor as voltage increases more like the graph of y=sqrt(x), rather than what I thought originally with constant resistance and linear voltage and current y=x.

How do I figure out the cold resistance of this element with out actually building it and fiddling with the resistance till I get the 1500 watts?

• Well you know what the hot resistance needs to be - 9.6 ohms - can't you find a graph for nichrome wire and work backwards to see what the cold resistance will be? I bet there's data on nichrome wire temperature for a given current. Dec 31, 2013 at 21:43
• @Andy : to do that you'd need to know the temperature of the heated wire... calculating that would be non-trivial, especially in airflow.
– user16324
Dec 31, 2013 at 21:45
• And then what happens when the fan slows a little, or the input air changes its temperature or humidity or turbulence? Some sort of feedback would appear to be required... Dec 31, 2013 at 23:10
• Right this seems pretty complicated to get a constant wattage no matter what. i'm just interested in pulling as much current without blowing the breaker. looks like from a table nichrome wire has about 4-6% more resistance at 800F to 1600F. So i was thinking to get "pretty close" I'd take off about 5% of the cold heating element and that would get me in the ball park. Thoughts? Dec 31, 2013 at 23:23
• @Maximilian89 sounds a good ploy if it's only a few percent. Dec 31, 2013 at 23:36