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?