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I am still not sure on the math of this whole idea. a hot water heater element is just a wire with something non conductive around it. so a heater element that was rated to produce 1500 watts at a given voltage would have a smaller wire than a element rated 4500 watts at the same voltage. more energy can fit thru the bigger wire. I am I think right ? if so if we put a lower voltage thru the any element will it still produce the 3.41 BTU per W.

this is the big question in my mind. if that conversion stays constant then the rest can be worked out