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By the way: What is the 8 kOhm solid state relay value? Are you saying it introduces 8 kilo-ohms of resistance to the 240V signal? That's... really weird, and I don't understand what that would be useful for. Could you elaborate?In general, heat generated equals resistance times current squared, so how much current are you controlling?
Are you able to discover how much current, exactly, or the exact resistance of the furnace load?Where did you get 8 kOhm internal resistance for the SSR please? I saw 1.5kOhm on the spec sheet but may have missed something. Looking at the Derating Curves, I would choose a proper heatsink as proposed on that sheet, not hope to manage it with an aluminium case or plate. Doing that (a proper heatsink) makes the rest of this rather moot.
That was a DC resistance with no load.Try measuring the Voltage drop with a know load an AC power. More info:http://en.wikipedia.org/wiki/Solid-state_relayI see in the specs an input impedance of 1.5k Ohm. and a Voltage drop at rated load of 1.5V. http://www.coleparmer.com/Virtual-Catalog/US/2136Using Ohms Law that means the resistance is 1.5V/40Amp = 37.5mOhm.This makes sense.Have you tried the SSR yet?