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Extruder heater overpowered to death?

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Ok so I know this happens often but I think I worked out why in my case and searching hasn't answered my question. My extruder heated up for the first time last night and then this morning nothing. Multimeter says open-circuit in the resistor so many google and forums searches say this is normal after a while and some can be faulty straight up (Mind you I bought a completed J-Head hotend from BilbyCNC here in Australia).

Getting a replacement is easy, even if it does take 7 days to get across the country and cost me 5 times as much in shipping :S But my calculations are showing that the 6.8ohm 3W resistor I was supplied is actually dissipating about 20W of power which I believe is the cause of the failure.

My power supply is a 12V ATX and the resistor is 6.8ohm so P = V^2 / R which is 12^2 / 6.8 = 21.17W.
Thats 7 times the rated power output of the resistor. I know enough about electronics to think that something isn't right here but I could be wrong. Will another resistor of the same values die early again?

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