Triac Heatup: 1000W Draw - Same Rate?

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In a comparison of two 120V AC circuits with triacs controlling heat elements, the circuit with a 50% duty cycle will heat up more than the one with a continuous gate on, despite both drawing 1000W. This is due to the triac conducting the same power in a shorter time frame, leading to increased heating. The triac in the second circuit is undersized for the 2000W load, presenting a fire hazard when exceeding 15A. Variations in triac quality can also affect performance, particularly under high loads. Additionally, using non-zero-point switching can introduce extra power during the triac's activation.
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Let's say I have two separate 120V AC circuits, each with a triac (15A) that controls a heat element. The first circuit has a heat element that draws a maximum of 1000W. The second circuit heat element draws 2000W. In the first circuit, I leave the triac gate on at all times, and in the second circuit, the triac has a 50% duty cycle, so that the total power drawn is 1000W.

If both of these circuits draw 1000W, will both triacs heat up at the same rate?
 
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Actually no, the one with the 50% duty cycle (estimated) will probably heat up more, because is is conducting the same power in less time. If this is 120V Branch ckts, the triac is undersized for the 2000W load. Also - there is pretty big variation between types / quality of triac dimmers, so running at > 15A is likely a fire hazard.
 
Assume the triac has a fixed resistance. Since power is I^2 * R, if there is twice the current, there is 4X the power. 4X the power for 1/2 the time is 2X the power (on average).

Also, if you do not use zero-point switching there will be additional power when the triac switches on.
 
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