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What would likely happen if a ceramic power resistor was powered well over its power rating (for test/learning purposes and likely buried inside a bucket of sand)? By "well over", I mean 10 to 100-fold.

Structurally these resistors seem like they would be refractory to temperature (up to 1000C even) as they are made of ceramic, resistance wire, fiberglass shell in some cases, and a crimp or weld. If the ceramic did not crack, the weld did not melt, no gasses were released, and the wire did not oxidize and crack, I would expect the answer is that it would get really hot, and that its resistance would increase to a point where it would be difficult to dissipate more energy through it at the same voltage.
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enter image description here A datasheet for a similar resistor to the one above shows that there is severe derating for ceramic resistors at high temperature. It seems the focus of the "power rating" when dealing with a ceramic power resistor is more about the resistance value being what you think it will be when it is dissipating energy at or below its rated value.

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    \$\begingroup\$ From experience I can tell you they glow a lovely shade of orange, smell somewhat different than regular burning electronics and eventually desolder themselves if at all possible. \$\endgroup\$
    – Bryan
    May 18, 2022 at 4:33
  • \$\begingroup\$ The resistance would also probably drift out of spec; even if they physically survive the resistance may change by a significant amount. \$\endgroup\$
    – Hearth
    May 18, 2022 at 4:35

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If you run the resistor at a higher and higher power (and amount of time) as listed in the "Short time overload" you will begin to degrade the internal materials. Most likely at some point the fine wires that you can see around the core or the internal connections will simply melt like a simple fuse, and that will be the end of the resistor. If you reach the overload point slowly you might expect the outside of the resistor to discolor, the printed markings may even fade. If the internal tube material is not ceramic it might even begin to burn and smoke.

The derating chart is the reduced maximum power dissipation when used in a hotter ambient temperature environment, not the nominal resistance change characteristic per temperature, (however going beyond this range may indeed put the resistance out of specification). As the ambient temperature rises there is less and less ability for the material to dissipate heat efficiently and stay below the maximum operating temperature. The potential resistance change per temperature is given by the "Temperature coefficient" specification as a change in resistance (in parts per million) per degree C.

I would just add that if nothing were to degrade while over heating the resistor with a high current, (as you allude to), then you would essentially have a ceramic heater element that increases in resistance according to the physical parameters of the internal wire material, somewhat like an incandescent light bulb filament, but with a ceramic outer covering. (And you could probably fry an egg on it too.)

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