We are definitely miss a variable that will give us the Wattage. Is my strong belief. But what is it?
It's what I've been saying all along - the maximum working temperature.
This depends on the type of materials used and the quality and method of construction of that particular resistor. For example, a silicone-coated wirewound will typically withstand 250°C or even 300° with no problems, but a carbon composition might fail rapidly at 120°. And with encased resistors there can be significant thermal resistance from the element to the dissipative surface, so the critical temperature (of the element) might be significantly higher than the temperature of the case.
My three samples all achieved nearly the same dissipation at the same temperature, meaning that they all have nearly the same thermal resistance from case to ambient. That is to be expected, because they are all the same size with similar radiation characteristics. The ambient temp was 18°C so the thermal resistance of all of them is about (100-18)/2 = 41°C/W. This gives the gradient of the line in the derating graph while the max temp gives its X-intercept.
The 1W was resistor C, a ceramic-cased carbon composition made in the 1960s. It's working temperature is limited by the tendency of the slug material to change in characteristics. Above its rated temperature, it will tend to drift badly out of tolerance, both reversibly with temperature change and permanently, and have a shortened life. At 2W it started oozing wax.
The 2W was resistor A, a carbon film type. These are more stable and can work at a higher temperature,. If overrun, the first thing to burn is usually the paint, even while the element stays in tolerance. They are not however as resistant to high pulse dissipations as carbon compositions.
The 3W was resistor B, a metal oxide film type. These have generally better characteristics than carbon-film, lower noise, better tempco and long-term stability, higher working temp. This one would probably withstand 6W or even 9W, 3x its rated dissipation, for a short time (its life span might be reduced) although the coloured bands would burn off. At that power, if mounted on a PCB it would scorch the PCB and the leads would desolder themselves but the resistor would survive. In the 1970s there were wirewound resistors in TVs with a thermal cutout that worked by desoldering a spring-loaded contact if the resistor overheated due to a fault in the line output stage.
So there you have it - you need at least two parameters to determine the rating (at a given ambient temperature):
- Thermal resistance to ambient (which we find out with the heating test but all similar case sizes will have similar thermal resistances.
- Maximum working temperature (which comes from manufacturer data or comparison with other resistors of similar construction)
