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I'm trying to characterise a resistor's temperature at equilibrium when I know the voltage on it and the ambient temperature. I have a few ways to measure but I get mixed results, so I'm searching for a theory to compare to. I'm a second year physics and EE student and I haven't done thermodynamics yet, so I'm kind of lost.

I can use curve fitting to find hard-to-reach constants like its heat capacity. I can also control the ambient temperature and the power supplied to it. In the measurements it seems like the temperature is rising exponentially (with a negative time factor).

Is there an equation or some models I can dive to?

Thanks in advance.

MadHatter
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Chen Tasker
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    The temperature of the resistor gets to is highly dependent on the environment around it and all the different ways that heat energy is flying out of it, conduction through leads, convection into the air. it's not a trivial problem. – MadHatter Nov 28 '19 at 19:40
  • Resistors are always rated by power dissipation. It is one of the key components to a resistor spec sheets really resistor selection in general right behind the actual resistivity of it. That is really all you need to know unless you're using a resistor in a very non-conventional manner. – MadHatter Nov 28 '19 at 19:49
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    One thing to know as an EE: Mechanical calculations of phenomena distributed over an area is never easy. An equation or model is usually nowhere near enough to actually tackle the problem. That's why those MechEs take so much math. As EEs, we're pretty lucky we can do quite a bit with lumped circuit models. MechEs aren't so fortunate. – DKNguyen Nov 28 '19 at 19:51
  • You have some really good comments, already, from MadHatter. With respect to DKNguyen's comments added to MadHatters, I also agree overall. Knowing the theory and, more important, knowing ***how*** to apply which theory where and how to combine the primary ones without getting bogged down in 3rd effects, takes experience and training. You might think it is as simple as just knowing the power, the thermal resistance to air, and the ambient temperature. But it's not. Resistors have leads, direct contacts, grime accumulation, and air circulates (or doesn't circulate) at differing rates, etc. – jonk Nov 28 '19 at 21:03
  • If you can work out the partial differential equations (and these are often relatively simple to conceive), then you make examine a technique discussed [here](https://electronics.stackexchange.com/a/437001/38098) or [here](https://electronics.stackexchange.com/a/397805/38098). The coding is trivial. The main thing is implementing the cell structure that best represents your object and its surroundings and plugging in the adjacent partials. Then you just "let it run" for a while, save data, and do post-analysis as you feel. – jonk Nov 28 '19 at 21:09
  • Thanks everyone. I know there are way too many variables to solve this problem, but I was hoping that they are constant in this situation and that I can derive then using curve fitting. I'm only interested in few specific set ups and not in the general case, basically the only thing that should be changing is the power supplied to the resistor and the ambient (or the initial) temperature. I just need a general form or model for the eq. temperature dependency on these values. – Chen Tasker Nov 28 '19 at 21:20
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    @ChenTasker Then make measurements for your specific setups that none of us know anything about, decide on the theoretical model you need to parameterize, and then work out its parameters from the data you develop in testing. If your theoretical model is good enough, you may get the needed parameters with a minimal number of calibration runs. – jonk Nov 29 '19 at 03:27
  • "I'm trying to characterise a resistor's temperature at equilibrium"- why? – Bruce Abbott Nov 29 '19 at 05:41

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