Yes. If you extrapolate the initial slope of an exponential like this, it intersects the asymptotic limit in 1 tau.
My initial wild-guess thinking was to guess the thermal time constant of a resistor (semething I do have a vague feeling for) and guess its joule capacity from its power rating and that. It is more scientific to look at the initial slope, degc/sec per watt, pick some peak temperature, and do the math from that.
Sort of the same thing.
So, using 150C peak, this resistor is good for about 200 joules. My
10-watt, hold-it-as-long-as-you-can estimate was similar.
"One experiment is worth a thousand expert opinions."
I had a bit of time to 'let the smoke' out of some carbon comps yesterday. The 10 ohm bin was depleted, but I have a lot of 15 ohm R's. These are 1/2 Watt. It was fairly easy to pulse the power supply on for 1 second, (watching on a 'scope). I measured the resistance before and after pulsing (and after waiting for the resistor to cool.) There was not much change until ~16 joule pulses. Then the resistance increased by an ohm or so with the first pulse, but then showed only smaller increases on subsequent pulses.
Here's some numbers for 16 joule pulses.
pulse number resistance
0 15.4
1 15.9
2 16.0
3 16.0
4 16.1
At higher energy levels the change was bigger. I had three different tolerance resistors. (5%, 10% and ones with a orange and silver band.) The 5% and 10% seemed about the same. The resistors with the orange band would crack open at lower energy levels and some sort of goo was visible. (at around the 25 joules.)
To scale for resistors of different power levels I observed that the area of a resistor is about proportional to its CW power. (this makes sense, but I=92d never measured.) Since you might expect the pulse power to scale as the volume, this should go as something like the CW power to the 3/2 power. (I=92m pretty much making this up, but I assume Phil A. will correct me (a verbal spanking) if I say something stupid.) So a 2 watt carbon comp might handle 8 times the energy... ~130 Joules. Pretty darn close to John L=92s 100 J number.
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