We want just a cheaper solution than NTC plus fuse.
RC time constant is τ=10Ω*10µF=100µs . For an approximation, we keep the initial voltage constant (which is a worst case scenario). The anti-log decay from I0=38A to I=10mA takes T=-τ*ln(I/I0)=-τ*ln(10mA/38A) ≈ 800µs . Taking a linear current decay vs. time instead of the anti-log decay provides a worst case electrical energy of (I0/2)2*R*T ≦ 3Ws. Any resistor ≧ ½W can stand this energy occurring during less than a millisecond - more important are sufficiently thick connection wires which can support the initial current of 38A. I'd use a 2W resistor.
This is the problem
The 2.5W resistor we use just blows immediately.
Initially, I estimate the power based on inrush energy for charging capacitor ~ 0.57 Joules. Compared to equivalent energy deduced from resistor graph (power vs. time blow) take some margin and I still was in 10% range.
Then, I tried more accurate calculation. I plotted resistor power starting from 0 (max. current 38A) and take the time when power decays to 2W, so under resistor withstand capability. The medium energy was computed as averaged power on this time 440uS and guess what, is ~0.528 Joules so almost the same energy as initial calculation.
We used Tyco FCR series, 1206 model, 2.5W "fuse power"
https://www.farnell.com/datasheets/1770680.pdf
But datasheet isn't clear about "fuse power" as impulse capability. I just assume that if at 2W "fuse" will blow in 8 sec., we can apply 20W for 0.8 sec. for the same result.
Other explanation can be over voltage. In other manufacturer 1206 specs, this resistors are rated for 200V (DC or RMS) so when apply 240 (or 260 with tolerance) it can blow.
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Hmm.... erikl, I suspect you're right!
The 1206 contacts just cannot handle the 38 Amps....
I'll ask my colleague to see at microscope the blown one.