Some of the resistors in a circuit I'm designing would be a liability in some failure modes, so I intended to use fusible resistors.
Unfortunately, the range of values available to me is somewhat limited.
So I'm thinking of putting 1/4W fusibles in series with 1/2W non-fusibles of about half the resistance. The theory is that the fusible will be dissipating twice as much power, at half the rating, and should fuse before the other one gets hot enough to be a problem.
The fusible resistor datasheets have graphs of fusing time vs. dissipated power. If the non-fusible resistor remains within its ratings all the time then pretty obviously it is ok. If not, you might need to do experiments to see what will actually happen, and for regulatory agencies it may not be good enough anyway as they may want a piece of paper saying that it will be safe and may not even care if it is actually safe (though they won't admit this of course).
You will probably find that the worst case is not the highest possible overload. For example some things would be perfectly safe (and fuse quickly) if you apply mains to them immediately, but will catch fire without going open-circuit if you turn the voltage up slowly from zero using a variac.
Unfortunately not. For the, hopefully brief, time before fusing, there'd typically be 200 watts in the 1/4 watt fusible resistor, and 100 watts in the 1/2 watt non-fusible.
Fortunately, I have no need to concern myself with such agencies, but I'd prefer to avoid burning my house down.
I may be overstating the risk, given that this stuff will be inside a metal box, with a thermal fuse that will break if things hot up.
Still, I'll do some experiments to see how this stuff behaves.
If you're doing single fault analysis, then having just one 'flame proof' part is normally considered as sufficient to demonstrate behavior under single fault conditions producing a local overload.
When single-fault short of the series limiter or single fault opening of a component or connection can result in unacceptible results; using two series or two parallel components or connections can avoid the effect.
Intermediate conditions, that cannot be acheived by single-fault opens or shorts over a specified operating range, are probably not worth considering. The same might be said of components that do not demonstrate either the open circuit or short circuit condition, unless bullets are anticipated.
If the aim is to prevent downstream damage, then inserting a shunting component that will characteristically short circuit on overvoltage first (in combination with the series flame-proof limiter) is a common defense. An axial 400/600mW zener, conducting at close to normal limiting node operating voltage, is quite reliable in this way. (Not the 1W axial parts). Other components are marketed specifically to provide overvoltage protection.
Both of these functions are more reliably provided by through-hole components, simply because of accumulated characteristic history, and because of the greater mechanical integrity afforded by the mech+solder attachment method. The longer lead-out can also act to isolate/concentate the thermal overload, so as not to damage the mounting substrate and make its performance leass dependent on board patterns.
You claim just to be saddled with a limited range of values - so choosing the closest-valued combination that perform the R total value function, with similar individual performances under fault, is the more sensible choice.
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