I suppose a pair of resisitors in parrellel would be best
How come? If a resistor can fail open or short parallel is not going to help, seriese may be. But if you know that little about it then you should not be doing it.
The problem is you want so much for it to be true it will be no matter what physically happens. Placebo.
Placebo? If that was all it took I'd be all for it. Much easier. You're right though, I can't be all that objective but that's what I'm using the published papers for. Obviously I'm not running a randomized double-blind study, I'm just following a given protocol and seeing what effect if any I notice. I've been both disappointed and also very surprised at the effects at other times.
There's nothing wrong with series, though if one resistor fails open everything stops. (Kind of the point I know but inconvenient.) If in parallel one fails short the total impedance is still the average of the two, right? So twice as much current flows rather than thousands of times as much. Since the "safe" current range presently extends more than two orders of magnitude from the minimum useful value a factor of two increase isn't much. Especially as it only has to be for the remainder of that session given I check impedance before each use. If wired in parallel I won't discover a problem to fix and find out I wasted all or part of the last session at the same time. See? No real change but much less frustrating if one does fail. I could even do that next run as planned and allow the time to fix it properly later. Resistor values need to be different in parallel vs series, of course.
I guess even one failed resistor is pretty rare if used within it's rating so while it's worth planning for I'm not sure it's worth fixing if a different arrangement allows an extra layer of redundancy with a safety margin maintained. Like maybe two serial pairs of resistors wired in parallel...so if one fails in either leg resistance is constant. Heck even if one failed short in each leg impedance would remain constant. Even one short in each leg with a third failed open would still match spec while both of one leg shorted or even that and a third from the other is not ideal but tolerable. According to present estimates at least.
Any more thought into it and it's just going to be a fused regulated circuit. It's going in that direction certainly.
If it shorts it will still cause excessive current flow, regardless of the other one
newbJohn:
There's nothing wrong with series, though if one resistor fails open everything stops. (Kind of the point I know but inconvenient.) If in parallel one fails short the total impedance is still the average of the two, right? So twice as much current flows rather than thousands of times as much. Since the "safe" current range presently extends more than two orders of magnitude from the minimum useful value a factor of two increase isn't much.
Total parallel resistance is 1/( (1/R1) + (1/R2) + ... +(1/Rn) ), not the average. With two 9k4 resistors(for 4k7 total), one shorting to .001?(I'm not sure if that's an accurate estimate, but I'll use it anyway) would result in a total of 0.0009999998936?. That'll be a [sarcasm]little[/sarcasm] more than twice the current