This is sort of a crazy question but it's been bugging me for some time: why are the values of resistors and capacitors often in multiples of numbers like 47, 33, or 22 ? I'm sure there must be a reason for this though it could be buried in the mists of time and no one here is old enough to remember :).

I believe it was so tolerances on resistors would cause bands to just overlap. In the bad old days, 20% tolerance resistors were the norm. So take a 22 ohm resistor. Add 20% and you get 26.4 ohms. Now subtract 20% from 33 ohms and you get 26.4 ohms. Bingo.

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Well that makes some sense.

But I was hoping for some really esoteric Pythagorean explanation.

The values given to resistors fall into a number of preferred or standard resistor values. These standard resistor values have a logarithmic sequence related to the component accuracy, enabling the standard resistor values to be spaced according to the tolerance on the component. These standard resistor values are also applicable for capacitors and other components as well as resistors.

Aha! So it is something mathematical. I figured I would hear something good from Lefty.

That's a good site you quoted from. I'll bookmark it.

Here's a related bit of trivia. In the olden times if you had a boxful of 100 ohm 10% resistors you would find few, if any, resistors between 95 and 105 ohms in that batch. I believe it was because they would (try to) build a bunch of 100 ohm resistors and they would then pull out all those between 95 and 105 ohms and give them a gold fourth band (5%), all those between 90 - 95 and 105 -110 ohms would get a silver (10%) band, and the rest would go un-banded. Manufacturing is a bit more accurate now so this no longer applies.

Don

The standard values come in ranges called E3, E6, E12, E24 etc Standard Resistor Values: E3 E6 E12 E24 E48 E96 Series » Electronics Notes

Basically a geometric series with 6, 12, 24 or whatever values per decade. "Standard" resistor values are the E12 series (1k, 1k2, 1k5 etc), for higher precision resistors the E24 and higher ranges are used. Capacitors are often only in E6 or E3 ranges (especially decoupling capacitors).

People often put two resistors in series or parallel to get intermediate values from the E12 values so E24 is seldom used these days (the exceptions being 200, 2k0, 20k0 (especially for R-2R networks) and 51ohm (nearest to 50ohm transmission line).

A little bit of thought should convince that a geometric series is most useful.