Standard resistor values ... Reasons?

[matrixofdynamism]

I understand that the standard resistor values are based on Renard series where values between a decade are a geometric series related by a root of 10. The root order depends on the series number e.g for E6 there shall be 6 values between a decade e.g 100 and 1000 which shall be related to each other via 6th root of 10.

I have 3 questions,

(1) What are the minimum and maximum available resistance values for E6, E12, E24 and E96 resistors? Do all series have a 1 ohm resistor? Which of them have fractional values like 0.1 ohm e.t.c?

(2) When I make mathematical calculations for E6, I get the numbers as 100, 146.78, 215.443, 316.228, 464.159, 681.292 and 1000. However, the actual numbers contained in E6 are 100, 150, 220, 330, 470, 680 and 1000. Why are these not merely round off values of the actual numbers thus giving 100, 145, 215, 316, 464, 681 and 1000 instead?

(3) Why are these values related by root of 10 rather than some other number?

 

[D.A.(Tony)Stewart]

Re: Origins of standard resistor values

You have more than 3 (?)
All have 1? Yes.
Extreme values? Depends on Mfg.

Equidistance spacing maximizes selection ratios with fewest numbers when using log value.

In electronics, it is more about ratios than absolute values and more often these ratios have logarithmic effects, like gain in dB.

Thus equi-log-spaced numbers work best.

https://www.radio-electronics.com/info/data/resistor/e-series-e3-e6-e12-e24-e48-e96.php

 

[KlausST]

Hi,

2) its rounding to two digits. 10, 15, 22...
with this it is possible to use two color rings on resistors plus one ring for the decade.

3) because it is easy to read. And the there is a color ring on the resistro for "decades"

example:
three rings on a resistor:
brown, green, red ---> stand for values 1, 5, 3 meaning 15 * 10^3 ohms = 15kOhms.

with just three values (color rings) you are able to represent resistor values from 0.10 Ohms to 68 GOhms. With a precision of 5%.
I can´t think of another system that is able to represent such a huge dynamic with that equal precision.

Klaus

 

[matrixofdynamism]

@SunnySkyguy. Could you give me a simple example as to how this logarithmic spread of values is superior to equal intervals?
How are values less than 1 presented on a resistor e.g 0.1 0.01 e.t.c since the third (for 3 band resistors) or fourth band (for 4 band resistors) gives the multiplier value and if this band is black, the multiplier is 1. I don't see how we can have reciprocal multipliers on resistors e.g 1/10, 1/100, 1/1000 e.t.c.

 

[KlausST]

Hi,

read:
https://en.wikipedia.org/wiki/Electronic_color_code
and find color "silver" and "gold"

equal interval:

imagine an equal interval of 1Ohms.
the step from 1 Ohm to the next value (=2Ohms) is a change in 100%, not good for fine tuning... (with E24 you have 6 values in between)

on the other side:
now you have the same (equal) step size of 1 Ohm with a 1MOhms resistor. This is a change of 0.0001%. Its hard to produce in that resolution...
1) How would you show this on a resistor?
2) you have one million steps to a 2MOhms resistor. How would you manage this?

I don´t want to think this in the GOhms area...

Klaus

 

[BradtheRad]

In early days, manufacturers had to make do with approximate values, because they were not able to make resistors with 1 or even 5 percent tolerance.

It was common for them to declare a tolerance of 10 percent (plus or minus). Say they wanted to make a run of 100 ohm values. They would mix up a batch of carbon slurry and pour some resistors.

Their values were not necessarily close to 100 ohms. So they measured each one. If it was within 10 percent of 100 ohms, they labelled it 100 ohms.

If it was 111 ohms or more, they labelled it with the next step up, 120 ohms. Etc.

That is the story I heard about the origin of standard component values.

By sorting them this way, every resistor in a batch could be used.

In fact, there might have been an earlier time when the best tolerance was 20 percent.