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Suppose you have resistors which have nominal values of \$R_0\$ or \$2R_0\$ but can vary to be anywhere between \$(1 ± .03)R_0\$ or \$(2 ± .06)R_0\$, respectively, so each can have about 3% error.

Is it correct to calculate the maximum error of two possible combinations of these resistors as follows? (These are the only two combinations I care about.)

Parallel connection of two \$2R_0\$ resistors: \$2.06R_0||2.06R_0 = 1.03R_0,\$ correct value is \$1R_0\$, so overall 3% error. Alternatively, \$1.94R_0||1.94R_0 = .97R_0,\$ so still 3% error.

Series connection of two \$R_0\$ resistors: \$1.03R_0 + 1.03R_0 = 2.06R_0,\$ correct value is \$2R_0\$, so overall 3% error. Alternatively, \$0.97R_0 + 0.97R_0 = 1.94R_0,\$ so still 3% error.

A text I'm reading suggests that the second case of two \$R_0\$ resistors in series should have a maximum error of 6% and not 3% but I don't understand how.

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Resistor networks consisting of the same tolerance resistors have an overall tolerance equivalent to that of the individual resistors.

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  • \$\begingroup\$ Thanks for your answer; I can see how this would intuitively be true but do you happen to have a source where I can read more about this? I can't find any other source that makes this claim. \$\endgroup\$
    – Halleff
    Commented May 2, 2020 at 7:05
  • \$\begingroup\$ I originally read about it in an electronic component supplier's catalogue. But it is best to prove it to yourself as you have started to do. You could try it with a more complicated network of parallel and series resistors. \$\endgroup\$
    – user173271
    Commented May 2, 2020 at 9:34

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