Litmux Studio

LessonReal resistors: values, codes and tolerance · 16 min

Standard values, tolerance and resistor types

You worked out that an LED needs 467 Ω - but nobody sells 467 Ω. Resistors come in a small set of preferred values, the E-series, and choosing among them sensibly is part of every design.

Why these numbers?

A 10 % resistor marked 100 Ω may be anything from 90 to 110 Ω. There is no point selling a 105 Ω part as well: the ranges would overlap. So the values are spaced so each one's tolerance band just meets the next - the same ratio apart, not the same number of ohms. For 12 values per decade (E12) each step is about 21 % (the 12th root of 10 = 1.21), and the pattern repeats in every decade: 10 Ω, 100 Ω, 1 kΩ, 10 kΩ...

The E-series. Today nearly all parts are 1 % or 5 %, but the E12 and E24 values are still what most kits and shops stock.
SeriesToleranceValues in each decade
E6±20 %10 15 22 33 47 68
E12±10 %10 12 15 18 22 27 33 39 47 56 68 82
E24±5 % (±1 %)10 11 12 13 15 16 18 20 22 24 27 30 33 36 39 43 47 51 56 62 68 75 82 91
E96±1 %96 values: 100 102 105 107 110 113 115 118 121 124 127 130 ... 953 976

Tolerance: designing for the worst case

Every resistor is somewhere inside its tolerance band. Where precision matters - a battery gauge, a voltage reference, a sensor - work out the worst case.

Worked example: a divider with 5 % parts

10 k / 10 k on 10 V should give 5.00 V. With ±5 % resistors, how far off can it be?

  1. Highest: R2 high (10.5 k), R1 low (9.5 k): 10 × 10.5 / 20 = 5.25 V.
  2. Lowest: R2 low (9.5 k), R1 high (10.5 k): 10 × 9.5 / 20 = 4.75 V.

Answer: 4.75 - 5.25 V: ±5 %. With 1 % parts: ±1 %. For a battery gauge, use 1 % metal film - the extra cost is tiny.

Making a value you do not have

2.2 kΩ + 330 Ω in series measure 2.53 kΩ. Series adds; two equal resistors in parallel halve.
2.2 kΩ + 330 Ω in series measure 2.53 kΩ. Series adds; two equal resistors in parallel halve.

Kinds of resistor

Choose by value, tolerance, power - and voltage.
TypeTypicalWhere it is used
Carbon film (beige body)5 %, 1/4 W, cheapGeneral use in kits and older designs
Metal film (blue body)1 %, low noise, stableToday's default through-hole resistor
Thick-film SMD (0402 - 2512)1 % or 5 %Almost every modern circuit board
Wirewound / ceramic "cement"5 - 10 W and morePower supplies, dummy loads, motor circuits
Current-sense (milliohm)0.001 - 0.1 Ω, 1 %Chargers, battery monitors, motor drivers

Practice 1Your calculation gives 5 kΩ. Which E12 value is nearest?

  1. 4.7 kΩ
  2. 5.1 kΩ
  3. 5.6 kΩ
  4. 6.8 kΩ
Show the answer

Answer: A. 4.7 kΩ

E12 has 4.7 k and 5.6 k (5.1 k is E24). 4.7 k is 6 % away, 5.6 k is 12 % away.

Practice 2What is the lowest value a 1 kΩ ±5 % resistor may have?

Show the answer

Answer: 950 Ω

1000 − 5 % = 950 Ω.

Practice 3Which pair in series gives closest to 7.5 kΩ using only E12 values?

  1. 6.8 k + 680 Ω
  2. 5.6 k + 1.5 k
  3. 4.7 k + 2.2 k
  4. 3.3 k + 3.3 k
Show the answer

Answer: A. 6.8 k + 680 Ω

6.8 k + 0.68 k = 7.48 kΩ (0.3 % low). The others give 7.1, 6.9 and 6.6 kΩ.

Challenge 4An LED (2.0 V) runs from 9 V through a 470 Ω ±5 % resistor. What is the HIGHEST current it may get, in mA?

Hint

The most current flows with the lowest resistance.

Show the answer

Answer: 15.68 mA

Rmin = 470 × 0.95 = 446.5 Ω. I = 7.0 / 446.5 = 15.7 mA - still safe for a 20 mA LED.

Challenge 5A 1 % resistor of 100 ppm/°C measures exactly 10.00 kΩ at 25 °C. What is its resistance at 75 °C?

Hint

100 ppm = 0.01 % per °C.

Show the answer

Answer: 10050 Ω

50 °C × 0.01 % = 0.5 %: 10.00 k × 1.005 = 10.05 kΩ.