Resistors: Colour Code, Series/Parallel and Voltage Dividers
The resistor is the most common part on any circuit board. Before you can use one you need to know its value, which on through-hole parts is printed as coloured bands. You also need to combine resistors to get values you do not have, and use pairs of them to produce a smaller voltage from a larger one. This tutorial covers all three skills with numbers you can check on the bench.
Reading the Colour Code
Hold the resistor so the tolerance band (usually gold, silver or brown with a wider gap) is on the right. On a 4-band resistor the first two bands are digits, the third is the multiplier and the fourth is tolerance. On a 5-band (precision) resistor the first three bands are digits, the fourth is the multiplier and the fifth is tolerance.
| Colour | Digit | Multiplier | Tolerance |
|---|---|---|---|
| Black | 0 | x1 | - |
| Brown | 1 | x10 | ±1% |
| Red | 2 | x100 | ±2% |
| Orange | 3 | x1k | - |
| Yellow | 4 | x10k | - |
| Green | 5 | x100k | ±0.5% |
| Blue | 6 | x1M | ±0.25% |
| Violet | 7 | x10M | ±0.1% |
| Grey | 8 | - | - |
| White | 9 | - | - |
| Gold | - | x0.1 | ±5% |
| Silver | - | x0.01 | ±10% |
Examples
Brown Black Red Gold -> 1 0 x100 = 1000 Ω = 1 kΩ ±5% Yellow Violet Orange Gold -> 4 7 x1k = 47 kΩ ±5% Red Red Gold Gold -> 2 2 x0.1 = 2.2 Ω ±5% Brown Black Black Brown Brown -> 1 0 0 x10 = 1 kΩ ±1%
Tolerance tells you the allowed spread. A 1 kΩ ±5% resistor can measure anywhere from 950 Ω to 1050 Ω and still be in specification. Resistors are sold in standard series; the E12 series used for 5% and 10% parts has the values 10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68 and 82, repeated in every decade (100, 120, 150 and so on).
Series and Parallel Combinations
In series, the same current flows through every resistor and the resistances add. In parallel, every resistor has the same voltage across it and the conductances (1/R) add, so the total is always smaller than the smallest resistor.
Series: R_total = R1 + R2 + R3 + ... Parallel: 1/R_total = 1/R1 + 1/R2 + 1/R3 + ... Two in parallel: R_total = (R1 x R2) / (R1 + R2) N equal resistors R in parallel: R_total = R / N
Worked example: making 150 Ω and 750 Ω
You need 750 Ω but only have 1 kΩ, 1.5 kΩ, 330 Ω and 470 Ω parts. Two 1.5 kΩ in parallel give 1500 / 2 = 750 Ω exactly. For 150 Ω, put 330 Ω and 470 Ω in parallel: (330 x 470) / (330 + 470) = 155100 / 800 = 193.9 Ω, which is too high. Two 330 Ω in parallel give 165 Ω; adding a 1.5 kΩ as a third parallel resistor gives 1 / (1/330 + 1/330 + 1/1500) = 148.6 Ω, within 1% of the target.
Power sharing
Combining resistors also spreads the heat. Four 100 Ω, 1/4 W resistors in a 2 x 2 series-parallel arrangement give 100 Ω total and can dissipate about 1 W together, because each one carries a quarter of the power.
The Voltage Divider
Two resistors in series across a supply divide the voltage in proportion to their values. The output is taken from the junction, across the lower resistor R2.
Vin ---[ R1 ]---+---[ R2 ]--- GND
|
Vout
Vout = Vin x R2 / (R1 + R2)
Divider current I = Vin / (R1 + R2)Worked example: 12 V battery to a 3.3 V ADC input
You want to monitor a 12 V battery that can reach 14.4 V while charging, using an input that must not exceed 3.3 V. Aim for about 3.0 V at 14.4 V to leave margin, so the ratio R2/(R1+R2) is 3.0 / 14.4 = 0.208. Choosing R2 = 10 kΩ gives R1 + R2 = 48 kΩ, so R1 = 38 kΩ. The nearest E12 value above is 39 kΩ.
Vout(max) = 14.4 x 10k / (39k + 10k) = 14.4 x 0.2041 = 2.94 V Vout(12 V) = 12 x 0.2041 = 2.45 V Current = 14.4 / 49k = 0.29 mA Power in R1 = (14.4 - 2.94)^2 / 39k = 3.4 mW
The loading effect
The formula assumes nothing draws current from Vout. Any load placed across R2 is in parallel with it and lowers the output. Suppose a 10 kΩ load is connected across R2 = 10 kΩ in a 10 kΩ / 10 kΩ divider fed from 10 V. Unloaded, Vout is 5 V. Loaded, R2 becomes 10k parallel 10k = 5 kΩ, and Vout = 10 x 5 / (10 + 5) = 3.33 V, a large error.
Rule of thumb: make the load resistance at least 10 times R2 for an error of a few percent, or 100 times for under one percent. If the load is heavy or changes, do not use a divider as a power supply; use a regulator instead. Dividers are for signals and references, not for powering circuits.
Common Mistakes
- Reading the colour bands from the wrong end. The tolerance band is usually separated by a larger gap.
- Using very low divider values, such as 100 Ω and 100 Ω on 12 V, which waste 0.72 W continuously.
- Using very high values (several MΩ) with an ADC or a multimeter, whose input resistance then loads the divider.
- Measuring a resistor while it is still in a circuit; parallel paths make the reading lower than the true value.
- Ignoring tolerance: two 5% resistors in a divider can shift the output by up to about 5% in the worst case.
Summary
Read colour codes digit by digit, then apply the multiplier and note the tolerance. Add resistances in series; add their reciprocals in parallel. A divider gives Vout = Vin x R2 / (R1 + R2) only when the load is much larger than R2, so always check loading and resistor power before you build. These three skills will be used in every later topic, from LED resistors to op-amp gain networks.