Robotics · Electronics basics · Grade 7

Resistors: the colour code

Which resistor in the box is 470 Ω? Read the bands and check with a multimeter.

The situation

The club’s box holds dozens of resistors, but no number is written on them — only coloured bands. The leader says: “Bring me a 470 Ω resistor.” Which one will you take? Learn to read the colour code, then check with a multimeter: why does the display show “1.” or OL, and why does an ohmmeter lie in a circuit with a battery? If the value you need is not in the box, make it from two resistors connected in series or in parallel.

Topic

Resistors: colour code, series and parallel connection. Resistors from the club box: reading the value from the colour bands, making the value you need from two resistors

Key ideas

Colour code
Series and parallel
Multimeter

Formulas

R = (10 d_{1} + d_{2}) \cdot 10^{m}

Four bands: two digits $d_{1} d_{2}$ and the multiplier $10^{m}$ (the third band); the fourth is the tolerance: gold ±5%.

R = (100 d_{1} + 10 d_{2} + d_{3}) \cdot 10^{m}

Five bands: three digits, the multiplier, the tolerance (brown ±1%) — precision resistors.

R = R_{1} + R_{2}

In series: the current passes through both resistors one after the other — the resistances add up.

\frac{1}{R} = \frac{1}{R_{1}} + \frac{1}{R_{2}} \Rightarrow R = \frac{R_{1} R_{2}}{R_{1} + R_{2}}

In parallel: the current has two paths — the total resistance is smaller than even the smallest one.

R = \frac{U}{I}

An ohmmeter passes its own small current $I$ through the resistor, measures the voltage $U$ and finds $R$ by Ohm’s law.

Theory

Why bands

The body of a resistor is only 6 mm long — you cannot write “470 Ω” on it, and if you could, you could not read it on a resistor that has rolled over. So the value is written with coloured bands: each colour is one digit. The table: black 0, brown 1, red 2, orange 3, yellow 4, green 5, blue 6, violet 7, grey 8, white 9. The bands start closer to one end of the body — you read from that end; a gold or silver band is never the first.

Four bands

An ordinary resistor has four bands: the first and second are digits, the third is the number of zeros (the multiplier $10^{m}$ ), and the fourth is the tolerance: gold ±5%, silver ±10%. Red-red-brown-gold: 2, 2, one zero → 220 Ω ±5%. Yellow-violet-red: 4, 7, two zeros → 4700 Ω = 4.7 kΩ. Brown-black-black: 1, 0, no zeros → 10 Ω. If the third band is gold, multiply by 0.1 (this gives small values such as 2.2 Ω).

Five bands and the tolerance

Precision resistors have three digits + the multiplier + the tolerance: brown-black-black-brown-brown → 100 × 10 = 1000 Ω ±1%. If the fifth band is brown it means ±1%, red ±2%. The tolerance shows how far the real value may differ from the nominal one: a 470 Ω ±5% resistor is really somewhere between 446 and 494 Ω. So if the multimeter shows 466 Ω, everything is fine — the resistor is not “wrong”.

Measuring with a multimeter

In Ω mode the multimeter passes its own small current through the resistor and measures the voltage — Ohm’s law works inside. The display is 3½ digits: at most 1999. Choose a range a little above the value: for 470 Ω that is 2000 Ω (the display shows “470”); on the 200 Ω range it shows “1.” — the value did not fit; on 20 kΩ it shows “0.47” — too few digits. OL means the circuit is open (probes in the air) or the value is outside the instrument’s limit. Rules: there must be no current in the circuit (a battery fools the ohmmeter), do not hold both probes with your fingers (your body, ≈ 200 kΩ, is connected in parallel), and the resistor must be disconnected from the circuit.

Series and parallel

In a series connection the current passes through both resistors one after the other — the path gets longer and the resistances add up: 330 + 1000 = 1330 Ω. In a parallel connection the current gets two paths — it passes more easily and the resistance is smaller than the smallest one: two identical resistors give half (1 kΩ ∥ 1 kΩ = 500 Ω), and if they differ, $R = R_{1} R_{2} / (R_{1} + R_{2})$ . This is how you make a value that is not in the box: in series — a larger one, in parallel — a smaller one, and “in-between” values.

About the model

The real value of each resistor in the box differs from the nominal one within the tolerance (470 → 466 Ω) — this is what the multimeter shows; in the series/parallel modes the values are nominal. The multimeter model: Ω — the test current is chosen so that the full scale of the range gives 0.2 V (1 mA on 200 Ω, 0.1 mA on 2000 Ω …), V⎓ — 10 MΩ input, A⎓ — a shunt; 1999 counts. Fingers — 200 kΩ (dry skin; less with damp skin). The ohmmeter reading in a circuit with a battery is a “meaningless” number calculated from the sum of the voltages; on a real instrument it could be even more random.

Did you know?

The colour code of resistors was introduced in the 1920s by the American association of radio manufacturers (RMA); today it is set out in the international standard IEC 60062 and is the same in boxes all over the world.
Neighbouring numbers of the standard E12 series differ by a factor of about 1.21 (the 12th root of 10): with a ±10% tolerance the range from 10 to 100 is covered “with no gaps” — that is why 100 is followed by 120, 150, 180, 220, and not by 130 or 200.

Inside the experiment

A real board in a hand-inked isometric drawing: turn it, place the parts, wire the circuit, write and upload the code — current and voltage are computed at once, and a wrong connection burns a part. Inside are missions, theory, a quiz and a guided tour.

More experiments in this section

The electric circuit: a torch — Grades 5–6
Breadboard: rows — Grades 5–6
LED and resistor: Ohm’s law — Grade 7
Voltage divider and potentiometer — Grade 7