Carbon Resistor Colour Coding
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Direct answer
Carbon resistors state their value in coloured bands: the first two (or three) bands give significant digits, the next band is a power-of-ten multiplier, and the last band is the tolerance — gold for ±5 percent, silver for ±10 percent, absent for ±20 percent. The digit sequence is Black 0, Brown 1, Red 2, Orange 3, Yellow 4, Green 5, Blue 6, Violet 7, Grey 8, White 9, preserved in Indian classrooms by the mnemonic "B B ROY of Great Britain had a Very Good Wife". A resistor banded red-violet-orange-gold is 27 × 10³ Ω = 27 kΩ with 5 percent tolerance, that is, anywhere from 25.65 to 28.35 kΩ. Reading starts from the end where the tolerance band (gold or silver) sits farthest from the rest — the anchor that fixes direction.
What you must remember
- The digit sequence: Black 0, Brown 1, Red 2, Orange 3, Yellow 4, Green 5, Blue 6, Violet 7, Grey 8, White 9 — "B B ROY of Great Britain had a Very Good Wife" carries the first letters in order.
- Band grammar: band 1 = first digit, band 2 = second digit, band 3 = multiplier power of ten, band 4 = tolerance; five-band precision resistors add a third significant digit before the multiplier.
- Tolerance colours: gold ±5 percent, silver ±10 percent, no band ±20 percent; brown (±1 percent) and red (±2 percent) appear on precision resistors and should not be misread as digit bands.
- Worked decode: brown-black-orange-silver reads 10 × 10³ = 10 kΩ ±10 percent, so the acceptable range is 9 kΩ to 11 kΩ; red-red-orange-gold is 22 kΩ ±5 percent.
- Multiplier arithmetic: the multiplier band is an exponent on ten — red means ×10², not ×2; orange ×10³; yellow ×10⁴. Most decoding errors are this band misread as a digit.
- Why carbon: carbon-composition resistors are compact and cheap (values from below 1 Ω to over 10 MΩ) but loose in tolerance and stability; wire-wound and metal-film types serve precision needs with their values printed instead.
- Reverse engineering: to encode 4.7 kΩ ±5 percent, write 47 × 10² and pick yellow-violet-red-gold — JEE asks encoding as often as decoding.
Decoding under exam pressure
Face a resistor banded yellow-violet-red-gold. Hold it so the gold band is on the right (tolerance always stands apart at one end), then read left to right: yellow = 4, violet = 7, red multiplier = ×10², gold = ±5 percent. The value is 47 × 100 = 4.7 kΩ, and the manufacturer guarantees it between 4465 Ω and 4935 Ω. The direction check matters more than students expect: read backwards, the same resistor would decode as red-orange... in practice the reversed reading gives a nonsense value like 2.7 kΩ ±... with the tolerance band misplaced — which is precisely the wrong option the paper offers. Anchor on gold or silver first, always.
Now the reverse drill. A circuit needs 560 kΩ ±10 percent. Write it in two significant digits: 56 × 10⁴. The digits 5 and 6 are green and blue; the multiplier 10⁴ is yellow; ±10 percent is silver — green-blue-yellow-silver. Encode 1 MΩ as brown-black-green with the tolerance of your choice (10 × 10⁵), and notice how every standard value in the E-series favours two significant digits, which is exactly why the code was built around two digit bands and a multiplier rather than printing numbers on curved, tiny cylinders.
Where students slip
The mnemonic is universal but the band roles are not: students who have memorised "B B ROY" sometimes still assign the multiplier as a digit, converting 27 kΩ into 273 Ω — the multiplier is an exponent, full stop. The tolerance anchor fixes reading direction; a resistor examined from the wrong end yields a plausible-looking but wrong value, and JEE options include exactly that reversal. Remember also that tolerance defines a manufacturing range, not a measurement error: a 10 kΩ ±10 percent resistor is within specification anywhere from 9 to 11 kΩ, and questions ask for this interval by name. Conceptual asides worth one read: why carbon resistors are rated also by wattage (heat dissipation darkens them — a burnt resistor can still be decoded, a viva favourite), and why the code needs no decimal point (the multiplier band absorbs magnitudes from 10⁻², silver multiplier historically, up to 10⁹).
Frequently asked questions
What is the mnemonic for the colour code?
B B ROY of Great Britain had a Very Good Wife — Black 0, Brown 1, Red 2, Orange 3, Yellow 4, Green 5, Blue 6, Violet 7, Grey 8, White 9, in order.
What do the four bands of a carbon resistor represent?
First band = first significant digit, second band = second digit, third band = power-of-ten multiplier, fourth band = tolerance (gold ±5 percent, silver ±10 percent, absent ±20 percent).
What is the value of a red-violet-orange-gold resistor?
27 × 10³ Ω = 27 kΩ with ±5 percent tolerance, so any actual value from 25.65 kΩ to 28.35 kΩ meets specification.
From which end should the bands be read?
From the end where the bands sit closest together, with the separately-spaced gold or silver tolerance band on the right — reading the wrong way silently swaps digits and multiplier.
How would you colour-code a 4.7 kΩ resistor with 5 percent tolerance?
Write 4.7 kΩ as 47 × 10², then choose yellow (4), violet (7), red (×10²) and gold (±5 percent).