Core answer: Resistor color bands encode value as: digit, digit, multiplier, tolerance. Brown-black-red-gold = 1-0-×100-±5% = 1,000 Ω ±5%. Read from the end where the tolerance band (gold/silver, slightly separated) is last. Series resistors add (R₁+R₂); parallel resistors shrink (product over sum for two).
The color code, once and for all
| Color | Digit | Multiplier | Tolerance |
|---|---|---|---|
| Black | 0 | ×1 | — |
| Brown | 1 | ×10 | ±1% |
| Red | 2 | ×100 | ±2% |
| Orange | 3 | ×1k | — |
| Yellow | 4 | ×10k | — |
| Green | 5 | ×100k | ±0.5% |
| Blue | 6 | ×1M | ±0.25% |
| Violet | 7 | ×10M | ±0.1% |
| Grey | 8 | — | ±0.05% |
| White | 9 | — | — |
| Gold | — | ×0.1 | ±5% |
| Silver | — | ×0.01 | ±10% |
Memory hook for digit order: Bad Beer Rots Our Young Guts But Vodka Goes Well.
Reading example. Yellow-violet-orange-gold: 4, 7, ×1k → 47,000 Ω = 47 kΩ ±5%.
Series and parallel
- Series: R = R₁ + R₂ + … Current identical; voltage divides in proportion to resistance. Two 10 kΩ in series = 20 kΩ.
- Parallel: 1/R = 1/R₁ + 1/R₂ + … For exactly two: R = (R₁R₂)/(R₁+R₂). Two 10 kΩ in parallel = 5 kΩ. Parallel always lands *below* the smallest branch.
- Making non-stock values: need 950 Ω? Use 1 kΩ ∥ 20 kΩ ≈ 952 Ω.
Power rating is the silent killer
P = I²R = U²/R. A 100 Ω resistor dropping 12 V dissipates 1.44 W — a standard 1/4 W part will brown and fail; use ≥ 2 W. Rule of thumb: run resistors at ≤ 50% of rated power for long life.
Common mistakes and myths
- Reading from the wrong end — start at the side with bands packed closer together; the tolerance band (gold/silver) sits slightly apart at the far end.
- Ignoring tolerance stacking — a 10 kΩ ±5% can legitimately be 9.5–10.5 kΩ; precision dividers need 1% (brown tolerance band, 4-band+1) or 0.1% parts.
- Forgetting power in parallel/series math — resistance math is right, but each part still must handle its share of watts.
- Assuming resistance is constant with temperature — typical metal film drifts ~100 ppm/°C; a 1 kΩ shifts 0.1 Ω/°C. Matters in sensors, irrelevant for LED droppers.
- Confusing 4-, 5-, 6-band parts — 5-band adds a third significant digit (red-red-black-black-brown = 220 Ω ±1%), misreading it as 4-band gives 22 Ω.