Cheat sheets
The tables everyone keeps re-Googling — printable for the lab wall.
Resistor color code
| Color | Digit | Multiplier | Tolerance |
|---|---|---|---|
| black | 0 | ×1 | — |
| brown | 1 | ×10¹ | ±1% |
| red | 2 | ×10² | ±2% |
| orange | 3 | ×10³ | — |
| yellow | 4 | ×10⁴ | — |
| green | 5 | ×10⁵ | ±0.5% |
| blue | 6 | ×10⁶ | ±0.25% |
| violet | 7 | ×10⁷ | ±0.1% |
| gray | 8 | ×10⁸ | ±0.05% |
| white | 9 | ×10⁹ | — |
| gold | — | ×10⁻¹ | ±5% |
| silver | — | ×10⁻² | ±10% |
| none | — | — | ±20% |
Read from the band nearest an end; the tolerance band (gold/silver) sits apart on the right. 4-band: digit·digit·multiplier·tolerance. 5-band: digit·digit·digit·multiplier·tolerance.
Capacitor codes
Common markings
| 100 | 10 pF |
| 220 | 22 pF |
| 101 | 100 pF |
| 102 | 1 nF |
| 103 | 10 nF |
| 104 | 100 nF |
| 105 | 1 µF |
| 4R7 | 4.7 pF |
| 479 | 4.7 pF |
Tolerance letters
| B | ±0.1 pF |
| C | ±0.25 pF |
| D | ±0.5 pF |
| F | ±1% |
| G | ±2% |
| J | ±5% |
| K | ±10% |
| M | ±20% |
| Z | +80/−20% |
First two digits × 10^(third digit), in pF. Third digit 8 = ×0.01, 9 = ×0.1. R marks a decimal point. Example: 104K = 10 × 10⁴ pF = 100 nF, ±10%.
SMD resistor codes
| 3-digit | 2 digits × 10^third — 472 = 4.7 kΩ |
| 4-digit | 3 digits × 10^fourth — 4702 = 47 kΩ |
| R notation | R = decimal point — 4R7 = 4.7 Ω, R22 = 0.22 Ω |
| EIA-96 | E96 code + letter — 68C = 499 × 100 = 49.9 kΩ |
| Zero-ohm | 0 or 000 = jumper link |
SI prefixes
| Prefix | Name | Factor |
|---|---|---|
| p | pico | 10⁻¹² |
| n | nano | 10⁻⁹ |
| µ | micro | 10⁻⁶ |
| m | milli | 10⁻³ |
| — | (base) | 10⁰ |
| k | kilo | 10³ |
| M | mega | 10⁶ |
| G | giga | 10⁹ |
Formulas that cover 90% of bench work
Ohm's lawV = I × R
PowerP = V × I = V²/R = I²R
Voltage dividerVout = Vin × R₂ / (R₁ + R₂)
Current divider (2 branches)I₁ = I × R₂ / (R₁ + R₂)
LED resistorR = (Vs − Vf) / If
RC time constantτ = R × C (full charge ≈ 5τ)
RL time constantτ = L / R
RC cutoff frequencyf = 1 / (2πRC)
Resistors in seriesR = R₁ + R₂ + …
Resistors in parallelR = 1 / (1/R₁ + 1/R₂ + …)
Capacitors in parallelC = C₁ + C₂ + …
Capacitors in seriesC = 1 / (1/C₁ + 1/C₂ + …)
Capacitive reactanceXc = 1 / (2πfC)
Inductive reactanceXl = 2πfL
AC circuits & signals — the exam layer
RMS ↔ peak (sine)Vrms = Vp / √2 ≈ 0.707 Vp
Average (sine, half cycle)Vavg = 2Vp / π ≈ 0.637 Vp
Series RLC impedanceZ = √(R² + (Xl − Xc)²)
Resonant frequencyf₀ = 1 / (2π√(LC))
Q factor (series)Q = (1/R) × √(L/C)
Real powerP = V × I × cos φ
Reactive / apparent powerQ = VI sin φ, S² = P² + Q²
Capacitor energyE = ½ C V²
Inductor energyE = ½ L I²
DecibelsdB = 20 log(V₂/V₁) = 10 log(P₂/P₁)
Op-amp inverting gainAv = −Rf / Rin
Op-amp non-inverting gainAv = 1 + Rf / R₁
555 astable frequencyf = 1.44 / ((R₁ + 2R₂) × C)
Wavelengthλ (m) = 300 / f (MHz)
Machines & power — the exam layer
Synchronous speedNs = 120f / P
Slips = (Ns − N) / Ns
Transformer EMF equationE = 4.44 × f × N × Φm
Transformer ratioV₁/V₂ = N₁/N₂ = I₂/I₁
DC machine EMFE = P Φ Z N / 60A
Torque from powerT (N·m) = 9.55 × P(W) / N(RPM)
Three-phase powerP = √3 × VL × IL × cos φ
Star connectionVL = √3 Vph, IL = Iph
Delta connectionVL = Vph, IL = √3 Iph
Efficiencyη = Pout / Pin × 100%
Energy (units)kWh = kW × hours (1 unit = 1 kWh)
Horsepower1 HP = 746 W
Illumination at a pointE = (I / d²) × cos θ
Magnetic circuit (Hopkinson)MMF = Φ × S = N × I