Core answer: Ohm's law: U = I × R (voltage = current × resistance). Any one unknown falls out of the other two: I = U/R, R = U/I. A 12 V battery across 100 Ω drives 0.12 A (120 mA). Power extends it: P = U × I = I²R = U²/R — that 12 V/100 Ω circuit dissipates 1.44 W, so a 0.25 W resistor would cook. Always run the power check after the current check.
The formula wheel
| Want | Given | Formula |
|---|---|---|
| U | I, R | U = IR |
| I | U, R | I = U/R |
| R | U, I | R = U/I |
| P | U, I | P = UI |
| P | I, R | P = I²R |
| P | U, R | P = U²/R |
Real-world readings
- Household (China 220 V): a 2,000 W kettle draws I = 2000/220 ≈ 9.1 A — fine on a 10 A socket, not to be shared with a heater on the same strip.
- LED drive: 3 V LED at 20 mA from a 5 V USB: drop 2 V across R = 2/0.02 = 100 Ω; power in resistor = 0.04 W → a standard 0.25 W part is comfortable.
- Wire heating: 10 A through 0.1 Ω of bad connection: P = 100 × 0.1 = 10 W in a contact — that's why loose terminals scorch.
Worked examples
Example 1 — Fuse sizing. A 220 V / 1,500 W heater: I = 6.8 A; choose a fuse ~1.3–1.5× running current → 10 A. A 16 A fuse would also "work" until a fault has to melt wiring before the fuse notices.
Example 2 — The hot resistance trap. A 100 W incandescent bulb: hot R = 220²/100 = 484 Ω. Cold, the filament measures ~40 Ω — inrush current at switch-on is ~5.5 A, 12× running current. This is why bulbs die at the moment of switching on.
Example 3 — Voltage drop on long runs. 12 V garden lights 30 m away, 2 A load, cable 0.75 mm² (loop R ≈ 1.0 Ω): drop = 2 × 1.0 = 2 V → lights see 10 V and run dim. Fix: thicker cable (halve R) or higher voltage transmission with local conversion.
Example 4 — Shunt measurement. Measuring current with a multimeter's 10 A shunt: at 5 A the meter reads U = 5 × 0.01 = 50 mV across its internal 0.01 Ω shunt. Every current measurement is secretly a voltage measurement across a known R.
Common mistakes and myths
- Applying it to non-ohmic devices — diodes, LEDs, motors don't have constant R; Ohm's law works only per-operating-point (with their curves or dynamic resistance).
- Ignoring power ratings — the right resistance with the wrong wattage desolders itself; always compute P and add 2× margin.
- Forgetting temperature — copper's R rises ~0.4%/°C; precision work and hot environments both need derating.
- Mixing RMS and peak on AC — 220 V mains is RMS; peaks hit 311 V. Ohm's law applies to AC magnitude for pure resistors, but reactance (motors, capacitors) needs impedance, not R.
- Trusting nominal values — a "100 Ω" 5% resistor is 95–105 Ω; precision circuits measure or buy 1%/0.1% parts.