Core answer: Ohm's law states that current through a conductor equals voltage divided by resistance — I = U / R. A 12 V source across a 10 Ω resistor drives 1.2 A; the same source across 100 Ω drives only 0.12 A. The law holds for "ohmic" devices (resistors, heaters) and fails for non-linear ones (LEDs, diodes, motors under load).
What Ohm's law actually says
Georg Ohm found (1827) that for a metallic conductor at constant temperature, the current is exactly proportional to the applied voltage. The constant of proportionality is resistance:
| Quantity | Symbol | Unit | Meaning |
|---|---|---|---|
| Voltage | U (or V) | volt (V) | The electrical "pressure" pushing charges |
| Current | I | ampere (A) | Charge flow per second |
| Resistance | R | ohm (Ω) | How much the material opposes flow |
The three equivalent forms — U = IR, I = U/R, R = U/I — let you solve any one quantity from the other two. The power triangle extends it: P = UI = I²R = U²/R.
Worked examples
Example 1 — LED current limiting. A red LED (forward voltage ≈ 2 V) on a 5 V supply needs ≤ 20 mA. The resistor must drop 5 − 2 = 3 V, so R = 3 V / 0.02 A = 150 Ω. Choose the next standard value (150 Ω or 180 Ω). Power in the resistor: P = I²R = 0.02² × 150 = 0.06 W, so a 1/4 W part is plenty.
Example 2 — Household heater. A 2,200 W heater on China's 220 V mains draws I = P/U = 10 A — exactly the limit of a standard 10 A socket. A 3,000 W instant water heater draws 13.6 A and requires a 16 A circuit; plugging it into a 10 A strip is a fire hazard.
Series vs parallel
| Property | Series | Parallel |
|---|---|---|
| Current | Same everywhere | Splits across branches |
| Voltage | Divides proportionally to R | Same across each branch |
| Total resistance | R₁ + R₂ + ... | 1/R = 1/R₁ + 1/R₂ + ... |
| One break | Whole circuit dies | Other branches keep working |
Common mistakes and myths
- Applying Ohm's law to LEDs directly — a diode's V-I curve is exponential; 0.1 V extra can double the current. Always use a series resistor or constant-current driver.
- Thinking a bigger wire has more resistance — resistance falls with cross-section area (R = ρL/A); thicker cable = less resistance = less heating.
- Ignoring temperature — a cold incandescent filament has roughly 1/10 its hot resistance, which is why bulbs usually blow at switch-on.
- Confusing rated power with actual power — a 2,200 W appliance only draws 2,200 W at exactly its rated voltage; at 200 V it draws about (200/220)² ≈ 83%.
- Measuring resistance in a live circuit — a multimeter's Ω mode injects its own test current and can be damaged or read garbage on a powered board. Power off first.