What is Ohm's law?
Ohm's law is the basic rule connecting voltage (V), current (I) and resistance (R) in an electric circuit. German physicist Georg Simon Ohm published it in 1827 in Die galvanische Kette, mathematisch bearbeitet. If resistance stays the same, current rises in step with voltage; if voltage stays the same, more resistance means less current.
| To find | Formula | Unit |
|---|---|---|
| Voltage | V = I × R | volt (V) |
| Current | I = V ÷ R | ampere (A) |
| Resistance | R = V ÷ I | ohm (Ω) |
The water-pipe analogy
Think of voltage as water pressure, current as the flow of water, and resistance as how narrow the pipe is. More pressure pushes more water through; a narrower pipe lets less through.
Worked examples
- A 4 Ω resistor on a 12 V battery: I = 12 ÷ 4 = 3 A.
- A 220 Ω resistor carrying 0.5 A: V = 0.5 × 220 = 110 V.
- 9 V produces 0.03 A: R = 9 ÷ 0.03 = 300 Ω.
Series, parallel and power
Resistors in series add up (R = R₁ + R₂ + …) and carry the same current. Resistors in parallel combine as 1/R = 1/R₁ + 1/R₂ + …, so the total is smaller, and each one sees the same voltage. Plugging Ohm's law into P = VI gives P = I²R = V²/R, which is how you work out the heat a wire gives off. How that heat spreads is covered in heat transfer.
Limits of Ohm's law
Ohm's law is not a universal law of nature but an empirical rule for ohmic materials, such as metals at constant temperature, whose voltage–current graph is a straight line. Diodes, transistors and incandescent filaments are non-ohmic because their resistance changes with temperature or voltage. The steady change of a metal's resistance with temperature is exactly what a resistance temperature detector (RTD) uses to measure heat.
FAQ
- Is high voltage always dangerous?
- What harms the body is current. But for the same skin resistance, higher voltage drives more current, so high voltage is dangerous.
- Does Ohm's law work for AC?
- Yes for purely resistive circuits, using instantaneous or RMS values. With coils or capacitors, you use impedance instead of resistance.
Sources reviewed: 2026-10-25
References
- Ohm, G. S. (1827). Die galvanische Kette, mathematisch bearbeitet. Berlin: T. H. Riemann.
- Halliday, D., Resnick, R., & Walker, J. (2014). Fundamentals of Physics (10th ed.). Hoboken, NJ: Wiley.
- BIPM. (2019). The International System of Units (SI) (9th ed.). Sèvres: Bureau International des Poids et Mesures.