Ohm's law and electrical power
Ohm's law states that the current through a resistor is proportional to the voltage across it: V = I · R. The power it dissipates (as heat) is P = V · I. Combining the two gives the twelve formulas that relate the four quantities, so any two of them give you the other two.
| To find | Formula 1 | Formula 2 | Formula 3 |
|---|---|---|---|
| Voltage V | I · R | P / I | √(P · R) |
| Current I | V / R | P / V | √(P / R) |
| Resistance R | V / I | V² / P | P / I² |
| Power P | V · I | I² · R | V² / R |
Example · LED current-limiting resistor
You drive a red LED (≈ 2 V drop) from 5 V and want 20 mA. The resistor drops 5 − 2 = 3 V, so R = 3 V / 0.02 A = 150 Ω, and it dissipates P = 3 · 0.02 = 60 mW: a 1/4 W resistor is fine. Look up the standard value and its colors in the resistor color code calculator.
Example · maximum voltage across a resistor
A 1 kΩ, 1/4 W resistor can take at most V = √(0.25 · 1000) ≈ 15.8 V across it. Above that it heats up more than it can dissipate.
Unit prefixes the calculator understands
You can type values with their SI prefix, with or without a space: p (10⁻¹²), n (10⁻⁹), u or µ (10⁻⁶), m (10⁻³), k (10³), M (10⁶) and G (10⁹). Careful: lowercase m is milli and uppercase M is mega.
Frequently asked questions
Does Ohm's law always apply?
Only to ohmic components, whose resistance does not depend on the voltage. Diodes, LEDs and transistors do not obey it: their V–I curve is not linear. It still applies to the resistor next to them, as in the LED example.
What power rating should my resistor have?
Calculate the power it dissipates and choose one rated for at least twice that. Common ratings are 1/8, 1/4, 1/2, 1, 2 and 5 W.
What about AC circuits?
For pure resistors the same formulas work with RMS values. With capacitors and inductors you need complex impedances.