Watt's law

Also known as the Electric power law.

The electrical power dissipated or delivered in a circuit equals the product of the voltage across it and the current through it.

Same trick as Ohm's triangle: P = V·I, V = P/I, I = P/V.

P = V × I = I²R = V²/R

P: power (watts)
V: voltage (volts)
I: current (amperes)
R: resistance (ohms)

In plain English: Volts are the push, amps are the flow — multiply them and you get how much energy per second is being converted. Combine with Ohm's law to get the I²R and V²/R forms.

Where you'll meet it: Choosing resistor wattage ratings, sizing power supplies and heatsinks, estimating battery life. If a part is getting hot, this law says exactly how hot-headed it is.

Calculators that use this law

Ohm's Law CalculatorV = I × R Electrical Power CalculatorP = V × I = I² × R = V² / R Joule Heating CalculatorH = I² × R × t LED Resistor CalculatorR = (V_supply − V_forward) / I_forward Power Triangle CalculatorS² = P² + Q² Three-Phase Power CalculatorS = √3 × V_L × I_L Power Factor Correction CalculatorQ_c = P × (tan φ₁ − tan φ₂), where φ = arccos(pf)RMS, Average and Form Factor CalculatorSine wave: V_rms = V_peak / √2 Energy and Electricity Bill CalculatorUnits (kWh) = (Watts / 1000) × hours Battery Life CalculatorRuntime (h) = (Capacity in mAh / Load in mA) × derating factor

Components this law governs

Resistor (fixed)P = I²R is what the wattage rating is protecting. A ¼ W part passing 30 mA through 470 Ω is fine; through 4.7 kΩ it is smoking.Capacitor (aluminium electrolytic)Ripple current through ESR is P = I²R inside the can. That self-heating is what dries the electrolyte out and kills the part.Capacitor (tantalum)Its low ESR keeps I²R self-heating small, but a surge into a tantalum can ignite it — hence the heavy voltage derating rule.LED (light-emitting diode)P = Vf × I is what the package must shed; it is why a 1 W LED needs a metal-core board and a 20 mA indicator does not.MOSFETConduction loss is I²·Rds(on), and it is why a 50 A part still needs a heatsink at 20 A if its Rds(on) is poor.Rectifier DiodeP = Vf × I is the diode's heat — 1 A through a 1N4007 is a steady watt to dissipate.

More in The foundation

Ohm's law Laws of resistance Joule's law of heating Capacitor charge law Self-induction law