Power (V²/R)
Power from voltage and resistance.
Formula
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Example
10²/5 = 20W
How it works
This formula tells you how much electrical power a resistor uses when you know the voltage across it. It comes from the basic power relation P = VI, combined with Ohm’s law V = IR; substituting I = V/R gives P = V²/R. It is useful because it lets you find power directly from voltage and resistance without needing current first.
When to use it
Use this when a resistor or resistive load has a known voltage across it and you want to know how much heat or electrical power it is dissipating. It is common in circuit design, resistor safety checks, and simple DC analysis.
Worked example, step by step
A resistor has 12 V across it and a resistance of 4 Ω. P = V² / R P = 12² / 4 P = 144 / 4 P = 36 W So the resistor dissipates 36 watts of power.
Common mistakes to avoid
- Using the total circuit voltage instead of the voltage across the specific resistor
- Forgetting to square the voltage before dividing by resistance
- Mixing up units and writing ohms or volts as part of the final power unit instead of watts
Did You Know?
This form of the power law lets you find a heater's wattage straight from its voltage and resistance.
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More in Electronics & Circuits
View allOhm's Law
BasicVoltage equals current times resistance.
Electrical Power (VI)
BasicPower dissipated by a component.
Power (I²R)
BasicPower lost as heat in a resistor.
Resistors in Series
BasicSeries resistances add directly.
Resistors in Parallel
IntermediateReciprocals of parallel resistances add.
Capacitors in Parallel
IntermediateParallel capacitances add.