Dissipated Power and the Joule Effect

The special case of ohmic devices

An ohmic device (a resistor) obeys Ohm's law: U = R x I. Combining this law with P = U x I gives two other very useful expressions for power:

P = R x I^2

P = U^2 / R

These three formulas (P = U x I, P = R x I^2, P = U^2 / R) always give the same result for an ohmic device: choose the one that uses the quantities known in the problem.

The Joule effect

When a current flows through a resistor, part (or all) of the electrical energy is converted into heat: this is the Joule effect. This phenomenon explains how toasters, heaters, and irons work, but also the unwanted heating of cables or electronic components.

Concrete example

A resistor of R = 20 ohms carries a current I = 3 A. The power dissipated by the Joule effect is:

P = R x I^2 = 20 x 3^2 = 20 x 9 = 180 W

If we instead know the voltage across it, say U = 60 V, we get the same result with P = U^2 / R = 60^2 / 20 = 3600 / 20 = 180 W.

Common pitfall

In P = R x I^2, it is the current that is squared, not the resistance! A common mistake is to calculate (R x I)^2 instead of R x I^2, which gives a completely different result. Likewise, in P = U^2 / R, it is the voltage that is squared: always check which quantity carries the exponent 2 before starting the calculation.