Power dissipated by resistors

A resistor of resistance $R$ carrying a current $i$ converts electrical energy into heat through the Joule effect. The electrons, colliding with the crystal lattice, give up the energy gained from the field, which appears as thermal agitation. The dissipated power is:

Key formula

$\ev{P_R = R\,i^2 \;\geq 0}$

Since the square of the current appears, this power is always positive, whatever the direction of $i$: a resistor never gives back the energy it absorbs, it simply dissipates it. This is the radical difference from the source, whose power can change sign.

Equivalent forms

Using $\Delta V = R\,i$ the same power can be written $P_R = R i^2 = \Delta V\, i = \dfrac{\Delta V^2}{R}$: three faces of the same law, useful depending on which quantities are known.

Links

Topics: Electric circuits Concepts: Power · Joule effect

Related exercises: Problem — heating resistor · Problem — underpowered heater · Worked exercise — resistor used as a heater