11.4 Electric Power

Electric power is the rate at which energy is transferred, converted, or dissipated in a circuit element. The basic relation is

Using Ohm’s law, this can also be written as

and

These forms are all equivalent, and the most useful one depends on which quantities are known. In simple lamp problems, larger power generally means greater brightness.

This formula can be derived directly from energy per charge. If a charge dq moves through a potential difference ${\Delta V}$, the energy transfer is ${dU = \Delta V \, dq}$. Dividing by dt gives

so

This is a very clean calculus derivation because it shows power as the time rate of energy transfer. It also makes the meaning of voltage more concrete: voltage is energy transferred per unit charge.