B.5.5—Electrical power

Electrical power

Power is the rate of electrical energy transfer. For a resistor,

$$P=IV=I^2R=\frac{V^2}{R}$$

Choose the convenient form

Use $$P=IV$$ when current and voltage are given, $$P=I^2R$$ when current and resistance are given, and $$P=V^2/R$$ when voltage and resistance are given.

Interpret the unit

A watt is a joule per second: $$1\,\mathrm W=1\,\mathrm{J\,s^{-1}}$$. In a resistor, the transferred electrical energy becomes mainly internal energy and may produce heating.

Worked example from the mapped local textbook

A heater is rated $230\,\mathrm{V}$ and $1100\,\mathrm{W}$. Since voltage and power are known, use $P=V^2/R$:

$$R=\frac{V^2}{P}=\frac{230^2}{1100}=48\,\Omega$$

The rating means the heater transfers about $1100\,\mathrm{J}$ each second when operated at $230\,\mathrm{V}$.

Common trap

For alternating-current questions, distinguish peak values from mean or rms values. Use the convention and data supplied by the question.