An electric kettle is rated 230 V; 1000 W. Calculate the resistance of its heating element when in operation.

The chapter defines electrical power as the rate at which electrical energy is dissipated in a resistor, expressed as $P=VI$, and using Ohm's law $V=IR$, this can be rewritten as $$P=I^2R=\dfrac{V^2}{R}$$ These three equivalent forms let power be calculated from any two of $V$, $I$, $R$.

Here, the kettle's rating (230 V, 1000 W) gives the potential difference and power directly, but not the current, so the most direct route is $R=V^2/P$ rather than first finding $I=P/V$ and then $R=V/I$ (both give the same result). Substituting $V=230\ \text{V}$ and $P=1000\ \text{W}$ gives $R=52900/1000=52.9\ \Omega$.

This resistance value is that of the heating element (a coil, typically of a high-resistivity alloy such as nichrome, as mentioned in the chapter's discussion of resistivity of alloys used in heating devices) when the kettle is operating at its rated voltage.