Editing Alternating current (section)

=== Examples of alternating current ===
To illustrate these concepts, consider a 230&nbsp;V AC [[Mains power systems|mains]] supply used in [[Mains power systems#Table of mains voltages, frequencies, and plugs|many countries]] around the world. It is so called because its [[root mean square]] value is 230&nbsp;V. This means that the time-averaged power delivered <math>P_\text{average}</math> is equivalent to the power delivered by a DC voltage of 230&nbsp;V. To determine the peak voltage (amplitude), we can rearrange the above equation to:
:<math>V_\text{peak} = \sqrt{2}\ V_\text{rms}</math>
:<math>P_\text{peak} = \frac{(V_\text{rms})^2}{R}\frac{(V_\text{peak})^2}{(V_\text{rms})^2} = \text{P}_\text{average}\sqrt{2}^2 = \text{2}P_\text{average}.</math>

For 230&nbsp;V AC, the peak voltage <math>V_\text{peak}</math> is therefore <math>230\text{ V}\times\sqrt{2}</math>, which is about 325&nbsp;V, and the peak power <math>P_\text{peak}</math> is <math>230 \times R \times W \times 2</math>, that is 460&nbsp;RW. During the course of one cycle (two cycle as the power) the voltage rises from zero to 325&nbsp;V, the power from zero to 460&nbsp;RW, and both falls through zero. Next, the voltage descends to reverse direction, −325&nbsp;V, but the power ascends again to 460&nbsp;RW, and both returns to zero.