A three-phase generator G produces electrical power that is transmitted by three wires as shown in the figure. The potentials (relative to a common reference level) of these wires are , , and . Some industrial equipment (for example, motors) has three terminals and is designed to be connected directly to these three wires. To use a more conventional two-terminal device (for example, a light bulb), one connects it to any tow of the three wires. We have to show that the potential difference between any two of the wires (a) oscillates sinusoidally with angular frequency and (b) has amplitude .

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The potentials (relative to a common reference level) of wires 1,2, and 3 are

,

,

and .

The potential difference between wires 1 and 2 will therefore be

Similarly, we can show that

We note that , , and oscillate sinusoidally with angular frequency and (b) have amplitude .