Single-phase versus three-phase

Explain why three-phase systems are used and convert between line and phase quantities in wye and delta.

Three-phase is three sinusoids of equal magnitude spaced 120° apart. The practical payoff is that the instantaneous total power is constant instead of pulsing, that rotating machines get a naturally rotating field with no starting trick, and that a given amount of power moves on less conductor material than single-phase.

Two connection shapes cover almost everything. In wye, each phase connects to a common neutral: line-to-line voltage is √3 times line-to-neutral, and line current equals phase current. In delta, phases connect end to end: line voltage equals phase voltage, and line current is √3 times phase current. A 480/277 V system is wye — 480 V between any two lines, 277 V from any line to neutral.

Balanced three-phase power is S = √3 × V_line × I_line. The √3 appears everywhere for the same reason: the geometry of three vectors spaced 120° apart.

Predicting before you experiment is what makes the result stick. There is no penalty for being wrong here.

Name a piece of equipment you have seen fed line-to-line and one fed line-to-neutral, and state the voltage each sees on a 480/277 V system.