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Wye Line and Phase Voltage

VL=3 VφV_{L} = \sqrt{3} \, V_{\varphi}

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3=1.7320508075688772\sqrt{3} = 1.7320508075688772Square Root of Three · exact

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Two phases of a wye are not simply additive because they peak 120° apart; the vector difference of two equal phasors 120° apart is √3 times either one. That single fact names every common system: 120/208 V (208 = √3 × 120), 277/480 V (480 = √3 × 277), and 230/400 V across most of the world. In a wye the line current equals the phase current — it is only the voltages that get the √3.

The practical consequence is that one transformer bank feeds two voltages: lighting and receptacles hang line-to-neutral at 120 V or 277 V, while motors and heaters take line-to-line at 208 V or 480 V. The trap is assuming 240 V single-phase equipment will work on a 208 V wye leg — it sees 208 V, and a heater delivers only (208/240)² ≈ 75% of its rated output.

Wye Line and Phase Voltage
VL=3 VφV_{L} = \sqrt{3} \, V_{\varphi}
Where
  • VLV_{L}= Line-to-line voltage
  • VφV_{\varphi}= Phase (line-to-neutral) voltage
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