What is the Line Voltage of a 208v/120v 3-Phase 4-Wire Wye Secondary?

To answer this question you’ll need to know the relationship between phase and line voltage in a 3-phase, 4-wire wye secondary.

Phase voltage (read between any line and the neutral) multiplied by the square-root of three or the constant 1.732 = line voltage.

120  phase volts x 1.732 = 208  line volts.

This is the case because when voltage is read between any two line conductors that voltage is actually being read between the two phases that feed each line. However the voltage is not completely additive, for example even though each phase has a voltage of 120 volts when voltage is read between two lines (and ultimately the two phases that supply those lines) only 208 volts not 240 volts is read. Why? Because there is a 120 degree phase difference or time difference between the time that the EMF or the electromotive force or electrical pressure of each phase is applied. The numeric equivalent of that phase or time difference is expressed by use of the square-root of three or the constant 1.732.

Line voltage (read between any two lines) divided by the square-root of three or  the constant 1.732 = phase voltage.

208 line volts ÷ 1.732 = 120 phase volts.

This is the case because all three line or (hot) conductors have equal access to the neutral conductor and therefore will always read 120 volts 1-phase which is the voltage across the coil or phase that feeds each line conductor.

So the relationship between phase and line voltage in a 3-phase 4-wire wye is governed by the square-root of three or the constant 1.732.

Understanding how to read and work through exam questions very much like this one will help you pass the electrical exam.

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