# Line Voltage and Phase Voltage

By Varadi Hema|Updated : July 22nd, 2022

If in a Y-connected ac generator, each phase voltage has a magnitude of 90 VRMS, what is the magnitude of each line voltage?

1. 0 V
2. 90 V
3. 156 V
4. 180 V

## The magnitude of line voltage is 156 V.

Solution:

The Y-connected ac voltage source is shown below.

Van, Vbn, and Vcn are voltages between lines a, b, c and neutral n, so we call them phase voltage of respective phases. And if voltage sources have the same voltages and same frequency f, and if each phase is displaced by 120°, then the voltage source is said to be balanced.

In a balanced system,

|Van|=|Vbn|=|Vcn|

Given,

Each phase voltage |Van|=|Vbn|=|Vcn|=90 V

|Van|=|Vbn|=|Vcn|= 90

Line voltage is the voltage (or) potential difference between two lines of the source like Van, Vbn, and Vcn.

And in a Y-connected source, line voltage =√3 (phase voltage) =√3×(90) V=155.88≈156 V

In a balanced system, line voltages have equal voltages and are displaced with each other by 120°.

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