# 3 phase AC circuit supply potential difference

How can the line voltage be 220 V when in actual line voltage is the potential difference between 2 different lines. For ex:- Vry= 220 V. And why do we divide it by root of 3 to get phase voltage. Isn't phase voltage supposed to be bigger than line voltage? How can a potential difference be greater than the individual phase voltage? And assuming a balanced load the potential difference between 2 connections is zero. Like connecting a voltmeter to 2 same potential which would cancel out each other.

• In a 415v three phase system, there's 415V between any two phases, hut there's only 240B between any one phase and ground/neutral. The phase to phase voltage is sqrt(3) times the phase to neutral voltage – Sam May 17 '16 at 8:55

## 3 Answers

Try the phaser diagram: -

Line voltages are red and phase voltages are blue. It's simple trigonometry to prove the $\sqrt3$ relationship.

Try multiplying by the root of 3, rather than dividing! The phase-to-phase voltage should be greater than the phase-to-neutral.

For 220V phase-to-neutral, you should get about 380V phase-to-phase.

• but how? how is potential difference greater than the potential itself? or is it because of the phase difference between the 2 phase voltage which makes this happen? – sudhanshu May 17 '16 at 17:06
• @sudhanshu It's down to the phase difference of 120 degrees between phases. Look at the diagram that Andy aka has posted. The red lines are longer than the blue ones. – Simon B May 17 '16 at 19:08

The voltage between two phase lines is greater than between one phase line and neutral.

Very simply put, it is because when one phase line peaks, the other phase line dips. When L1 is at +310V (against neutral), L2 is at -155V (against Neutral). That is not yet the maximum peak voltage between the two phase lines, this occurs 60° later, as until then, L1 drops off slower than L2 "rises" towards negative voltage. The peak voltage will then be 535V, which means that the RMS voltage will be around 380V.

Note that the typical "220V line" is running nominally at 230V nowadays, with the voltage between two phase lines being around 400V.