# square root of 3



## trainee (Nov 17, 2007)

This concept has never been clearly explained to me ...fortunately, I've memorized the formulas during the exams but I want to be able to make heads and tails of it now....of course we're talking about 3 phase systems.

First of all, how come root 3? What's the reasoning behind using sqrt(3)? Can someone clearly explain when root 3 is used, when it isn't?

Thanks


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## mascott (Jan 6, 2008)

Actually, it's Sqrt(3) divided by 2 that shows up everywhere, but the 2 often gets hidden. Basic equilateral triangle geometry. Phasors are separated by 120 degrees. Points comprise an equilateral triangle.

Sin (60) = Sin (120) = 0.866 = Sqrt (3) / 2

2 * Sin (60) = 1.732

(2 * Sin (60))^2 = 3

In all the conversions for 3 phase power, the equilateral triangle always shows up.

Hope this helps!


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## RIP - VTEnviro (Jan 7, 2008)

Looks like less than 120 degrees to me. :dunno:


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## Wolverine (Jan 7, 2008)

That's only a two phasor system.


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## Art (Jan 11, 2008)

envision a Y phasor diagram...

VLL = Y tip to Y tip

VLN = tip to center

draw the line from tip to tip and bisect it....

2 triangles: 90 (from perpendicular intersection), 120/2 (1/2 of the angle between phases), and 180 - 120/2 - 90 = 30

looking at 1 triangle resulting from the bisection we observe that VLL/2 = VLN cos(30)

VLL = (2 x cos(30)) VLN

cos 30 = sqrt(3/4) from unit circle...

therefore: (2 x cos(30)) = 2 x sqrt(3/4) = 2 x sqrt(3) / 2

2's cancel

so (2 x cos(30)) = sqrt(3)

therefore: VLL = sqrt(3) VLN


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