# derivation square root of 3 for for delta and wye transformers

Discussion in 'Math' started by EL7819, Oct 13, 2011.

1. ### EL7819 Thread Starter New Member

Apr 15, 2011
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0
Hello,

I hope I have this in the right forum. I was wondering how mathematicians and or engineers derived the square root of 3 as a constant for delta and wye balanced 3 phase transformers mostly? If not an answer articles to read is fine, anything to point me in the right direction.
My guess would be that there are three
branches and it has something to do with the pythagoreom thereom. I am not sure? If my spelling and or grammer is in some way wrong, I apologize for my insolence.
Thank you, any help is greatly appreciated.

2. ### steveb Senior Member

Jul 3, 2008
2,433
469
You are close. It is a generalization of that theorem called the cosine law. The three branches imply that the angles between the vectors is 120 degrees, and the cosine law allows the vector length to be calculated for angles other than 90 degrees (which Pythagorus' theorem is limited to).

http://mathworld.wolfram.com/LawofCosines.html

so $c^2=a^2+b^2-2ab \cos(\theta)$

becomes

$c^2=V^2+V^2-2V^2 \cos(120)$

or

$c^2=2V^2(1-\cos(120))=3V^2$

then take the square root of each side to get the following.

$c=\sqrt{3}V$

So c represents the line to line voltage Vab or Vbc or Vca, and V represents the phase voltage Va, or Vb or Vc, and the calculation is basically a vector addition (or more accurately vector subtraction) problem.

Last edited: Oct 14, 2011
3. ### MrChips Moderator

Oct 2, 2009
12,648
3,458
Just a minor typo. I know you meant

$c=\sqrt{3}V$

4. ### steveb Senior Member

Jul 3, 2008
2,433
469

Thank you! I corrected it. That damn cut and paste operation gets me every time.

Apr 15, 2011
20
0

6. ### Georacer Moderator

Nov 25, 2009
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@EL7819

You can use the "Thanks" button to show your gratitude towards another member. This way the forum can stay clutter-free.

7. ### Denny Singleton New Member

May 11, 2016
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