1. Member
Join Date
Nov 2007
Posts
76

phase to phase voltage

Can someone explain to me why phase to phase voltage is multiplied by radical 3 in a three phase system? I just asked my trig teacher and he couldn't help!

2. In a 3 phase wye system, the voltage measured line to line is not the
sum of the phase voltage, because the voltage potential are out of phase by 120 degrees.

3. Draw a Y with three equal-known-length and equally-spaced arrows. Now, measure the distance from arrowtip to arrowtip, as the side of an equilateral triangle, and compare it to the arrow length.

4. Originally Posted by wankster
Can someone explain to me why phase to phase voltage is multiplied by radical 3 in a three phase system? I just asked my trig teacher and he couldn't help!
Sinusoidal waveform formulas:
L1-N voltage = cos(ωt)
L2-N voltage = cos (ωt - φ)
L1-L2 voltage = cos(ωt) - cos (ωt - φ)
where:
ω = angular frequency, i.e. 360°×60cycles/sec = 21,600°/sec
t = time in seconds
φ = phase difference, here it is 120° or (120/180*pi) radians
When you plot out the last waveform, you will find:
L1-L2 voltage = √3 × cos(ωt - 330°)

5. You may be thinking of the Square Root of 3, which is 1.732 - 3 phase multiplier.

6. Senior Member
Join Date
Nov 2004
Posts
3,172
Originally Posted by LarryFine
Draw a Y with three equal-known-length and equally-spaced arrows. Now, measure the distance from arrowtip to arrowtip, as the side of an equilateral triangle, and compare it to the arrow length.
Isosceles triangle maybe?

7. Originally Posted by rattus
Isosceles triangle maybe?
No question here... isoceles triangle definitely!

120° at the vertex of the equal sides; 30° at the vertices of the equal sides with the unequal side. The relationship can be depicted as two back-to-back 30°-60°-90° triangles. As trig goes, the relationship of the long leg to hypotenuse is (√3)/2. So two long legs ios √3 times either hypotenuse.

8. Supporting graphic...

9. Originally Posted by Pierre C Belarge
You may be thinking of the Square Root of 3, which is 1.732 - 3 phase multiplier.
The OP said "radical 3." The term "radical" is equivalent to "square root of."

10. Originally Posted by wankster
I just asked my trig teacher and he couldn't help!
Send me a PM with your email address. I can send you a trigonometric derivation of the formulas for power in single phase and three phase systems. Give them to your trig teacher, and let us know what he says.

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