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!
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!
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.
Bottom line: if you are doing this for money, do it right or walk away.
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.
Master ElectricianCode references based on 2005 NECLarry B. Fine
Electrical Contractor
Richmond, VA
Sinusoidal waveform formulas:
L1-N voltage = cos(ωt)where:
L2-N voltage = cos (ωt - φ)
L1-L2 voltage = cos(ωt) - cos (ωt - φ)
ω = angular frequency, i.e. 360°×60cycles/sec = 21,600°/secWhen you plot out the last waveform, you will find:
t = time in seconds
φ = phase difference, here it is 120° or (120/180*pi) radians
L1-L2 voltage = √3 × cos(ωt - 330°)
I will have achieved my life's goal if I die with a smile on my face.
You may be thinking of the Square Root of 3, which is 1.732 - 3 phase multiplier.
Instructor, Industry Advocate
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.
I will have achieved my life's goal if I die with a smile on my face.
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I will have achieved my life's goal if I die with a smile on my face.
Charles E. Beck, P.E., Seattle
Comments based on 2017 NEC unless otherwise noted.
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