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Thread: phase to phase voltage

  1. #1

    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. #2
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    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.
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  3. #3
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    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.
    Code references based on 2005 NEC
    Larry B. Fine
    Master Electrician
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    Richmond, VA

  4. #4
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    Quote Originally Posted by wankster View Post
    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°)

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  5. #5
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    You may be thinking of the Square Root of 3, which is 1.732 - 3 phase multiplier.
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  6. #6
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    Quote Originally Posted by LarryFine View Post
    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?
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  7. #7
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    Quote Originally Posted by rattus View Post
    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.
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  8. #8
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    Supporting graphic...

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  9. #9
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    Quote Originally Posted by Pierre C Belarge View Post
    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."

    Charles E. Beck, P.E., Seattle
    Comments based on 2014 NEC unless otherwise noted.

  10. #10
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    Quote Originally Posted by wankster View Post
    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.

    Charles E. Beck, P.E., Seattle
    Comments based on 2014 NEC unless otherwise noted.

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