### Re: Why are you dividing power by the square root of 3?

Date: Wed Dec 21 08:26:36 2005
Posted By: Donald Howard, Nuclear Engineering, Retired
Area of science: Engineering
ID: 1134021259.Eg
Message:

Talking strictly AC, it is not necessarily true that if you're pulling 10 amps on a 120 Volt, single phase line, that is 1200 Watts. It is true only if the load is pure resistance, like a dozen 100 watt light bulbs. If it is a motor, then part of that current is "circulating current" tied up in building and collapsing the magnetic field(s) in that motor. The current that builds the field collapses and kicks back, and though it is measured as current it doesn't produce any watts.

When talking about three phase circuits, vectors become a consideration as the voltage and the current in those circuits are "out-of-phase" by 30 degrees, and that is where the square root of three comes in. Depending on whether the three phases are connected as a "Y" or a "Delta" [a triangle] either the voltage or the current in the line leading away from the transformer will be larger than the current/voltage in the transformer winding by a factor of the square root of three.

Try picturing this:

A triangle with a 30 degree, a 60 degree and a 90 degree angle. Make the side opposite the 30 degree angle 1 inch. Then the line on the other side of the 90 degree angle will be two inches and the hypotenuse, by the Pythagorean Theorem must equal the square root of three... or 1.732 inches. That's basic Trigonometry.

If you haven't gotten to "Trig" or the Pythagorean Theorem yet, trust me - it really works that way. You can draw the triangle and measure it for yourself.

Any Electrical Engineering text can help further - reference "Power in ______ (Single, Two and Three Phase AC Circuits)"

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