Why the √3?
Why the square root of 3?
In electrical engineering calculations involving three phase power systems, there is a mysterious √3 (square root of three) that always seems to work its way into the calculations.
Where did it come from, what does it represent, and why do we use it?
Before we delve into answering these questions, it is important to touch on a little bit of electrical theory regarding three phase systems. In a 3-phase system, there are three sinusoidal waves, each separated by 120 degrees as shown to the right. This sequence is repeated 60 times a second in a 60Hz power system. The horizontal axis is considered ground or zero. The magnitude of each of the three phases above or below the horizontal axis is called the line to ground voltage, which we represent as VLG. The magnitude of a positive peak of one phase above the above the horizontal axis and the negative peak of a different phase below the horizontal axis is called the line to line voltage, which we represent as VLL.