# Three phase circle

- Author:
- Conor McDonagh

## Using points on a circle to describe phases in three-phase electricity

This file shows an animation of the voltage and how it relates to points on a circle.
The 3 live wires in a 3-phase cable each carry an AC voltage - a voltage that varies in time as a sine wave.
The voltages are shifted in "phase" so that each one peeks at a different time and the peeks are evenly spaced in time.
A sine wave can be seen as a sideways projection of a point moving around a circle.
Take the point V1 on the circle. It is projected onto the vertical line at
point V1y. The height of this point above the x-axis represents the size
of the voltage. We use a peek height of 1 (which is the radius of the
circle). In electricity, the peak voltage is 325 volts (RMS voltage is
230 V) but we're scaling down that 325 to 1. As V1 moves around the
circle, the height if V1y increases and decreases as a sine wave, going
from zero to maximum positive to zero to maximum negative and back to
zero. This cycle repeats continuously.
The graph of this height versus time is shown to the left of the line, just over a single time
period after which the cycle repeats.
See how V1, V2 and V3 are equally spaced around the circle (120 deg apart) and the time graph
shows that the peeks (maximum heights) are reached at equally spaced
time intervals.
The heights of points V1y, V2y, V3y give the voltage (scaled) on each of the 3 live wires with respect to a neutral wire at
zero volts.
The difference in voltage between two wires is the same as the difference in heights between the projected points, e.g. V1y -
V2y is the voltage between wire 1 and wire 2. On the circle, the length
of the green out to V12 is the same as the distance from V1 to V2 and it
has the same direction as the line joining V1 to V2. The length of the
green radial line is √3 times bigger than the radius of circle. If you know about vectors, V12 is the subtraction of vector V2
from vector V1. The height of projected point V12y is equal to the
difference in height between V1y and V2y, including the +/- sign
depending on which is higher. The height of V12y goes to a maximum that
is √3 times higher than the maximum of V1y or V2y.
The voltage difference between any two of the live wires in a three phase power cable is √3 times the voltage of each wire with respect to neutral.