Lessons · Engineering · Three phases, and the root-three that follows
Three supplies, one root three
A three-phase supply carries three alternating voltages a third of a cycle apart. Because they are out of step, the voltage between two lines is not twice the voltage to neutral but root three times it -- about 1.732. The same factor turns up in three-phase power.
Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.
In beta. This lesson was written for Hone and has not yet been checked by a licensed engineer. Practice material, not professional advice. What that means.
What it is for
It is the number that separates people who can read a three-phase nameplate from people who cannot, and getting it wrong is out by 73%, which is not a rounding error.
How to think about it
Decide whether the figure you have is line-to-line or line-to-neutral before using it. If you need to move between them, multiply or divide by root three, and sanity check against the two standard voltages you know for your region.
Worked example
Three voltages, a third of a cycle apart.Not three copies of the same.
Line-to-line = root three x line-to-neutral.About 1.732 times.
Three-phase power carries the same root three.P = root3 x V_L x I_L x power factor.
Check which voltage a nameplate quotes.Almost always line-to-line.
Your turn
Line-to-neutral is 230 V. Write the line-to-line voltage in volts, to the nearest volt. (root 3 = 1.732)
230 x 1.732 = V
Solve one, graded on the server
The trap
Doubling instead of multiplying by root three. The three phases are not opposite each other, they are a third of a cycle apart, and the geometry gives 1.732.