Radical 3 Power calculations

[NEC User]

I understand the formulas but can someone explain the technical engineering theory about the radical 3 used in the calcuations.
Example Formulas in a 277/480V service:
Single Pole Singe Phase: P=IV => P=I277
Two Pole Single Phase: P=IV => P=Ix277xradical3=Ix480
Three Pole Three Phase: P=IVradical3 => P=Ix480xradical3

Where is the radical 3 coming from in the two pole single phase equation and the three pole three phase equation. i think it's something to do with sine and cosine and being out of phase. I'd really like to understand this theory.

 

[steve66]

I understand the formulas but can someone explain the technical engineering theory about the radical 3 used in the calcuations.
Example Formulas in a 277/480V service:
Single Pole Singe Phase: P=IV => P=I277
Two Pole Single Phase: P=IV => P=Ix277xradical3=Ix480
Three Pole Three Phase: P=IVradical3 => P=Ix480xradical3

Where is the radical 3 coming from in the two pole single phase equation and the three pole three phase equation. i think it's something to do with sine and cosine and being out of phase. I'd really like to understand this theory.

A very oversimplified answer is that its due to the 60 degree phase differences that result from voltages and currents being out of phase.

 

[Smart $]

Go to All About Circuits website. Volume II...

http://www.allaboutcircuits.com/vol_2/index.html

Read at least AC Phase in Chapter 1, then practically all of Chapter 2. Then come back here for additional questions...