Power

Three-phase (and for that matter other numbers of phases) can be modeled as vector diagrams. The length of the vectors corresponds to their voltage. Moreover, the phase angles in question also conform to the angles in the diagram. In the case of balanced three-phase, √3 is a common factor; it's just geometry.

3 ph balanced power=3*1ph power=3*Vline/root3*Iline=root3 Vline*Iline

where did you find this?...in text books?...then answer will be already there. If you are working and it found in any documents, please ask your boss or who selected you there. He is responsible and ought to answer this type of question for the reason of selecting you.

And also too many this question in CR4, search in the left box "serch this forum"

Mathematical equivalent

You will find your answer when you can apply Calculus and the classical thermodynamic law of the conservation of energy to a three phase electric power problem.

A simpe search of CR4 would have lead you here

Yes it would've, he should've and that was certainly an exceptional answer you produced then. But as far as why the square root of three instead of two, seven or some other irrational number to convert 3Ø voltages and amperages into real power does require some Calculus if one won't just accept the number. Then again, some people won't accept Calculus as an answer to anything too.

RF, I believe my answer is why the sqrt 3 enter into the power calculation. It is a trig solution for sine wave problems. However I would like to see your idea regarding "You will find your answer when you can apply Calculus and the classical thermodynamic law of the conservation of energy to a three phase electric power problem." Can you provide a reference that I could check out.

Just the simple derivation of root mean square calculation of the actual (real) power produced by each phase (Calculus). Combine that with the need to combine the power produced by each phase as opposed to the voltage of each phase and the current of each phase, for at any given instant in time since the three phases summation of the voltages and the currents equal zero for they are always 120° out of phase. V_total=V1(t)+V2(t)+V3(t)=0 Yet each phase must be adding power aka energy per unit time and energy cannot be destroyed. Thus making the requirement to do the RMS summing over a cycle. (Thermodynamics)

Thanks for the information.

it depends how you are calculating

in a 3 phases system, power = line to neutral voltage * phase amp *3

there is no sq root 3 here,

if you use phase to phase voltage , phase to phase voltage = phase to neutral voltage * sq root (3)

it comes fom the fact that phase to phase voltage = vectoriel summ of two phase to neutral voltages, phase by 120 deg,

it is a trigonometric equation, sq root (3) come from sin(120 deg)

actually it is a mistake. somebody started with root three and everybody following it. I am using root 1. you can use any number if you are not an employee.

Er, um, because it is the right answer?