From Newsgroup: uk.d-i-y

Carrying on from my question about alternators.

A single sine wave has an RMS value of 0.707.

Does this same figure apply to polyphase things like a three phase alternators?

My gut is telling me that it would be higher than that figure but I
can't quite articulate why other than looking at a graph ther appears to
be more "area under the graph". I am sure I have explained this very poorly.

What about greater number of phases?

Thanks again in advance.
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From Newsgroup: uk.d-i-y

On Mon, 11 May 2026 13:18:01 +0100, David Paste <pastedavid@gmail.com>
wrote:

Carrying on from my question about alternators.

A single sine wave has an RMS value of 0.707.

Does this same figure apply to polyphase things like a three phase >alternators?

For each individual phase, the RMS value will be the same 0.707
figure. But the average power delivery will be greater the more phases
there are (allowing for reactive loads, that is).

My gut is telling me that it would be higher than that figure but I
can't quite articulate why other than looking at a graph ther appears to
be more "area under the graph". I am sure I have explained this very poorly.

What about greater number of phases?

Thanks again in advance.

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From Newsgroup: uk.d-i-y

On 11/05/2026 13:18, David Paste wrote:

Carrying on from my question about alternators.

A single sine wave has an RMS value of 0.707.

Does this same figure apply to polyphase things like a three phase alternators?

Yes...

Basically multiply the RMS voltage by sqrt( 2 ) to get the peak voltage

(or multiply peak to peak by 1/sqrt(2) to get the RMS)

This would work also on the phase to phase voltages with other number of phases:

Phase# RMS Peak
2 480.0V 678.8V
3 415.7V 587.9V
4 339.4V 480.0V
5 282.1V 399.0V
6 240.0V 339.4V

My gut is telling me that it would be higher than that figure but I
can't quite articulate why other than looking at a graph ther appears to
be more "area under the graph". I am sure I have explained this very
poorly.

It is the same calculation for calculating the peak voltage for any
number of phases.

What about greater number of phases?

The phase to phase voltage changes with more phases - you get the
highest possible value with 2 phase (or split phase) where the two
phases are in antiphase. Additional phases lower the phase to phase
voltage. Beyond 6, the phase to phase is lower than the single phase
voltage.

Calculating the phase to phase voltage uses the same basic calculation:

Phase to phase V = 2 x Vrms x sin( 180 / N )

(Where 180 is pi radians in degrees, and N is the number of phases)

So for 3 phase at 240V per phase that is 2 x 240 x sin( 180 / 3) = ~415V

(note sin( 60 ) = sqrt ( 3 ) - which is why that shortcut works for 3 phase)

If you had 6 phases, then:

2 x 240 x sin( 180 / 6 ) = ~164V

(the more phases you add, the lower the adjacent phase to phase voltage becomes)
--
Cheers,

John.

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