On Fri, 29 Sep 2006, Ken Cox wrote:
somewhere in the remote parts of my gray matter when
calculating resistance i keep getting a nudge to remind me to
do something with the square root of 3
If you had been talking about power, the square root of three
is used in calculating power in three phase ciruits. :)
---------------------------------
<http://www.madsci.org/posts/archives/jan2001/979920827.Eg.r.html>
Subject: Why is the Square root of Three a factor in 3 phase
power calculations?
[snip]
There are two phases connected between each pair of lines in a
"Y" circuit, and since the voltages are not in phase, they do
not add together to make the line voltage twice the phase
voltage. It turns out through some basic trigonometry, that the
line voltage is equal to each of the two phase voltages times
the sine of 120 degrees, and the sine of 120 degrees is
"one-half" the square root of 3. Adding those two halves
together gives the LINE voltage as the square root of 3 times
the phase voltage. Or conversely the phase voltage is the line
voltage DIVIDED by the square root of 3.
So the power in any phase, assuming, again, a balanced load is
the line voltage times the line current divided by the square
root of 3.
For the three phases, then, the total power is three times the
power in any phase. 3 X the line voltage X the line current
divided by the square root of 3. 3 divided by the square root
of 3 simplifies to just the square root of 3. Multiplying that,
as you noted, by the power factor converts volt-amps to watts
assuming the power factor is other than one.
[snip]
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