On Nov 22, 2006, at 8:39 PM, Dan wrote:
In my understanding, phasors are rotating vectors.

Take a simple voltage vector at an angle of zero. That is precisely
defined.

Now consider a an x-y coordinate system to the right of the voltage vector.
The y part of the coordinate system is the instantaneous voltage; the x part
is time.

So I rotate my voltage vector counter-clockwise. At 45 degrees, the voltage
is one-half the peak value. At 90 degrees, the voltage is at its positive
peak value. So, as I rotate my voltage vector, from zero degrees to 90
degrees, it traces out a nice sine wave.

So the need for phasors, in my opinion, is when you deal with other vectors
tied to the same system frequency. In other words, the current with respect
to the voltage could be described as a phasor that typically lags the
voltage. The phasor satisfies the need for "with respect to" in dealing
with various vector quantities.

So the vectors represent a snapshot of what the vectors do with respect to
each other. More importantly, phasors are important with three-phase
systems where you maintain a 120 degree displacement between the source
voltages.

So I tend to think of a vector as being a phasor at some instant in time.

Maybe some learned fellow like Don Kelly can shine some further light on
this matter.

If it works for you, use it.

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The phasor is a representation of A***exp(j***w*t) where A is a complex number
representing amplitude and includes phase information. Usually, only the A
is drawn as the"vector." You call it a vector because when you add complex
numbers together the corresponding arrows add as vectors do. BUT ONLY IN TWO
DIMENSIONS. This is a very special case. It cannot be extended to find
accelerations for curvilinear motions in three dimensions.

Hamilton extended the concept of complex numbers to three dimensions so that
he could handle what we now call vectors. To do so, he had to abandon having
a single imaginary unit, what is usually called j in electrical engineering.
He had to use three, i, j, and k. Because of that quaternions do not
commute. That is necessary because cross multiplication of vectors does not
commute. Quaternion multiplication also leads to to scalar and vector
products. In the end quaternions have not been used much by electrical
engineers. Heavyside detested them and he also detested Tait who promulgated
their use. In the end, the vector analysis popularized by Gibbs and others
prevailed.

Bill