On Jun 6, 9:45*am, Cecil Moore wrote:
On Jun 5, 6:28*pm, Keith Dysart wrote:

There are indeed negative values. These occur when the energy is
flowing in the other direction, ...

Let's take a close look at the illusion that you are seeing and not
comprehending. Observe a snapshot of the instantaneous power envelope
of a traveling wave. It is a sinusoidal envelope with peak
instantaneous power levels and zero instantaneous power levels. When
it is traveling in the forward direction we consider that to be
positive power. When it is traveling in the reverse direction, we
consider that to be negative power. It is only a directional
*convention* not proof that negative power exists. The only waves that
can exist as waves on a transmission line are traveling waves.

Ahhh. I see part of your problem. You are thinking envelopes.

You need to change your point of view to be a particular point on the
line.
At this point, there is a function that describes the voltage: V(t).
It
may or may not be a sinusoid. There is a function for the current:
I(t).
And from these can trivialy be derived a function for power:
P(t)=V(t)I(t).

When I clip my instantaneous voltmeter across a line and measure 0 for
all time, I can confidently say that no energy is flowing, for there
is
not. I am curious as to what you would answer?

In "Optics", Hecht says instantaneous power is "of limited utility."
You seem to have discovered that limit, stepped over it, and stepped
in it. :-)

Well, Hecht may have his limitations when dealing with Optics, but
there
is no reason to expect these same limitations to apply to circuit
analysis.

....Keith