On Jun 5, 10:22*am, Cecil Moore wrote:
On Jun 5, 7:08*am, Keith Dysart wrote:

We need to carefully understand the meaning of the words. Power is
energy that is moving;

Correction, it must be moving past a point, not just moving laterally
from an inductance to a capacitance and back.

Yes, indeed. And so it does. At any point where the voltage or current
is not always 0, energy moves back and forth. This can be readily seen
by computing P(t)=V(t)*I(t) at such a point. P(t) will be a sinusoid
describing the energy flow in the time domain.

There is zero net
average power anywhere on a wire containing a pure standing wave.

Yes, but to understand the details, time domain analysis is a great
asset. You need to move away from just averages to understand what
is going on.

Therefore, there is zero net energy flow anywhere on a pure standing
wave, not just at the zero current and zero voltage points. The
average power in a pure standing wave is zero whether the current or
voltage is zero or not.

True, but the instantaneous power is not.

What is important for power is the phase angle
between the net current phasor and the net voltage phasor which is
always 90 degrees for a pure standing wave. The fact that *power is a
scalar with no negative values* and *the average power is zero*, leads
one to conclude that instantaneous power is just a mathematical
curiosity.

On the contrary. It is computable and measurable.

Exactly how can the instantaneous power average out to zero
average power if there are no negative values of instantaneous power?

There are indeed negative values. These occur when the energy is
flowing
in the other direction, i.e. the direction opposite to that
represented
by positive values of power.

In P(t)=V(t)I(t), when V(t) and I(t) have different signs, P(t) is
negative.

Seems to me to be one of those numerous "undefined" or "indeterminate"
conditions that unfortunately exists in mathematics. When you solve a
quadratic equation for a resistance and get plus or minus 100 ohms, do
you actually start searching for a -100 ohm resistor? Then why, when
you know the average power is zero, do you ask us to go searching for
some negative instantaneous power that doesn't exist?

Ahhhhh, but it does. One does not need to search far if one starts
with
a time domain analysis.

Since power is energy flow *per unit time*, I don't see how power
calculated over zero unit time can be anything more than a
mathematical curiosity existing in human brains - and unrelated to
reality.

Well, this is the basis for calculus...
- instantaneous velocity
- instantaneous acceleration
- instantaneous jerk
- instantaneous voltage
- instantaneous rate of change of voltage
- instantaneous power

All are well understood concepts... and related to reality.

When one integrates instantaneous standing wave power over
one cycle and gets anything except zero, one needs to recognize the
error or one's ways.

In a 'pure standing wave', such integration does result in zero, as
expected. But looking at the time domain details helps reveal the
fine grained behaviour that is obscured when only averages are
considered.

....Keith