On Jan 15, 2:27*pm, Roger Sparks wrote:
On Tue, 15 Jan 2008 06:44:05 -0800 (PST)

Keith Dysart wrote:
[snip]
Well I start with P = V * I, so whenever the current or the voltage
is zero, there is no power. Specifically, V and I are measured at
the terminals of a network and P will be the power flowing into or
out of the network.

I can see why you find "no power" at the zero voltage point, but does that imply that there is no energy flow and no power from every perspective? *As I write, I am struggling how to clearly differentiate between "power" as "work done" and energy as "capacity to do work", and what "network" are we defining.

Let's begin with the network. *Drawing from your words below, we have two networks, one to the left and one to the right of our zero voltage point. *When we test voltages on either side of the zero point, we find voltage. *The question now is: "Which network did we join when we measured voltage?". *The answer is: "We joined the network that we measured.". *When we measure exactly in the center between networks, we join neither network. *

That is the best way. And that way we can measure the flow between the
networks.

For another way of looking at the two networks, *let us place our voltage probes on each side of the zero voltage point on a/the wire connecting the two networks. *We will detect a voltage and a current for any of the standing wave systems we are discussing. *By changing our points of reference, we find that power is applied to the zero voltage zone during the instant of time the measurement is made.

But if we move the probes, we have changed the amount of 'network' on
either
side.

I personally define power as a state/condition where "work 'is being' done", . *Power must act over time and have a physical movement component. *Voltage by itself does not fulfill this definition because no movement is observed. *Current is movement, voltage is only an indication of where a concentration of charges is found.

I am not convinced about 'physical'. Consider heat, light.

In the case under discussion, there are two networks, one to
the left of the point on the line and one to the right and
we are measuring the power flowing between these two networks.

For an example of current without power, consider a loop of
superconductor with a current flowing in it. No voltage, no
power, but there is current.

I agree. *We could place voltage probes between any two points on the superconducting loop and not find voltage. *Power is not being applied nor extracted from the superconducting loop system. *I think we would all agree that energy is stored in the superconducting loop with current flowing.

Current is defined as movement of charges, and charges have energy by definition (how can they be charges without energy?).

Consider an object flying through space. No work is being done
(and therefore there is no power), but the object still has
kinetic energy.

Another point, the current is observed to change directions during the cycles, polarity also changes on each side of the zero voltage point. *Where might the polarized energy come from if it does not cross the zero voltage point?

A thought experiment I have found useful is to consider a simple
resonant circuit made of an ideal capacitor and inductor. Charge
the capacitor to 10 volts and then connect the inductor. A sinusoidal
voltage and current will appear in the circuit.

Just as the inductor is connected:
- all the energy is stored in the capacitor
- the voltage on the capacitor is maximum
- there is no current in the inductor
After connecting the inductor:
- energy starts to transfer to the inductor
- the voltage on the capacitor is dropping
- the current in the inductor is increasing
Some time later:
- the voltage on the capacitor is 0
- the current in the inductor is maximum
- there is no energy stored in the capacitor
- all the energy is stored in the inductor
- no energy is moving from the capacitor to
* the inductor
But the inductor insists that current continue
to flow:
- the capacitor begins to charge with a negarive
* voltage
- energy begins to transfer from the inductor
* back to the capacitor (note the change in the
* direction of energy flow)
- the voltage on the capacitor is increasing
* negatively
- the current in the inductor is dropping
Sometime later:
- the current in the inductor has dropped to
* zero
- the capacitor has a maximum negative voltage
- all the energy is in the capacitor
And this continues forever at the resonant
frequency of the capacitor and inductor circuit.

But no energy is moving from the capacitor to
the inductor when the voltage on the capacitor
is zero and the current in the inductor is
maximum. It is at these times that the direction
of energy flow is changing, as well as when the
voltage in the capacitor is maximum and the
current is zero.

When the voltage on the capacitor is zero, the voltage on the entire system is zero, no matter our reference point. *The system energy is completely contained in the moving current with a direction of energy flow completely defined. For an instant, the inductor is like a superconducting loop.

From a traveling wave standpoint, the resonant capacitor/inductor system contains a positive wave and a negative wave, equally balanced energy wise. *When the capacitor is completely charged, the positive and negative waves are at the reversal/mid point of the cycle where each wave is maximally displaced from center (which is at the electrical center of the inductor). *When the capacitor is completely discharged, the two waves superimpose and both reside in the inductor at identical times. *The energy of both waves is completely contained in the electromagnetic field that exists outside the wires containing the two traveling waves. *Do the waves exist on the wire at this instant, or have they completely desolved into a space field we observe as magnetic force? *The current seems to be flowing so I would say the waves both continue to exist.

When using lumped elements, I do not think I would try to write a
description
in terms of waves.

I can kinda see how like charges could repell so that waves of like polarity might "bounce" but I can't see how waves of opposite polarity might "bounce". *If waves of opposite polarity "bounced", why would the polarity change during the cycle on each side of the "bounce" point?

An excellent counter-example. I may have fallen into
the trap of looking at the examples that support the
argument rather than looking for the ones that don't.
This will take some cogitating. Maybe its the end
of the line for the "bounce hypothesis".

To me, it is much more rewarding to work with traveling waves that pass through one another, *interacting to create standing waves.

I don't object to this view, as long as the waves are
viewed as having voltages or currents but no power.

Have you considered how energy is transfered between elements of the transmission line over time if we do not have an ongoing application of power? *Doesn't one section of line apply power to the next successive section of line an instant of time later after it received applied power? We agree that a transmitter applies power at the input of a transmission line. *Isn't the first section of transmission line just the power source for the second piece of line?

Yes. And that is especially visible when the line is excited with a
pulse.

I think of the traveling waves as transporting power and energy through time and physical distance. *The highest voltage points physically "move" (found in a new location) as time passes, as do the highest current points, and always together in phase. *



The difficulty is that some waves definitely transport
energy while others do not and I do not see a good
explanation for what turns the former into the latter,
as happens, for example, when the pulses collide.

Some waves transport energy, and some do not! *That distinction bothers me less now that I have participated in this thread for a while. *For me, the traveling wave always has current and voltage in phase, and always carries power. *If I can not find power, then we must have a standing wave. *For me, traveling waves is all that we really have, they are primary. *All other waves flow/result from the traveling waves. *

But then do the two travelling waves that make up the standing wave
transport
energy? When no energy crosses the voltage or current zeroes?

And when there are multiple reflections, there are multiple travelling
waves
in each direction. Do each of these multiple travelling waves
independantly
transport energy?

And even a standing wave has energy moving. Just not past the voltage
and
current zeroes.

[snip]

...Keith