On Apr 12, 3:39*pm, Cecil Moore wrote:
Keith Dysart wrote:
It would be helpful, however, if you could actually demonstrate a
system where the energies balance, but the flows do not.

That's obviously easy to demonstrate in a distributed
network system. We can have energy flowing into both
ends of a loading coil at the same time and 180 degrees
later, energy flowing out of both ends at the same time.
The energies balance but the flows are completely
unbalanced and indeed defy the lumped circuit model.

You are not quite looking at the system correctly.

It is a system with two ports (bottom and top) where
energy can enter or leave, and one element (coil)
which can store energy.

The energy that flows in the bottom either flows out
the top or increases the energy stored in the coil.
The energy flowing into the bottom is equal to
the sum of the energy flowing out the top plus the
increase in the energy stored in the coil.
Expressed arithmetically
Pbottom(t) = Pcoil(t) + Ptop(t)

For the specific situation you describe above:
"energy flowing out of both ends at the same time"
means that the energy stored in the ooil is being
reduced to supply the energy leaving the top and
the bottom. The sum of the energy flows out of
the top and the bottom is exactly equal to the rate
at which the stored energy is being reduced.

Lumped or not lumped is moot.
The same analysis can be applied to a transmission
line. The energy flow into the left is exactly
equal to the energy flow out on the right plus
the rate of increase in the energy stored in the
line.

Energy flows (aka power) do indeed balance, though
you certainly have to correctly pick the flows that
should balance.

...Keith