On Apr 13, 8:41*pm, Cecil Moore wrote:
Keith Dysart wrote:
Your imcompleteness is that you forgot to include the
energy flow into the electric and magnetic fields around
the coil. When one does not forget this flow, all of
the flows will balance at every instant.

Sorry, it may or may not be a coil. It is in a black box
whose contents are unknown. Including the energy flows
inside the black box is impossible. The instantaneous
power into the black box does not balance the instantaneous
power out of the black box.

Black boxes are an excellent way to set problems which help us
learn about the meaning of theories.

Conservation of energy and its corollary, conservation of power,
is used in a different way for analyzing black boxes than it
is when we analyzed the fully specified circuit in your Fig 1-1.

With the black box, knowing the power function on the two ports,
we can compute the energy flow into the storage elements within
the box. If the flow out of one port is not always exactly
balanced by the flow into the other, then we know that the black
box is storing some energy and therefore that it has some elements
which store energy. In a more typical situation, we do not have
a completely black box, but we know some of its elements. We can
use the balance of energy flows to help us decide if we have all
the elements. If some of the energy flow is unaccounted for, then
we have not yet found all the elements.

If the box is truly opague, then all we can say is that it has
some energy storage elements and that collectively, the flow
into these elements is described by
Pport1(t) - Pport2(t)

The situation is somewhat different in Fig 1-1. All the elements
of the system are completely specified in Fig 1-1 and we used
circuit theory to compute the energy flows. Not surprisingly, they
completely balanced:
Ps(t) = Prs(t) + Pg(t)
Associated with Fig 1-1, there is a secondary hypothesis that it
should be possible to account for another energy flow, the imputed
flow in the reflected wave on the line. The inability to account
for this flow, given the conservation of power corollary to the
conservation of energy law, is a very strong indicator that the
energy flow imputed to the reflected wave is not an actual energy
flow.

...Keith