Keith Dysart wrote:
When does P(x,t) not equal V(x,t) * I(x,t)?

Any time the angle between V(x,t) and I(x,t) is
not 0 or 180 degrees. The correct equation is:

P(x,t) = V(x,t) * I(x,t) * cos(A)

If you write the above equation as:

P(x,t) = V(x,t) * I(x,t)

then you have implied the *dot product* of those
terms. The *cross product* will give you the wrong
answer. The dot product and cross product are both
ways of multiplying so to be technically correct,
you must specify which method of multiplying that
you are talking about.

When is my bank account zero? When I have drawn out
all the money I deposited. Power is a scalar like
money. If you put in 10 watts and take out 10 watts,
the balance is zero.

If you try to put 10 watts into a load and the load
rejects it, that energy flows in the opposite direction.

P(x,t) = V*I*cos(A) = Pfor - Pref

If Pfor = 10 watts and Pref = 10 watts then
P(x,t), i.e. the *NET POWER* equals zero.
--
73, Cecil http://www.w5dxp.com