On Dec 27, 12:39*am, Cecil Moore wrote:
Keith Dysart wrote:
The expression you really mean is

Pavg = Vrms * Irms * cos(A)

Yep, that's what I meant.

No. I mean multiply the instantaneous value by
the instantaneous value, ...

It is not clear to me what physical meaning, if any,
can be attached to such a product.

When V(t) is the function describing the instaneous
voltage and I(t) is the function describing instaneous
current then

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

is the function describing the instantenous power,
that is, the rate at which energy is being transferred
at any particular instant.

You can then integrate P(t) over the time of interest,
call it the interval from t0 to t1, divide by (t1-t0)
and obtain the average power for that interval. For
periodic functions, one period is an appropriate
interval to integrate over.

If you substitute
V(t) = Vpeak sin(wt)
I(t) = Ipeak sin(wt+alpha)
compute P(t), integrate and divide, you will obtain
Pavg = Vrms * Irms * cos(alpha)
which is how that convenient expression is derived.

It is worth doing to convince yourself. Then examine
P(t) to understand how the instaneous energy transfer
varies with time.

Even for a line without reflections, it is valuable
to understand that the energy flow is not continuous
but varies with a period of twice the frequency of
the voltage or current sinusoid.

...Keith