On Jan 12, 11:13*am, Cecil Moore wrote:
On Jan 12, 8:10 am, Keith Dysart wrote:

P(t) = V(t) * I(t) is simple, and always holds.

But one must remember the units of that result is Volt*Amps, not
watts.

You really should put a bit of effort into understanding
the different expressions for power.

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

is saying that the function which describes power with
respect to time, P(t), is the product of the function
describing voltage with respect to time, V(t), and the
function describing current with respect to time, I(t).

As corollary, the power at an instant of time is equal
to the voltage at that instant times the current at
that instant.

And, of course the unit watts is the same as the units
volts times amperes. Just do the substitution.

V = J/C
A = C/s

V A = (J/C) x (C/s)
= J/s
= W

You are confused with the common use in power
engineering where VA is used to mean Vrms*Irms.
Whether VA is equal to watts depends on the
phase relationship of the voltage and current.

When the voltage and current are not in phase, then
the expression
Pavg = Vrms * Irms * cos(A)
can be used to derive the average power.

This is a special case of P(t) = V(t) * I(t).
It is applicable when V(t) is a sinusoid of
a single frequency, and I(t) is related to V(t)
using the expression V(t) = Z * I(t).

Pavg = Vrms * Irms * cos(A)
is completely derived from P(t) = V(t) * I(t)
by appropriately substituting for V(t) and I(t)
and then averaging P(t) over an appropriate
interval (typically one cycle).

Bottom line:
P(t) = V(t) * I(t)
is always correct.

The other variations only work when
applied under the appropriate conditions.

...Keith