On Jan 13, 8:54*am, Cecil Moore wrote:
If "V(t)" is commonly used outside of the Ramo&Whinnery definition
above, I apologize for being confused by the notation being used.

Apology accepted. As a cautionary note....
It is unwise to take the notation used in one text and blindly
substitute into another, especially when the text is deriving
for a specific case.

The IEEE dictionary (see 'instantaneous power') starts with
p = ei
and then goes on to derive the special case for sinusoids.

Desoer and Kuh, "Basic Circuit Theory", start with
p(t) = v(t)i(t)
then derive the special case for sinusoids by substituting
v(t) = Vm * cos(wt+a) = Re[Vm * e^ja * e^jwt] {taking some liberties
to make it ascii}
Note that Re[] is only needed when using the exponential form
and not the trigonometric form.

And, from your post, it appears that Ramo and Whinnery start with
W(t) = V(t) I(t)
and do the derivation for the special case of sinusoids by
substituting
V(t) = Re[Vm*e^j(wt+A1)]

These are all equivalent derivations using different notations.

A key point is that they all start with "instanteous power
being equal to instantaneous voltage times instantaneous current"
as the general case and derive the special case by appropriate
substitution.

And a second key point is that Re[] is not needed in the general
expression for power, (choose the form you like)
p = ei
p(t) = v(t) i(t)
P(t) = V(t) I(t)
, because it is already in the expressions for voltage and current
when the exponential form is used.

...Keith