I apologize if my response seemed argumentative. It wasn't intended that
way. Certainly, sin^2(wt) has the same shape as the power waveform I
derived -- the only difference is its fixed D.C. term. And I certainly
agree that letting delta t approaching zero doesn't make any function of
t become zero at that point. And just as the analysis I've presented is
in your first year college electronics book, so is the point about delta
t in everyone's high school or first semester college calculus book. But
it's evident that some number of participants in this thread have either
forgotten, never seen, or never understood those basic principles. And
quite a few people either don't have any textbooks, don't understand
them, or are unwilling to open and read them. Hence the postings
containing information that you or I could find in moments.

Roy Lewallen, W7EL

Jim Kelley wrote:

You seem to be looking for an argument any way you can, Roy. ;-)
Sin^2(wt)/2 is the general form of any equation with the shape you
described in your previous post. Furthermore, instantaneous power can
be evaluated at any time t, irrespective of relative phase. The point
is simply that instantaneous power isn't necessarily zero as a result of
delta t's approaching zero.


Given that v = V * sin(wt + phiv)
i = I * sin(wt + phii)

Then p = v * i = VI * sin(wt + phiv) * sin(wt + phii)

The product of the sines can be transformed via a simple trig identity
to give

p = VI * 1/2[cos(phiv - phii) - cos(2wt + phiv + phii)]

The first term in the brackets is D.C. -- it's time-independent. The
second term is a pure sine wave. So the result is a pure sine wave with
a D.C. offset.

I've described the meaning and significance of the power waveform in at
least one earlier posting on this newsgroup. If anyone is interested who
can't find it on Google, I'll look it up and post the subject and date.


Yes. It's also in my first year college electronics book.

Thanks and 73,

AC6XG