On Mar 22, 10:14*am, Cecil Moore wrote:
Keith Dysart wrote:
Ps(t) = 100 + 116.6190379cos(2wt-30.96375653)
Prs(t) = 68 + 68cos(2wt-61.92751306)
Pg(t) = 32 + 68cos(2wt)
Pf.g(t) = 50 + 50cos(2wt)
Pr.g(t) = -18 + 18cos(2wt)

Now it is time for you to explain exactly why you
believe in a conservation of power principle. Do
you demand that the instantaneous power delivered
by a battery charger be instantaneously dissipated
in the battery being charged?

Are you making this a trick question by using the
word "dissipated"?

If not, then yes. Consider my laptop which has an
external power supply connected by a cord to the
laptop.

Conservation of energy means that the instantaneous
energy flow (i.e. power) along this cord into the
laptop is always exactly equal to the sum of
- the sum of energy being dissipated as heat
in each individual component
- the increase in energy being stored in
components such as capacitors, inductors
and batteries, minus any stored energy
being returned from components such as
capacitors, inductors and batteries
- energy being emitted such as
- light (e.g. display)
- sound (e.g. fans, speakers)
- RF (e.g. Wifi antennas, RFI)
- etc.

So yes, the phrase "conservation of power" is
appropriately descriptive and follows from
conservation of energy.

If not, why do you
require such for the example under discussion?

I require it for both.

The correct equation for adding the powers above is?

Prs(t) = Pf.g(t) + Pr.g(t) +/- 2*SQRT[Pf.g(t)*Pr.g(t)]

The last term is the interference term. The sign of
the interference term is negative if Vf.g(t) and
Vr.g(t) are out of phase. The sign of the interference
term is positive if Vf.g(t) and Vr.g(t) are in phase.
Vf.g(t) and Vr.g(t) are in phase for half of the cycle.
Vf.g(t) and Vr.g(t) are out of phase for the other half
of the cycle. The "excess" energy from the destructive
interference is dissipated in the source resistor as
constructive interference after being delayed by 90
degrees.

Where is "cos(theta)" in this?
And what "theta" is to be used?
Is it the same theta that was used to conclude that
this was a "no interference" example?
See "A Simple Voltage Source - No Interference" at
http://www.w5dxp.com/intfr.htm

So the plus/minus in the equation aboves means that
for part of the cycle we should add and part of the
cycle we should subtract.
This equation is ambiguous and is therefore incomplete
since it does not tell us when we should add and when
we should subtract.
Could you provide a mathematically precise description
of when we should do each?

Where is this destructive interference energy stored
while waiting to be dissipated constructively later?
If it is in a capacitance, which one? Does the
voltage on the capacitance increase appropriately
to account for the energy being stored?
Similarly if it is stored in an inductance.

...Keith