> The principle is not a difficult one.  It is simply a situation where
> the RMS power exceeds the average power.

Oh no, here we go again with voodoo physics and math!

RMS power is not a meaningful concept.  RMS voltage and current do make
sense, but RMS power, while mathematically possible to compute, has
little relevance to real systems.  RMS voltage and current are useful
precisely because they can determine the *average* power into a resistor.

> In your example, the average power is:
>
> (24*.5)^2/R

Unfortunately you didn't define your example.  I assume the lamp is being
driven with a 0V to 24V square wave.  In that case this formula is wrong.
During the 24V phase the power is:

  P = 24V**2 / R

During the 0V phase the power 0.  The average power is therefore:

  p = 1/2 * 24V**2 / R

which is twice the result of your formula.

> The RMS power for a 50% duty cycle like you propose is
>
> Prms = (RMS voltage)^2/R

No, that is the *average* power.

> RMS voltage = sqrt(V^2*Duty)
> So,
>
> V^2*.5/R = 24^2*.5/R

This is the correct expression for the average power.

> Now, the comparison between average power and RMS power for this case
> is then:
>
> (24*.5)^2 : 24^2*.5
> .5^2 : .5
> .25 : .5
> 1 : 2

This is total nonsense.  Your calculation of "RMS power" is actually average
power, and RMS power is a flawed concept in the first place.

> So you double your effective power.

No, you don't.

> By the same principle, for any
> rectangular wave that goes from 0V to some other voltage, the average
> power can be compared to the RMS power by a ratio of
>
> duty% : 1
> or
> 1 : 1/(duty%)

Nonsense perpetuated.  Going deeper into this gibberish is a waste of time.

> ...

> Now I'll be told to re-take freshman physics, I'm sure.

Basic high school algebra should do in this case.

People will probably say I'm being hard on you, but I don't think so.  I
wouldn't have a problem with this sort of misconception if you weren't
spouting it as fact.  If you are going to profess some knowledge as
definative fact, some people may take it as such.  That's why I just felt
obligated to waste 5 minutes of my life debunking this BS.  If it were left
unchallanged, some newbie might legitmately think it correct.  It's no sin
if math and physics aren't your thing, but then you should label any
assertions properly, like "I'm not sure, but maybe it...".


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