DAMMIT! I just typed all this crap out and the forum failed me... attempt #2
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Assume:
V = 12V
I = 1A
P = 12W
For Average power,
Vrms = 12 ^2 ...divided by 2...and then take the square root of that
Vrms = 8.49V
Irms = 1^2 ...divided by 2 and then teh square root of that
Irms = .707A
Assuming it's purely resistive so the phase difference is zero, then the power factor becomes 1...(cos(0-0) = 1)
Average Power = Vrms * Irms * cos( phase angle of voltage - phase angle of current)
Average Power = Vrms * Irms * 1 = 8.49 * .707
Average Power = 6W
Using the idea of RMS Power,
Prms = 12W ^ 2...divided by 2...and take the square root of that...
Prms = 8.49W
The two obviously aren't equal, and Prms is no good because it doesn't rely on Vrms and Irms. But like you said above, the higher the power rating, the more power you can put into the system and the better your gain will be, (ie the louder you can play your music).
But the way that car audio companies use the term RMS Power, then mean it to be the average power when a single tone is presented which as you can see above is completely wrong. Giving the consumer the belief they can get more power out of the system than it can really handle
Oh yeah one other thing, this is for AC analysis, for DC anlysis, if you had a constant DC value, then average, peak and RMS values would all be equal to each other.
-Derek