I'm not sure if that is a passive agressive answer... Anyway if this is a genuine question, if I'm correct, for a sine waveform :
Peak Voltage = ?2.VRMS
Peak-to-peak Voltage = 2.Peak Voltage = 2.?2.VRMS
Yes, but when you cut half of the sine wave off, it's no longer a sine wave. The RMS voltage of half of a sine wave is not half of the RMS voltage of a full sine wave, it's 70.7% of it.
For a sine wave:
Vrms = Vpeak*0.707
For a sine wave that has the bottom half cut off:
Vrms = Vpeak*0.5
Since power is proportional to V^2, this means you're cutting the RMS voltage by 70.7%, and cutting the power in half, as DmitryL said.
Sorry, I didn't check if my copy/paste of the square root symbol worked, and it didn't! My previous (unedited) message was indeed weird.
Now, you mention the .707 figure, which equals 1/(2
1/2) a.k.a. the reciprocal of the square root of 2. So, V
RMS = V
PEAK x 2
-1/2. I get that, no prob.
But you say that if you cut the lower half (or any half actually, once it's squared we get absolute values), V
RMS = V
PEAK/2.
I don't get it. If you cut a sine wave in half, both have the same RMS value, since as soon as you use the square function, both are positive. Therefore the square roots of the means of these two halves are equal. So, I don't see why the RMS half of the sine for a full period is not half the RMS value of a full sie wave, therefore V
PEAK/2 x 2
-1/2.
Since the load can be reduced to a simple resistance (no power factor), RMS power is directly proportionnal to V
RMS. Therefore halving voltage halves power.