The area of the curve under the product |V|*|I| is the real power. You can draw two sine waves with the two separated by 90deg, then multiply it graphically, so you get a picture of it.
Not quite, the area under the v*i curve represents energy. You must divide by time to obtain average, real power.
If you integrate magnitudes, I don?t know what you get.
In your example, we see alternate lobes of positive and negative power which average out to zero as we would expect.
The product at any given instant is zero (assuming your drawing is good).
Not so again. The vi product is zero only when either v or i is zero. The average over a period is zero in your example.
Vrms * Irms (each computed separately, then multiplied) gives apparent power. Since they're not multiplied together simultaneously, you'll see that the phase shift does not affect apparent power.
Well yes, that is the idea.
What you're describing as efficiency is W/VA which is power factor.
Oops again! W carries the units of energy while the Vrms*Irms product carries the units of power. PF is dimensionless.
What I am saying is the average value of v*i is real, not apparent, power into the device since the positive and negative reactive powers cancel in the integration. Call this value Pi, and call the power to the load, Po. Then,
Po/Pi = efficiency, not PF.
On third thought, I no longer believe you can integrate the vi product to obtain apparent power. You can however write,
Pa = Vrms*Irms
But I am not sure what the advantage is with a strongly non-linear load..