Electronic – What gets wrong when I average AC voltage and current to get power

accurrentpowervoltage

Power is half the product of peak AC voltage and current (or product of its RMS voltage and current). But why is it wrong when I average first the voltage and current before getting the power?

I get that the average of AC voltage and current is zero. But what is then the use of the formula:

V(ave) = 2V/pi
AND
I(ave) = 2I/pi

This is the formula for averaging sinusoidal 360 degree voltage and current, right? Why can't I average the voltage and current to find power?

Best Answer

You have made a false math assumption. You have caught from the wind "taking average and multiplication are distributive". That's not true as you have already found. You can check it with two voltage samples U1, U2 and two current samples I1, I2

The average power is (U1*I1 + U2*I2)/2. There's no way to reduce this to ((U1+U2)/2)*((I1+I2)/2)

You must calculate P(t)=U(t)*I(t). That's the momentary power. The average power is the average of U(t)*I(t) calculated over the period of interest. With sinusoidal current and voltage we calculate the average over one cycle.