I know that I'm missing something but I don't know what I'm missing.
Power factor is the ratio between real power and apparent power. So, I will get the equations of real power and apparent power then, I will divide them.
I'm going to start with real power which is the average power. The average of a sine wave is always zero so, I will rectify it then calculate the average.
Second, I will calculate the apparent power. We can get it by multiplying the root mean square values of voltage and current.
After calculating the real power and apparent power, I'm going to get the power factor and the result is surprising!! Would you tell me where the mistake is, Please?
Thank you very much,
Best Answer
if you assume \$i(t) = Ipk \cdot\sin(t)\$ and \$v(t)=Vpk\cdot\cos(t)\$ i.e. \$90^o\$ out of phase then Average power is
\$\frac{1}{2\cdot\ \pi}\int_{-\pi}^{\pi} \left( Vpk \cdot Ipk \cdot \sin(\theta) \cdot \cos(\theta) \right) d \theta = 0\$
That is zero power, so no power factor is not fixed for sine waves you have to take into account the relative phases of the voltage and current.
In general real power is: \$ Vrms \cdot Irms \cdot \cos(\theta) \$ where \$\theta\$ is the phase difference between voltage and current.