Quick Question about power factor angle

[FrogPad]

I just took an exam, and one of the questions had a load with a power factor that was leading. ALL of our examples have dealt with LAGGING power factors, so I was unsure about determining the angle.

So for example)
Find the power factor angle of the following load (load 1):

$$pf_{load1}=0.9\,\,\,LEADING$$

would the angle be negative? like...
$$\theta_{z\,\,load1}=-\cos^{-1}(0.9)$$

 

[quantumdude]

Hi there,

The answer to your question is "yes". The power factor is defined as: $pf=\cos(\theta_V-\theta_I)$. The terms "leading" and "lagging" pertain to the relationship that the current has with respect to the voltage.

So when you have $\theta_V-\theta_I>0$, the current lags the voltage and the power factor is said to be "lagging". When the current leads the voltage then we have $\theta_I>\theta_V$, which of course implies that the argument of the cosine function, $\theta_V-\theta_I$, is negative.

 

[FrogPad]

Thank you for the thorough reply. I really didn't want to just memorize that I should toss a negative sign in there. Thanks for the background