# Power factor angle (leading)



## mofet (Oct 2, 2011)

Hi

I was reading Guru's book on Electric machinery (page 38, 2nd edition) and I stuck here in this:

"The sign of the power factor angle teta can be easily determined from

the type of load. The power factor angle teta must be negative for an inductive load (R + jX) and positive for a capacitive load (R - jX)."

Well, Sadiku's book (fundamentals of electric circuits) tells the opposite...

So when the current leads the voltage then we have θI&gt;θV, which of course implies that the argument of the cosine function, θV−θI, is negative.... (leading pf is seen for capacitive loads...) So the power factor angle for capacitive load should be NEGATIVE and not positive as Guru tells...

I wonder why Guru wrote that power factor angle is positive for capacitive load... well I'm seeing this image...

http://oee.nrcan.gc.ca/industrial/eq.....;/figure-23.jpg (as Sadiku shows in his book) and it is clear that phi (the angle of power factor) is positive for inductive loads , and negative for capacitive loads!

I got confused.. hope you can help to solve this apparent dilemma..

Thanks in advance!


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## mofet (Oct 2, 2011)

NOTE: I used to think that the terms "leading" and "lagging" pertain to the relationship that the current has with respect to the voltage... in the graph I presented... they seem not use this relationship as PF of capacitive loads is said to be lagging?!

This graph - http://www.nepsi.com/images/CDIA150.gif - shows the one that Sadiku uses...


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## DK PE (Oct 2, 2011)

mofet said:


> Hi
> 
> I was reading Guru's book on Electric machinery (page 38, 2nd edition) and I stuck here in this:
> 
> ...


I don't have the Guru reference you mentioned and also can not get your link in first post to work but very simply, the power factor angle is the angle which the voltage phasor leads the current phasor. In a series RL circuit for example, the current lags and therefore (thetaV - thetai) is positive.

Edit --&gt; We were posting on top of each other. I think you may be confusing the power triangle and the voltage and current phasors. The elements of a power triangle are NOT phasors and by convention, reactive power Q absorbed by a circuit (i.e. an inductor) is considered positive and is drawn UPWARD in the power triangle. The reference by Wildi is good one if you can locate a copy. The link in your second post is correct.


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## benbo (Oct 2, 2011)

> The sign of the power factor angle * teta * can be easily determined fromthe type of load


Yes, the angle of the "tetas" do vary according to the load.

Sorry, just cracked me up.

Carry on with the serious discussion.


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## mofet (Oct 2, 2011)

benbo said:


> > The sign of the power factor angle * teta * can be easily determined fromthe type of load
> 
> 
> Yes, the angle of the "tetas" do vary according to the load.
> ...



I see that you know the meaning of "tetas". arty-smiley-048:

Yes, it was a typo and it should be "theta".


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## mofet (Oct 2, 2011)

thanks DK. It really helped.


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