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I'm not sure what you are saying. Is my equation wrong?

OK
you said V = IR
I am saying V = IZ
Z is as described above
make sense?

I know what a phasor diagram is but I don't know how to use it in this instance.

sounds good.
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I am assuming that they are connected in series.

Then work under that assumption, what did you get for \[X _{L}\]\[X _{C}\]??

The inductive reactance at the 1000 Hz source frequency would be around 188.5 Ohms

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According to my calculator R=236.56 Ohm, @eabollich What did you get for R?

PF =Real Power (PW)/Apparent Power (PA
PF = (.4^2)(236.5)/(120)(.4)
PF = 37.84/48 = 0.789

Are you saying that a lower number is more power factor?

Great! I think I understand it better now!