What is the Impedance Value for a Circuit with Given Parameters?

[justadaftspark]

Homework Statement

Find Z R=10Ω
Vs=120v
(PF)=0.72 Lagging

Homework Equations

I=P/Vs(PF)
Z=Vs/I

The Attempt at a Solution

I have I=P/Vs(PF) and transpose for I to get 4.34A
Then to find Z Z=Vs/I which gives 27.65ohm
When I put this back into (PF)=R/Z to confirm i don't get the right answer


Any help would be great

 

[gneill]

What value do you use for P in your equations?

As an alternative, consider that the power factor is the cosine of the angle of the apparent power phasor, and that the impedance will have the same angle. Here the PF is 0.72 and is said to be lagging, which means the impedance will appear to have an inductive reactance component. You can draw the triangle for the impedance:

You should be able to write an expression to relate XL to given cosine of the angle θ.

 

[justadaftspark]

Thanks for getting back, so

arcos( 0.72 ) = 43.95deg
Tanθ o/a
Tan 43.95 * XL/10 transpose for XL
XL = Tan 43.95*10 = 9.64 ohm
using trig Z^2 = R^2 + XL^2
= Drum roll..... 13.89 ohm

Does this seem closer to the mark? it works when i put it into a known equation

P was from a earlier part of the question which i used to find I

Thank you, its much appriciated

 

[gneill]

Looks good!

 

[justadaftspark]

Awesome, Thanks a lot