I cannot seem to wrap my head around this problem...

If the voltage across and the current through the series combination of a resistance and an unknown energy-storage (presumably an inductor) element are:

v=200cos(10^2t + 60°)
i=5.547cos(10^2t + 93.96°)

then find the resistance as well as the unknown element

Any help would be much appreciated.

 

a hint: you could use phasors/polar coordinates to solve this problem.

 

Yeah. I am just learning about them now. I have been stuck on this problem for awhile....

So, I have two unknowns (R and L)

I know that Z=R+jwL
I know that V/I=Z

I just cannot seem to come up with two equations that will allow me to solve this...

any stronger hints that you can help with??

 

also, I know:

This is a simple voltage divider circuit....
hence

Vr= R/(r+jwL)Vs where Vs is 200arg(60deg)

If I found Vr I could use that to find R by dividing by the current i. This is true because the circuit is in series...

But again... I need values for R and L so I am thinking this is the wrong way to go...

 

You were on the right track with Z = V/I. If you perform the phasor division you can obtain Z, then convert that into rectangular complex to find the values that you are looking for.

Phasor: Z = Zmag<(argZ)

Rectangular: Z = R + jwL

 

Convert it to the phasor and Use R= V/ I and make some algebra in complex numbers , its pretty easy

Regards

Lazukan