Finding X of L for an inductor

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LeatherNeck

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I’m very lost with this problem. I thought I knew this stuff. This is a exercise problem.
What is the value XL in the circuit. The absolute value of Es is 100V. It says, first find Z, noting E and I are given. Next Find X, then XL.
Where does X come in? I’m just drawing a blank on this one.View attachment CIE 5231-2.pdf
 

XL conventionally is inductive reactance.
Basic formula:

XL = 2 * Pi * f * L

This does not necessarily pass the same current as a pure ohmic resistance. To be accurate you need to make the adjustment by drawing the parallelogram angles, which has to do with phase.
 

Hi,

1) Z = E/I = (100<alpha)/(2<0) = 50<alpha
2) X = sqrt (Z^2 - R^2) --- complete this one yourself. I believe alpha is 90deg so take note.
3) X = XL-XC... XL = X+XC (complete this one too)
 

Yes, thank you but I knew that one. However they do not mention any frequency in this problem.
But I appreciate your response. I believe the next response from Akanimo is what I was missing. But really, thank you so much for replying.
 

Akanimo said:
Hi,

1) Z = E/I = (100<alpha)/(2<0) = 50<alpha
2) X = sqrt (Z^2 - R^2) --- complete this one yourself. I believe alpha is 90deg so take note.
3) X = XL-XC... XL = X+XC (complete this one too)
Click to expand...

Not there yet. Still confused.

 

Not there yet. Still confused...
Click to expand...

You are not alone.

Your calculation of ZL=20+j20 is correct.

The imaginary part is the XL; The inductor has a DC resistance component of 20ohm.

The question (or the problem) is badly set; the capacitor is ideal but the inductor is not.
 

Z = Zm<alpha = 50<alpha
Zm = sqrt(R^2 +X^2)
X^2 = sqrt(Zm^2 - R^2) = sqrt(2500-900) = 24.49 ohms

X=XL-XC ... but in this case, XC is already given as negative so we'll use:
X = XL+XC
Therefore, 24.4989 = XL-20
XL = 44.4989 ohm
 

There is a little mistake in the Akanimo answer: sqrt(2500-900)=40 ohm, then XL=60 ohm

Furthermore if you want to calculate alfa, we know that tg(alfa)=im(Z)/real(Z), that is tg(alfa)=X/R.
In our case alfa=atan(40/30)=53.1 deg.
 

Yes albbg, you are right. I made mistakes with the computation. There is even another one in line 3 of post #7. It should have been X = sqrt (2500-900)... but I wrote X^2 = sqrt (2500-900)... by mistake.

I'm sorry about that.
 

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