The potential difference across an inductor

[Asmaa Mohammad]

Homework Statement

In a circuit, a capacitor (Xc=30Ω, R=44Ω) and an inductor (Xl=90Ω, R=36Ω) are connected in series with an AC source (ƒ=60Hz, V=200V). Determine:
1-current intensity
2-the voltage across every component in the circuit.

Homework Equations

Z=√R²+(Xl-Xc) Where: Z is the impedance, Xl is the inductive reactance, and Xc is the capacitive reactance.
I=V/Z

The Attempt at a Solution

That is how I solved the problem:

And that is how my textbook solved it:

I get confused when I saw it, because I don't know why it consider the resistance of the capacitor to be an independant resistance while it didn't do with the resistance of the inductor, and determined the equivalent impedance of it, and consequently, it determined the potential difference across the inductor as 193.86V and not 180V as I did.
Could someone explain it for me?

 

[cnh1995]

This is how a lossy capacitor is represented:

But then Z is not 100 ohm as both the resistances are no longer in series.
Perhaps there is a mistake in the book's solution.

 

[gneill]

This is how a lossy capacitor is represented:
View attachment 112591But then Z is not 100 ohm as both the resistances are no longer in series.
Perhaps there is a mistake in the book's solution.

I've a feeling that they're not looking to introduce the complication of a parallel RC component. I'd judge from the solution method being used (dealing with reactances algebraically) that complex impedance hasn't yet been introduced in the course, and the circuit analysis would be fairly nasty and certainly not as simple as what the textbook indicates even allowing for an error on their part. But I do agree that the textbook solution is wrong in either case.

@Asmaa Mohammad is right to question the book's discrepancy in dealing with the resistance and reactance components differently for the two components. For the apparent course level I would be inclined to interpret the circuit as follows:

and to treat the capacitor and inductor in the same fashion mathematically.

 

[Asmaa Mohammad]

This is how a lossy capacitor is represented:
View attachment 112591But then Z is not 100 ohm as both the resistances are no longer in series.
Perhaps there is a mistake in the book's solution.

Actually, I didn't have an interpretation of a lossy capacitor in my assignment, I don't know why there are excerecises about it in my textbook, may be for this the book treated its resistance as a separate resistance connected in series with the inductor and the capacitor.

@Asmaa Mohammad is right to question the book's discrepancy in dealing with the resistance and reactance components differently for the two components. For the apparent course level I would be inclined to interpret the circuit as follows:

and to treat the capacitor and inductor in the same fashion mathematically.

Gneill, still I don't know if my answer is correct or not?

 

[cnh1995]

Gneill, still I don't know if my answer is correct or not?

No. You should use your book's approach. Their calculation of inductor voltage is correct and they should have taken the 44 ohm resistor in series with the capacitive reactance. See gneill's diagram.
That's what I meant when I said,

Perhaps there is a mistake in the book's solution.

 

[gneill]

Gneill, still I don't know if my answer is correct or not?

I would say it is not correct. I feel that the components of the circuit are the non-ideal capacitor and inductor and that their internal resistance can't be separated as separate components.

The textbook's approach for the inductor is valid and they have obtained a correct result for it. My advice is to do the same thing for the capacitor.

When you submit your work for marking you might want to include a brief argument for not treating the resistance as separate components when judging the voltage across the "real" components.

 

[Asmaa Mohammad]

Their calculation of inductor voltage is correct and they should have taken the 44 ohm resistor in series with the capacitance

I would say it is not correct. I feel that the components of the circuit are the non-ideal capacitor and inductor and that their internal resistance can't be separated as separate components.

The textbook's approach for the inductor is valid and they have obtained a correct result for it. My advice is to do the same thing for the capacitor.

When you submit your work for marking you might want to include a brief argument for not treating the resistance as separate components when judging the voltage across the "real" components.

Ok, guys, is this answer correct?

 

[cnh1995]

Ok, guys, is this answer correct?

Looks good!

 

[Asmaa Mohammad]

Looks good!

Thank you, cnh1995!

 

[cnh1995]

Thank you, cnh1995!

You're welcome!