Finding R2 and Xl in an RLC circuit with given power and reactive power

[ragamuffin_8]

Homework Statement

An RLC circuits consists of R1 a 10-ohm resistor, R2 a resistor that takes 50 W, C1 a capacitor with 5-ohm reactance, and L1 an inductor that takes 100 var. Find the value of R1, R2, and Xl (inductive reactance).

Homework Equations

P = (I^2)R
Xc = 1/(2∏fC)
Xl = 2∏fL
Z = √(R^2 + XeqL^2)

The Attempt at a Solution

I tried equating the currents but I don't know what to do next. I tried to solve for the equivalent impedance but without the frequency of the source, my efforts were futile. Perhaps I could assume a frequency of 60 Hz?

 

[jegues]

Homework Statement

An RLC circuits consists of R1 a 10-ohm resistor, R2 a resistor that takes 50 W, C1 a capacitor with 5-ohm reactance, and L1 an inductor that takes 100 var. Find the value of R1, R2, and Xl (inductive reactance).

Homework Equations

P = (I^2)R
Xc = 1/(2∏fC)
Xl = 2∏fL
Z = √(R^2 + XeqL^2)

The Attempt at a Solution

I tried equating the currents but I don't know what to do next. I tried to solve for the equivalent impedance but without the frequency of the source, my efforts were futile. Perhaps I could assume a frequency of 60 Hz?

Is this parallel or series RLC?

 

[ragamuffin_8]

Is this parallel or series RLC?

I forgot to mention, this is connected in SERIES. I'm sorry

 

[NascentOxygen]

I think we need another clue, such as the line voltage, or that the load has unity power factor.

By assuming a current, I, in all the elements I can find the voltage across each in terms of that I, but that's as far as I can get without more information.

 

[ragamuffin_8]

I'm sorry I forgot to mention the line voltage. 100 Vac. But the frequency was not given, how do I start attacking this problem?

 

[NascentOxygen]

I'm sorry I forgot to mention the line voltage. 100 Vac.

Forgot?!

how do I start attacking this problem?

Start by drawing a large schematic, and mark on the quantities you are given for each element.

Assume a branch current, I, and using what you are told about each element, determine the voltage across that particular element in terms of I. The only unknown on the right-hand side of each equation will be I, any other terms on the right-hand side will be known numbers that you can work out from the information provided.

You do not need to know the line frequency.

Good luck!

 

[ragamuffin_8]

Forgot?!



Start by drawing a large schematic, and mark on the quantities you are given for each element.

Assume a branch current, I, and using what you are told about each element, determine the voltage across that particular element in terms of I. The only unknown on the right-hand side of each equation will be I, any other terms on the right-hand side will be known numbers that you can work out from the information provided.

You do not need to know the line frequency.

Good luck!

Thanks Sir NascentOxygen!

I was not thinking of KVL that's why I'm having a hard time in this problem. :shy: I'm sorry

My attempt:

100 V = IR₁ + IXc + IR₂ + IX^L

but:
P = V_R2I
V_R2 = 50/I

P = I²X_L
X_L = 100/I²

so:

100 = 10I + 5I + 50/I + 100/I

Solving for I, I got two values I = 4.39 and I = 2.28, which value should I choose?

 

[ragamuffin_8]

Forgot?!



Start by drawing a large schematic, and mark on the quantities you are given for each element.

Assume a branch current, I, and using what you are told about each element, determine the voltage across that particular element in terms of I. The only unknown on the right-hand side of each equation will be I, any other terms on the right-hand side will be known numbers that you can work out from the information provided.

You do not need to know the line frequency.

Good luck!

Thanks Sir NascentOxygen!

I was not thinking of KVL that's why I'm having a hard time in this problem. :shy: I'm sorry

My attempt:

100 = IR₁ + IXc + IR₂ + IX_L

but:
P = V_R2I
V_R2 = 50/I

P = I²X_L
X_L = 100/I²

so:

100 = 10I + 5I + 50/I + 100/I

Solving for I, I got two values I = 4.39 and I = 2.28, which value should I choose?

 

[NascentOxygen]

My attempt:

100 = IR₁ + IXc + IR₂ + IX_L

That's a good start, but we distinguish resistance from reactance by associating an angle with reactance. So the equation above needs to be fixed to include this. There are a couple of ways to represent angle, use whichever you like to correct the above equation.

but:
P = V_R2I
V_R2 = 50/I

yes

P = I²X_L
X_L = 100/I²

What law did you rely on here?

 

[ragamuffin_8]

That's a good start, but we distinguish resistance from reactance by associating an angle with reactance. So the equation above needs to be fixed to include this. There are a couple of ways to represent angle, use whichever you like to correct the above equation.

I don't quite understand sir. Would you please elaborate?

 

[NascentOxygen]

We write V_L for an inductor as ${\color{Blue} {j I X_{L}}} \text{ or as } {\color{Blue}{IX_{L} \angle 90^{\circ}}}\text{ where } X_{L}$ is the magnitude of the inductive reactance.

And something similar for the voltage across a capacitor. Then addition of voltages takes the form of addition of vectors.