Calculate RLC Circuit Values: R1, R2, and Xl | Step-by-Step Guide

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Discussion Overview

The discussion revolves around calculating the values of resistors and inductive reactance in an RLC circuit. Participants explore the relationships between voltage, current, resistance, and reactance, while addressing the lack of certain parameters such as frequency and line voltage.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Participants present an RLC circuit with specified values for resistors, reactance, and power, but express uncertainty about how to proceed without the frequency of the source.
  • Some participants suggest assuming a frequency of 60 Hz to facilitate calculations.
  • There is a clarification that the circuit is connected in series, which is noted by one participant.
  • One participant emphasizes the need for additional information, such as line voltage or power factor, to progress further in solving the problem.
  • Another participant provides a method for approaching the problem by suggesting to draw a schematic and express voltages in terms of current, while asserting that the line frequency is not necessary for the calculations.
  • One participant attempts to apply Kirchhoff's Voltage Law (KVL) but expresses confusion about their approach and the resulting equations.
  • There is a discussion about distinguishing between resistance and reactance by incorporating angles into the equations, with a request for further clarification on this point.
  • Another participant explains how to represent the voltage across an inductor and capacitor using complex notation, indicating the need for vector addition of voltages.

Areas of Agreement / Disagreement

Participants do not reach a consensus on how to proceed due to the lack of certain parameters and differing approaches to the problem. Multiple competing views on the methodology and necessary information remain present.

Contextual Notes

The discussion highlights limitations such as missing assumptions about frequency and power factor, as well as the need for clarification on the application of KVL and the representation of reactance.

ragamuffin_8
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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?
 
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ragamuffin_8 said:

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?
 
jegues said:
Is this parallel or series RLC?

I forgot to mention, this is connected in SERIES. I'm sorry
 
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.
 
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?
 
ragamuffin_8 said:
I'm sorry I forgot to mention the line voltage. 100 Vac.
Forgot?! :frown: :mad:

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!
 
NascentOxygen said:
Forgot?! :frown: :mad:



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 + IXL

but:
P = VR2I
VR2 = 50/I

P = I2XL
XL = 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 said:
Forgot?! :frown: :mad:



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 + IXL

but:
P = VR2I
VR2 = 50/I

P = I2XL
XL = 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 said:
My attempt:

100 = IR1 + IXc + IR2 + IXL
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 = VR2I
VR2 = 50/I
yes

P = I2XL
XL = 100/I2
What law did you rely on here?
 
  • #10
NascentOxygen said:
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?
 
  • #11
We write VL 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.
 

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