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Hard RLC Series Circuit

  1. Dec 21, 2011 #1
    1. The problem statement, all variables and given/known data

    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).


    2. Relevant equations

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

    3. 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?
     
    Last edited: Dec 21, 2011
  2. jcsd
  3. Dec 21, 2011 #2
    Is this parallel or series RLC?
     
  4. Dec 21, 2011 #3
    I forgot to mention, this is connected in SERIES. I'm sorry
     
  5. Dec 23, 2011 #4

    NascentOxygen

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    Staff: Mentor

    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.
     
  6. Dec 24, 2011 #5
    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?
     
  7. Dec 24, 2011 #6

    NascentOxygen

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    Staff: Mentor

    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!
     
  8. Dec 24, 2011 #7

    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?
     
  9. Dec 24, 2011 #8

    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?
     
  10. Dec 25, 2011 #9

    NascentOxygen

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    Staff: Mentor

    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.


    yes

    What law did you rely on here?
     
  11. Dec 26, 2011 #10
    I don't quite understand sir. Would you please elaborate?
     
  12. Dec 26, 2011 #11

    NascentOxygen

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    Staff: Mentor

    We write VL for an inductor as [itex]{\color{Blue} {j I X_{L}}} \text{ or as } {\color{Blue}{IX_{L} \angle 90^{\circ}}}\text{ where } X_{L} [/itex] 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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