Impedance Function

Discussion in 'Homework Help' started by cramerica, Mar 15, 2011.

  1. cramerica

    Thread Starter New Member

    Mar 15, 2011
    3
    0
    Hello all.

    I am a lowly mechanical engineer, studying for an equivalence exam through my employer (a regulated utility operator), to allow me to bid positions on the electric side of the house. I am currently a gas engineer.

    I already failed my first attempt at the test, due in no small part to questions like this:

    "Given an impedance function [Z=60<pi/3], determine the values of the parallel elements".

    Now, I have no problem with vector math, or calculating total impedance from given values of R, C and L. But I think even a mechanical engineer can see that this problem is indeterminant. Am I right? Even if I assume a voltage, say 100V<0, I still have too many unknowns.

    Isn't there an infinite number of possible combinations to result in any arbitrary total Z?

    I apologize if this question seems beyond basic - but I've been wracking my brain trying to see a solution! Any help would be greatly appreciated.
     
  2. someonesdad

    Senior Member

    Jul 7, 2009
    1,585
    141
    I'm not an EE, but I did take a networks class back in the 60's. I hope my info isn't out of date... :p

    If one assumes that the impedance is 60 ohms with an angle of 60 degrees and they're asking for the parallel components, then I'd assume this is an inductor in parallel with a resistor. Should be straightforward to resolve into the real and reactive components...
     
  3. Ron H

    AAC Fanatic!

    Apr 14, 2005
    7,050
    657
    It would be handy to know the frequency...
     
  4. Papabravo

    Expert

    Feb 24, 2006
    10,140
    1,789
    First attempt failed -- see below
     
    Last edited: Mar 15, 2011
  5. cramerica

    Thread Starter New Member

    Mar 15, 2011
    3
    0
    Thanks for the replies. I like the idea of assuming, since the circuit is net-inductive, that it could be resolved into an inductor and a resistor. Trying to model it as a capacitor and inductor inherently opens Pandora's box - as Ron H said, what is the frequency?

    To quote the ProTrain curriculum: "Reverse design a circuit from a total impedance to show circuit basic elements".

    It's also entirely possible the question was incorrectly written - after all, it came from the engineering offices of a utility company...

    Thanks again - any other input is appreciated.
     
  6. Papabravo

    Expert

    Feb 24, 2006
    10,140
    1,789
    This problem has two steps. The first step is to find the series resistance and reactance that give you the required impedance.
    Code ( (Unknown Language)):
    1.  
    2. Rs = 60 * cos(π/3) = 30 Ω
    3.  
    4. Xs = 60 * sin(π/3) = 60 * (√3/2) ≈ 51.96 Ω
    5.  
    Now we need to apply a transformation that will give us the values for an equivalent parallel circuit.
    Code ( (Unknown Language)):
    1.  
    2. Compute Q:
    3. Q = Xs/Rs = 51.96 / 30 ≈ 1.732
    4. Compute Rp:
    5. Rp = (Q^2 + 1)*Rs = 4 * 30 = 120 Ω
    6. Xp = Rp / Q = 69.28 Ω
    7.  
    We can check this answer by computing the (complex) impedance of Rp in parallel with Xp as follows:
    Code ( (Unknown Language)):
    1.  
    2. Zt = (Rp)(jXp) / (Rp + jXp)  : where j is the imaginary unit
    3. Zt = (120)(69.28j) / (120 + j69.28)
    4. Zt = (j8313.6)(120 - j69.28) / (120 + j69.28)(120 - j69.28)
    5. Zt = (575966.208 + j997632) / (14400 + 4799.7184)
    6. Zt = 30 + j51.96
    7.  
    8. QED
    9.  
    If we also know the frequency of interest we can compute the implied inductance.
     
  7. cramerica

    Thread Starter New Member

    Mar 15, 2011
    3
    0
    Thanks PapaBravo. I think I understand - but you also have to work under the assumption that the 'circuit elements' in question are an inductor and resistor?

    Thanks!
     
  8. Ron H

    AAC Fanatic!

    Apr 14, 2005
    7,050
    657
    A picture is worth a few equations...
    I'm guessing the frequency is 60Hz.
    60 ohms at 60 degrees at 60Hz.
     
  9. justtrying

    Active Member

    Mar 9, 2011
    329
    349
    I don't think it is necessary to assume any frequencies, but to work with what is given - so the angle will tell you whether the combination is an inductor plus resistor or capacitor plus resistor and you need that information to solve the problem. As per diagram, its all in the angles, the rest is just math.
     
  10. Papabravo

    Expert

    Feb 24, 2006
    10,140
    1,789
    There is no assumption here. Since the impedance is in quadrant 1, the only possible series circuit, with two elements, is a resistor and an inductor. This leads to the parallel circuit of a resistor and an inductor. It is true that at sufficiently high frequencies that capacitors look like inductors and inductors look like capacitors, bat that is a story for another time.
     
    Last edited: Mar 16, 2011
  11. Ron H

    AAC Fanatic!

    Apr 14, 2005
    7,050
    657
    Serial RLC and parallel RLC circuits can be designed which will meet the criterion Z=60<60°.
     
  12. Papabravo

    Expert

    Feb 24, 2006
    10,140
    1,789
    Yes they can because the inductive and capacitive reactances will cancel each other since they are of the opposite sign. Ultimately though the resulting reactance will look like the appropriate inductor alone. This may be what the OP was refering to when he wondered if there wasn't a multiplicty of possible solution. The one with only two components certainly represents the simplest solution.
     
Loading...