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Calculating impedance in complex number and polar form

  1. Oct 26, 2009 #1
    1. The problem statement, all variables and given/known data
    I have a motor with a full load output rating of 2.8 kW with an effciency off 70% and at 80% of full load runs with a Power Factor of 0.8 lagging.

    A second motor has afull load output of 4.2kW with an effciency of 85% and at 80% of full load runs with a PF of 0.75 lagging.

    They are fed by a generator which has an output resistance of 0.2 ohms and an output inductance of 1mH. 400volts.

    I am stuck trying to answer - In complex number form and polar form calculate the overall impedance for the two motors in parallel. It appears to me that I have no value for the jX portion of the complex number so does that mean it is 0 or should I already know where this should have been calculated from. Our previous class examples have given values to calculate the inductive or capacitive values.

    However our notes also state that a current lagging at phase angle to voltage then I in complex number form can be expressed as a - jb and v +j0. Where do a and b come from?

    Now it may well be I am thick but I cannot see for the life of me where these missing pieces come from and no information I have read over the last 12 hours of study has enlightened me so some assistance would be gratefully received.

    Many thanks in advance.

    Dumbkiwi.





    2. Relevant equations



    3. The attempt at a solution
    Had I the information I seek I may well have supplied this bit.
     
  2. jcsd
  3. Oct 26, 2009 #2

    tiny-tim

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    Hi dumbkiwi! :smile:

    The "jX portion" (of R + jX) has been given to you, since you can work it out from the power factor.

    The power factor is the cosφ in the polar form Z = |Z|cosφ + j|Z|sinφ.

    In other words, R= |Z|cosφ, and X = |Z|sinφ. :wink:

    (and be careful of the + or - sign for sinφ, which depends on whether the current or the voltage is lagging)
     
  4. Oct 28, 2009 #3
    Hi Tiny Tim,

    Ah ha - I was thinking thats all it could be but was finding it difficult to find confirmation but easy to pull my hair out.

    Lets hope I can now get this kicked into touch.

    Many thanks.

    Regards Dumbkiwi.
     
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