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Homework Help: 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.


    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


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    Science Advisor
    Homework Helper

    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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