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DC Shunt Motor Starting Current

  1. Dec 2, 2017 #1
    1. The problem statement, all variables and given/known data
    upload_2017-12-3_9-16-47.png

    2. Relevant equations
    Efficiency = o/p divided by i/p
    I/P KW divided by input voltage gives input current
    Field Current = voltage divided by field resistance
    armature current = total current - field current
    Back Emf = V - IaRa
    T proportional to Ia
    Back Emf proportional to flux and N

    3. The attempt at a solution
    For 1st part:
    we have efficiency = 0.75 = o/p divided by input
    o/p = 18KW
    So we get i/p = 24KW

    So Vt * (Total current) = 24kW
    Vt = 200V
    So Total current = 24000/200 = 120A
    Field current = voltage / Rf = 200/100 = 2A --- (constant all the time)
    Now to limit starting current to three times we have,
    Total current must be 120 * 3 = 360A
    Field current = 2A
    Armature current = 358A
    At start Eb = 0
    Terminal Voltage = Armature Current times Ra
    So 200 = 358 times Ra
    This gives Ra = 0.558
    Given Ra = 0.3
    So we need to add extra 0.26 ohm
    So for first part answer is B

    But I am not able to solve second part.
    At full load Torque is same irrespective of starting resistance since torque depends on load.
    In shunt motor Torque proportional to Ia
    So Ia is same in both cases
    Back Emf is proportional to Speed times flux
    Flux is same in both cases of armature resistance as Field Current is same.
    So Eb1/Eb2 = 1500/(Nx)
    Eb1 = 200 - 118 * 0.3 = 164.6
    Eb2 = 200 - 188 * 0.56 = 133.92
    So Eb1 / Eb2 = 1.23

    So 1.23 = 1500 / Nx
    Nx = 1220 rpm
    But that is not even in the options.
    Where am I wrong, or is the question wrong?
     
  2. jcsd
  3. Dec 4, 2017 #2

    cnh1995

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    Homework Helper
    Gold Member

    I beileve the starting current is the armature current at the start and not the total current.
    Here, the starting current would be 120-2=118A and you need to limit it at 118*3=354A and not 358A. But the answer is still B).

    I agree with your calculations for the second part. I believe all the options are incorrect.
     
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