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27 July, 16:23

Purely resistive loads of 24 kW, 18 kW, and 12 kW are connected between the neutral

and the red, yellow and blue phases respectively of a 3-0, four-wire system. The line

voltage is 415 V. Calculate:

i. the current in each line conductor (i. e., IR, Iy and IB); and

ii. the current in the neutral conductor.

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Answers (1)
  1. 27 July, 16:48
    0
    (i) IR = 100.167 A Iy = 75.125∠-120 IB = 50.083 ∠+120 (ii) IN = 43.374∠ - 30°

    Explanation:

    Solution

    Given that:

    Three loads 24 kW, 18 kW, and 12 kW are connected between the neutral.

    Voltage = 415V

    Now,

    (1) The current in each line conductor

    Thus,

    The Voltage Vpn = vL√3

    Gives us, 415/√3 = 239.6 V

    Then,

    IR = 24 K / Vpn ∠0°

    24K/239.6 ∠0° = 100.167 A

    For Iy

    Iy = 18k/239. 6

    = 75.125A

    Thus,

    Iy = 75.125∠-120 this is as a result of the 3 - 0 system

    Now,

    IB = 12K / 239.6

    = 50.083 A

    Thus,

    IB is = 50.083 ∠+120

    (ii) We find the current in the neutral conductor

    which is,

    IN = Iy + IB + IR

    = 75.125∠-120 + 50.083∠+120 + 100.167

    This will give us the following summation below:

    -37.563 - j65.06 - 25.0415 + j 43.373 + 100.167

    Thus,

    IN = 37.563 - j 21.687

    Therefore,

    IN = 43.374∠ - 30°
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