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25 August, 18:36

A 25 kVA transformer has an iron loss of 200 W and a full-load copper loss of 350 W. Calculate the transformer efficiency for the following load conditions: a. Full load at 0.8 power factor lagging b. 70% of full load at unity power factor c. 40% of full load at 0.6 power factor lagging

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  1. 25 August, 19:42
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    a. 97.32 percent

    b. 97.92 percent

    c. 95.91 percent

    Explanation:

    given parameters

    apparent power, S = 25 kVA

    Iron Loss, Piron = 200 W

    copper Loss at full load, P cufl = 350 W

    let the transformer efficiency at full load be E

    let the real power be P out

    a.

    at full load and 0.8 power factor

    P out = Scos∅

    = 25 x 10³ x 0.8

    =20000 W or 20 kW

    efficiency at full load is

    E = (P out) / (P out + P iron + P cufl) x 100%

    = (20000) / (20000 + 200 + 350) x 100%

    = 97.32%

    b.

    at 70% of full load at unity power factor of 1

    Pout = 70% x Scos∅

    = 0.7 x 25 x 10³ x 1

    = 17,500W or 17.5kW

    copper loss at 70% full load

    P cu0.7fl = (70%) ² x 350

    = (0.7) ² x 350

    = 171.5 W

    Iron loss remain the same, P iron = 200 W

    Efficiency of transformer at 70% of full load

    E = (P out0.7) / (P out0.7 + P iron + P cufl0.7) x 100%

    = (17500) / (17500 + 200 + 171.5) x 100%

    = 97.92%

    c.

    at 40% of full load at a power factor of 0.6

    P out = 40% x Scos∅

    = 0.4 x 25 x 10³ x 0.6

    = 6000 W or 6 kW

    copper loss at 40% full load

    P cu0.7fl = (40%) ² x 350

    = (0.4) ² x 350

    = 56 W

    Iron loss remain the same, P iron = 200 W

    Efficiency of transformer at 40% of full load

    E = (P out0.4) / (P out0.4 + P iron + P cu0.4) x 100%

    = (6000) / (6000 + 200 + 350) x 100%

    = 95.91%
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