GATE Electrical Engineering (EE) 2019 Solved Paper

Question : 59 of 65

Marks: +1, -0

A single -phase transformer of rating

25 {kVA}

, supplies a

12 {kW}

load at power factor of

0.6

lagging. The additional load at unity power factor in

{kW}

(round off to two decimal places) that may be added before this transformer exceeds its rated kVA is ____________.

Solution:

Let rated voltage

= {V}

volts

12 {kW}, 0.6 {lag} → {V} × {I}_{1} × 0.6=12000

{I}_{1}=\;{12000}/{0.6 {V}}=\;{20,000}/{ {V}} {A}

\ov{ {I}}_{1}=\;{20000}/{ {V}} ∠-53.13^{∘}

Let UPF load

=

{kW}

{VI}_{2}= {W} 1000

{I}_{2}=\;{1000 {W}}/{ {V}}

\ov{ {I}}_{2}=\;{1000 {W}}/{ {V}} ∠ 0^{∘}

When both loads are present, total current

\ov{ {I}}=\;{1000}/{ {V}}[20 ∠-53.13+ {W} ∠ 0^{∘}]

=\;{1000}/{ {V}}[12- {j} 16+ {W}]

{I}=\;{1000}/{ {V}}[√{(12+ {W})^{2}+256}]

{kVA}=√{(12+ {W})^{2}+256}=25

(12+ {W})^{2}+256=625,

(12+ {W})^{2}=369,

2+ {W}=19.21,

{W}=7.21 {kW}

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