GATE Electrical Engineering (EE) 2020 Solved Paper

Question : 24 of 65

Marks: +1, -0

A single-phase,

4 {kVA}, 200 {V} {/} 100 {V}, 50 {Hz}

transformer with laminated CRGO steel core has rated no-load losses of

450 {W}

. When the high-voltage winding is excited with

160 {V}, 40 {Hz}

sinusoidal ac supply, the no-load losses are found to be

320 {W}

. When the high-voltage winding of the same transformer is supplied from

100 {V}, 25 {Hz}

sinusoidal ac source, the no-load losses will be ___________ W (rounded off to 2 decimal places).

Solution:

P_{i}=P_{h}+P_{e}

\table {P}_{ {h}}= {KhfB}_{ {m}}^{1.6}= {K}_{1} {f};P_{e}=K c f^{2} B m^{2}=k_{2} f^{2}\}\;\Keeping{V/f}=\constant

{K}_{1} ⋅ 50+ {K}_{2} ⋅(50)^{2}=450

{K}_{1}+ {K}_{2} ⋅(50)=\;{450}/{50}=9

\;\text " at "\; 160 {V}_{1}, 40 {Hz}

{K}_{1} ⋅ 40+ {K}_{2} ⋅(40)^{2}=370

{K}_{1}+ {K}_{2} ⋅(4)=\;{370}/{40}=8

K_{1}+K_{2} .50=9

K_{1}+K_{2} .40=8

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──────────

{K}_{2} .10=1 ⇒ {K}_{2}=\;{1}/{10}

K_{1}=9-\;{1}/{10} × 50=4

∴ 100 {V}, 25 {Hz}

{Pe}= {p}_{ {h}}= {K}_{ {c}}

=K_{1} ⋅(25)+K_{2} ⋅(25)^{2}

=4 × 25+\;{1}/{10} ×(25)^{2}

=100+62.5=162.5

watt

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