GATE Electrical Engineering (EE) 2021 Solved Papers

Question : 36 of 65

Marks: +1, -0

A three-phase balanced voltage is applied to the load shown. The phase sequence is RYB. The ratio

\;{I_{8}|}/{I_{R} ∣}

is____________.

Solution:

Phase sequence is RYB,

{V}_{ {R}}= {V} ∠ 0^{∘}, {V}_{ {Y}}= {V} ∠-120^{∘}, {V}_{ {B}}= {V} ∠-240^{∘}

{I}_{R}=\;{ {V}_{R}}/{ {z}}=\;{ {V} ∠ 0^{∘}}/{j 10}=\;{ {V}}/{10} ∠ 90^{∘} {A}

I_{y}=\;{V ∠-120^{∘}}/{j 10}=\;{V}/{10}<-210^{∘} {A}

I_{Y}=\;{V ∠-120^{∘}}/{j 10}=\;{V}/{10} ∠-210^{∘} {A}

\ov{ {I}}_{ {B}}=-({ {I}↖{∧}_{ {R}}+{ {I}↖{∧}_{γ})

=-(\;{ {V}}/{10}<90^{∘}+\;{ {V}}/{10}<-210^{∘})

=-\;{V}/{10}(1 ∠ 90^{∘}+1 ∠-210^{∘})=\;{-V √{3}}/{10} ∠+120^{∘}

\;{|\ov{ {I}}_{ {s}}|}/{|\ov{ {I}}_{ {R}}|}=√{3}=1.732

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