A three-phase load is connected to a three-phase balanced supply as shown in the figure. If V_{ {an}}=100 \angle 0^{\circ} {V} \cdot V_{ {b} n} \angle-120^{\circ} {V} and V_{ {cn}}=100 \angle-240^{\circ} {V} (angles are considered positive in the anti-clockwise direction), the value of {R} for zero current in the neutral wire is _________Ω (upto 2 decimal places).

GATE Electrical Engineering (EE) 2018 Solved Paper

Question : 50 of 65

Marks: +1, -0

A three-phase load is connected to a three-phase balanced supply as shown in the figure. If

V_{ {an}}=100 ∠ 0^{∘} {V} ⋅ V_{ {b} n} ∠-120^{∘} {V}

and

V_{ {cn}}=100 ∠-240^{∘} {V}

(angles are considered positive in the anti-clockwise direction), the value of

{R}

for zero current in the neutral wire is _________Ω (upto 2 decimal places).

Solution:

From the given voltages

I_{R}=\;{V_{R N}}/{R}=\;{100 ∠ 0^{∘}}/{R}

I_{Y}=\;{V_{Y N}}/{j X_{L}}=\;{100 ∠-120^{∘}}/{j 10}=10 ∠-210^{∘}

I_{B}=\;{V_{B N}}/{-j X_{C}}=\;{100 ∠-240^{∘}}/{-j 10}=10 ∠-150^{∘}

For

I_{N}=0

I_{R}+I_{Y}+I_{B}=0

\;{100}/{R}+10 ∠-210^{∘}+10 ∠-150^{∘} \;\; =0

R \;\; =5.77 Ω

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