A 230 V (phase), 50 Hz, three - phase, 4

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A 230 V (phase), 50 Hz, three - phase, 4 – wire system has a phase sequence ABC. A unity power - factor load of 4 kW is connected between phase A and neutral N. It is desired to achieve zero neutral current through the use of a pure inductor and a pure capacitor in the other two phase. The value of inductor and capacitor is

1. 72.95 mH in phase C and 139.02 μF in phase B
2. 72.95 mH in phase B and 139.02 μF in phase C
3. 42.12 mH in phase C and 240.79 μF in phase B
4. 42.12 mH in phase B and 240.79 μF in phase C

Correct Option: B

Inductor is connected in phase-B and capacitor is connected in phase-C
I_B lagging V_BN by 90°.
I_C leading V_CN by 90°.
V_AN = 230° ∠0° [V_AN is reference phasor)
V_BN = 230° ∠– 120
V_CN = 230° ∠– 240
Given, I_A is drawn at unity pf.

I_A =	P	=	4 × 10³	= 17.4∠0°
	V_ANcosφ		230

The current into the central will be zero
I_B = I_C
as I_A = I_Bcos60 + I_C cos60
= 2I_B sin 60_B = √3I_B

⇒ I_B = I_C =	I_A	=	17.4	amp = 10.05 A
	√3		√3

as \|I_B\| = \|	V_BN	\| =	230
	ωL		(314)L

⇒ L =	230	= 72.86 mH
	314 × 10.05

and |L_C| = |C_CN|. ωC = (230) × 314 × C

⇒ C =	10.05	= 139.08 uf.
	230 × 314