A three phase balanced star connected voltage source with

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A three phase balanced star connected voltage source with frequency ωrad/s is connected to a star connected balanced load which is purely inductive. The instantaneous line currents and phase to neutral voltages are denoted by (i_a, i_b, i_c) and (v_an, v_bn, v_cn) respectively and their rms values are denoted by V and I.

then magnitude of R is

1. 3 VI
2. VI
3. 0.7 VI
4. 0

Correct Option: A

Assume v_an as reference phasor,

V_an = V∠0°
V_bn = V – 120°
V_cn = V ∠120°
As load is purely inductive, I_a lags V_an by 90°,
I_b lags V_bn by 90° and I_c lags V_an by 90° as shown in the phasor-diagram
I_ab = I_a - I_b = I∠-90° - 210° = √3I ∠-60°
I_bc = I_b - I_c = I∠- 210° - I∠30° = √3I ∠-180°
I_ca = I_c - I_a = I∠30° - I = ∠- 90° = √3I ∠60°

=	1	[V_anI_bc + V_bnI_ca + V_cnI_ab]
	√3

=	1	√3I[V∠180° + V∠60° + V∠60°] = 0
	√3