Three identical star connected resist or s of 1.0 pu are

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Three identical star connected resist or s of 1.0 pu are connected to an unbalanced 3 phase supply. The load neutral is isolated. The symmetrical components of the line voltages in pu are:
V_ab1 = X ∠1, V_ab2 = Y∠2.
If all the pu calculations are with the respective base values, the phase to neutr al sequence voltages are

1. V_an1 = X ∠ (θ₁ + 30°),
  V_an2 = Y ∠(θ₂ – 30°)
2. V_an1 = X ∠ (θ₁– 30°),
  V_an2 = Y ∠(θ₂ + 30°)
3. V_an1 = 1/√3 X ∠ (θ₁ – 30°), V_an2 = 1/√3 Y∠(θ₂ – 30°)
4. Van1 = 1/√3 X ∠ (θ₁ – 60°),
  V_an2 = 1/√3 Y ∠(θ₂ – 60°)

Correct Option: C

Assuming V_a as reference phasor,
V_an1 = V∠0°
V_bn1 = V∠– 120°
V_ab1 = V_an1 - V_bn1
= V∠0° – V∠– 120°
= √3V_an1 ∠30°
Given, V_ab1 = X ∠θ₂
Then, Y ∠θ₂ = √3 V_an2 ∠ - 30°
⇒ V_an2 = Y√3 ∠θ₂ + 30°