A balanced three-phase Δ-connected generator delivers phase currents of 12 A (rms). If Iθa = 12 ∠30° A, determine the polar forms of the other two phase currents (positive-sequence spacing).

Introduction / Context:This question checks phasor literacy for balanced three-phase systems. In a balanced generator (Δ or Y), the three phase quantities are equal in magnitude and separated by 120° in phase. Correctly assigning the angles for phases b and c after one phase is given is a core skill for system analysis, phasor diagrams, and power calculations.

Given Data / Assumptions:

• Balanced three-phase Δ-connected generator.
• Phase current magnitudes are all 12 A(rms).
• Given: Iθa = 12 ∠30° A.
• Assume positive sequence ordering (a→b→c with 120° separation).

Concept / Approach:For a positive sequence, the three phasors are separated by +120° steps when rotating from a to b to c (or equivalently, b lags a by 120°, c lags b by 120°). Because angles can be expressed modulo 360°, equivalent representations appear as additions or subtractions of 360° without changing the phasor.

Step-by-Step Solution:

Verification / Alternative check:Plot on a phasor diagram: one vector at 30°, the next at 150°, and the third at −90°. The separations are all 120° (from 30° to 150° is +120°, from 150° to −90° is +120°, from −90° to 30° is +120°), confirming balance and correct ordering.

Why Other Options Are Wrong:

• I θb = 12∠120°, I θc = 12∠30°: b is only 90° from a here (120° − 30°), breaking 120° balance.
• I θb = 12∠30°, I θc = 12∠120°: b duplicates a; not 120° separated.
• I θb = 12∠90°, I θc = 12∠90°: identical angles for b and c, not a balanced three-phase set.

Common Pitfalls:

• Reversing phase sequence (positive vs negative) or mixing line and phase currents.
• Forgetting that multiple angle representations are equivalent modulo 360°.

Final Answer:I θb = 12 ∠150° A, I θc = 12∠–90° A