Three-phase generator with neutral: Each phase (coil) produces 120 V (rms) and feeds a 90 Ω resistive load; the system is balanced with a common neutral. What current flows in the neutral conductor?

Introduction / Context:
Neutral current in multi-phase systems depends on balance and phase displacement. In a balanced three-phase Y system with equal resistive loads on each phase, the vector sum of the phase currents at the neutral node is zero, leading to no neutral current. This is a fundamental property leveraged in three-phase distribution.

Given Data / Assumptions:

• Three-phase generator, Y-connected with neutral.
• Each phase voltage (line-to-neutral) = 120 V (rms).
• Each phase load is 90 Ω, purely resistive and equal.
• System is perfectly balanced; phase angles are 120° apart.

Concept / Approach:

Phase current magnitude per phase: I_phase = V_phase / R = 120 / 90 = 1.333… A. The three currents are equal in magnitude and displaced by 120°. The neutral current is the phasor sum of the three returning currents; for a balanced set, this sum is zero.

Step-by-Step Solution:

Verification / Alternative check:

Phasor diagram shows three equal vectors at 120°; their head-to-tail addition forms a closed triangle, confirming zero resultant. Practical systems see negligible neutral current when loads are closely balanced.

Why Other Options Are Wrong:

1.33 A, 2.66 A, and 3.99 A arise from arithmetic (scalar) addition instead of phasor addition, ignoring 120° displacement.

Common Pitfalls:

Adding magnitudes rather than phasors; assuming some neutral current must flow regardless of balance.

Final Answer:

0 A