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?
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A0 A
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B2.66 A
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C3.99 A
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D1.33 A
Answer
Correct Answer: 0 A
Explanation
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:
Compute I_A = 1.333…∠0° A, I_B = 1.333…∠−120° A, I_C = 1.333…∠+120° A.Sum: I_A + I_B + I_C = 0 (vector sum of a balanced three-phase set).Therefore, I_neutral = 0 A.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