In a balanced three-phase system with a solidly connected neutral, what is the magnitude of the neutral current under perfectly balanced loading conditions?

Introduction / Context:
The neutral conductor in three-phase systems returns the vector sum of the three phase currents. Knowing when that current is zero is key for conductor sizing, fault analysis, and power quality considerations in balanced vs unbalanced loads.

Given Data / Assumptions:

• Balanced three-phase system (equal magnitudes, 120° separated).
• Sinusoidal steady-state; no harmonics considered.
• Neutral conductor is present and solidly connected.

Concept / Approach:
In a perfectly balanced system, the instantaneous sum of the three sinusoidal currents is zero at every moment. In phasor form, the vector sum I_a + I_b + I_c = 0, so no current flows in the neutral. Unbalance, harmonics (notably triplen), or asymmetry changes this outcome, but that is beyond the ideal case specified.

Step-by-Step Reasoning:

Verification / Alternative check:
Draw a phasor triangle: equal-length vectors at 0°, −120°, +120° form a closed triangle. The resultant is the null vector, confirming zero neutral current.

Why Other Options Are Wrong:

• One-third / two-thirds / at maximum: These values imply unbalance or non-sinusoidal conditions; not applicable to the strictly balanced, sinusoidal case stated.

Common Pitfalls:

• Confusing real-world lightly unbalanced systems with the ideal balanced definition used in theory problems.

Final Answer:
zero