Balanced Y–Y system: If each source phase current has magnitude 9 A, what is the magnitude of each load current under balanced conditions?

Introduction / Context:
In a balanced Y–Y system, the current in each source phase equals the current in the corresponding load phase, because the line current passes directly through each phase element. Recognizing this identity prevents misapplication of √3 factors that apply to Δ connections for currents, not to Y loads.

Given Data / Assumptions:

• Balanced three-phase system with Y-connected source and Y-connected load.
• Source phase currents have magnitude 9 A.
• Negligible line impedance; purely resistive or any balanced impedance per phase.

Concept / Approach:

For a Y-connected load, each line conductor feeds one phase element directly. Therefore, line current equals phase current: I_line = I_phase(load). If the source is Y-connected and balanced, the source phase current is the same magnitude as the load phase current (ignoring line drops).

Step-by-Step Solution:

Verification / Alternative check:

Phasor diagrams show equal-magnitude currents per phase in Y–Y. Measurements in lab setups confirm equality when lines are short and impedances matched.

Why Other Options Are Wrong:

3 A and 6 A incorrectly imply division or transformation. 27 A suggests summation of phase currents, which is not how three-phase branch currents behave.

Common Pitfalls:

Applying Δ current relationships to Y; forgetting that the √3 factor relates Δ phase vs line currents, not Y.

Final Answer:

9 A