For a Y-connected (wye) three-phase circuit, what is the relationship between line current and phase current in magnitude?

Introduction / Context:
Correctly relating line and phase quantities for Y and Δ connections is a frequent task in power systems. For Y connections, the node at the center ties each phase to the neutral, and currents flow in each line through a single phase branch, leading to a simple equality between line and phase currents.

Given Data / Assumptions:

• Balanced, sinusoidal three-phase Y connection.
• Ideal lines and connections (no additional paths).

Concept / Approach:
In a Y connection, each line conductor feeds one phase element directly. Therefore, the current in any line equals the current in that phase element: I_line = I_phase. (By contrast, in Δ, line current equals √3 times the phase current due to the vector sum of two branch currents.)

Step-by-Step Reasoning:

Verification / Alternative check:
Phasor analysis or simple circuit inspection of a Y-connected load confirms this direct equality. Measured values in laboratory Y-connected loads also show this relationship in balanced conditions.

Why Other Options Are Wrong:

• One-third / three times: These do not apply to Y; “√3 times” belongs to Δ (line vs phase currents).
• Zero: Not unless the circuit is de-energized or open-circuited.

Common Pitfalls:

• Swapping the Y and Δ current/voltage relationships; remember: Y → I_line = I_phase, Δ → V_line = V_phase.

Final Answer:
equal to the corresponding phase current