In a Y-connected (wye) three-phase circuit, what is the phase angle between any line voltage and its nearest corresponding phase (line-to-neutral) voltage?

Introduction / Context:
In Y-connected systems, line-to-line (line) voltages are the phasor differences of two line-to-neutral (phase) voltages. This vector subtraction introduces both a √3 magnitude factor and a 30° phase shift between a line voltage and the nearest phase voltage, a key fact for transformer connections and motor analysis.

Given Data / Assumptions:

• Balanced Y-connected source or load.
• Sinusoidal steady state and equal magnitudes per phase.
• Standard phasor reference where one phase voltage is at 0°.

Concept / Approach:

For Y: V_line = √3 * V_phase ∠(±30°). Specifically, a given line voltage leads its 'near' phase voltage by +30° (or lags by −30°, depending on sign convention). Thus, the angular separation between any line voltage and the closest phase voltage is 30°.

Step-by-Step Solution:

Verification / Alternative check:

Phasor diagram geometry confirms a 30° rotation between the line vector and the nearest phase vector. Magnitude relation √3 and 30° phase shift are standard results derived from vector subtraction of equal-magnitude 120°-spaced phasors.

Why Other Options Are Wrong:

0° would imply the same phasor, which is untrue. 60° and 120° correspond to larger separations not produced by the line-to-phase relation in Y systems.

Common Pitfalls:

Confusing line-to-line with line-to-neutral quantities; forgetting that line voltages are differences of phase voltages, not equal to them.

Final Answer:

30°