For a Δ-connected source feeding a Y-connected load, how does each source phase voltage relate to the corresponding load terminal voltages (line-to-line relationship)?

Introduction / Context:Mixed Δ–Y connections are common in transformers and generator–load interfaces. Understanding how source phase voltages map to load terminal voltages avoids confusion when converting between line-to-line and line-to-neutral measures and when drawing phasor diagrams for interconnections.

Given Data / Assumptions:

• Source: Δ-connected, providing line-to-line (phase) voltages directly.
• Load: Y-connected, with each load phase connected from a line to the neutral.
• Balanced, sinusoidal conditions assumed.

Concept / Approach:In Δ, each phase element is across a pair of lines; thus the source phase voltage is a line-to-line voltage (difference of two line phasors). The Y load phase voltage is a line-to-neutral voltage. Because line-to-line voltages are differences of line-to-neutral voltages, one can say each Δ phase voltage equals the vector difference of two corresponding Y load (line-to-neutral) voltages.

Step-by-Step Reasoning:

Verification / Alternative check:Draw the phasor diagram: V_an, V_bn, V_cn are 120° apart. The vector subtraction V_an − V_bn produces the familiar line-to-line magnitude √3 times the phase magnitude, aligning with Δ phase values.

Why Other Options Are Wrong:

• Equals the corresponding load voltage: Load phase is line-to-neutral; Δ phase is line-to-line; magnitudes differ by √3 in balanced systems.
• One-third the load voltage: No standard three-phase relation yields 1/3 here.
• 60° out of phase: Line-to-line vs line-to-neutral phasors exhibit 30° shifts in common representations, not 60°, and this option is not a correct general statement.

Common Pitfalls:

• Confusing phase vs line voltages and their vector differences when mixing Δ and Y.

Final Answer:each phase voltage equals the difference of the corresponding load voltages