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)?

Difficulty: Medium

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

Explanation:


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:

Let V_an, V_bn, V_cn be load phase (line-to-neutral) voltages.Line-to-line voltage V_ab = V_an − V_bn → that is also the Δ source phase voltage across the ab side.Thus each source phase voltage equals the difference of two load phase voltages.


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

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