In a three-phase power system where both the source and the load are connected in a delta (Δ–Δ) configuration, identify the correct relationship among the load phase voltage, the line (line-to-line) voltage, and the source phase voltage for any given phase.

Difficulty: Easy

Correct Answer: load voltage, line voltage, and source phase voltage are all equal for a given phase

Explanation:


Introduction / Context:
Three-phase AC systems commonly use delta (Δ) and wye (Y) connections. Understanding how phase and line quantities relate within these connections is foundational for analyzing motors, transformers, and distribution networks. This question targets the voltage relationships in a Δ–Δ system, which often confuses learners who recall the √3 factor from Y systems and apply it incorrectly to delta circuits.


Given Data / Assumptions:

  • The source is delta-connected (Δ) and the load is also delta-connected (Δ).
  • Balanced, sinusoidal three-phase conditions are assumed.
  • No line impedance is considered (ideal conductors for clarity).


Concept / Approach:

In a delta connection, each phase element (source or load) is connected directly between two lines. Therefore, the phase voltage of that element is the line-to-line voltage. This is true on both the source side and the load side of a Δ–Δ system (assuming no significant voltage drops in the lines).


Step-by-Step Solution:

Identify connection: Δ means each phase winding sits across two lines.Hence: V_phase(source) = V_line(source).On the load: V_phase(load) = V_line(at the load terminals).With ideal lines: the line voltage delivered equals the line voltage applied; thus all three quantities are equal in magnitude.


Verification / Alternative check:

Contrast with Y systems: In Y, V_line = √3 * V_phase. In Δ, there is no √3 factor between line and phase voltage; they are the same, validating the equality statement.


Why Other Options Are Wrong:

Fractions like one-third or two-thirds have no basis in Δ voltage relations. 'Cancel' is incorrect; voltages are phasors between conductors and do not cancel for a single phase element.


Common Pitfalls:

Confusing delta with wye and misapplying the √3 relationship; overlooking that in Δ the element endpoints are lines, not line-to-neutral points.


Final Answer:

load voltage, line voltage, and source phase voltage are all equal for a given phase

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