Difficulty: Easy
Correct Answer: False
Explanation:
Introduction / Context:
Understanding the phasor relationship between line and phase quantities in three-phase systems is essential for power calculations and fault analysis. In a delta (Δ) connection, the line current is related to the difference of two phase currents; this produces a characteristic magnitude scaling and a specific phase shift, not 120° as sometimes misconceived.
Given Data / Assumptions:
Concept / Approach:
In Δ connection, each line is connected to the junction of two phase windings. The line current equals the phasor difference of the two phase currents meeting at that junction. This leads to a magnitude factor of √3 between line and phase currents and a phase displacement of 30°, not 120°.
Step-by-Step Solution:
Verification / Alternative check:
Using standard three-phase relations: in Δ, V_line = V_phase; I_line = √3 * I_phase at a ±30° shift. Draw the phasor diagram for the three branch currents and compute their vector differences to confirm the 30° shift.
Why Other Options Are Wrong:
“True” contradicts the Δ phasor geometry. “True only for unbalanced loads” is incorrect; unbalance complicates angles but does not create a systematic 120° difference. “True only when power factor is zero” confuses load angle with the inherent topology. “Indeterminate without line impedance” is unnecessary for the ideal relationship.
Common Pitfalls:
Mixing Y and Δ results (in Y, line voltage is √3 times phase voltage with a 30° shift). Also, assuming the 120° phase separation of phase quantities carries to the line–phase relationship directly; it does not.
Final Answer:
False
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