Three-Phase Circuits (Δ Connection): Line Current vs. Phase Current In a delta-connected (Δ-connected) three-phase generator, it is claimed that there is a 120° phase difference between each line current and the nearest phase current. Decide whether this statement is correct.
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AFalse
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BTrue
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CTrue only for unbalanced loads
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DTrue only when power factor is zero
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EIndeterminate without line impedance data
Answer
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:
- Balanced, sinusoidal three-phase source.
- Ideal Δ connection (line connected directly across each phase winding).
- Negligible line impedance for fundamental relationships.
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:
Let I_phase be the current in a Δ branch; the three branch currents are separated by 120°.The line current I_line is the vector difference of two adjacent branch currents: I_line = I_phase(θ) − I_phase(θ − 120°).Phasor subtraction of two equal-magnitude vectors separated by 120° yields |I_line| = √3 * |I_phase|.The resulting I_line leads (or lags) the corresponding branch current by 30°, not 120°.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