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In a three-phase system, phase values are measured across one winding/coil, while line values are measured between two supply conductors. In a star (wye) connection the windings share a common neutral point, so line voltage is √3 times phase voltage but the current is the same. In a delta connection the windings form a closed triangle, so line and phase voltage are equal but line current is √3 times phase current.
| Connection | Voltage relationship | Current relationship |
|---|---|---|
| Star (Wye) | Vline = √3 × Vphase | Iline = Iphase |
| Delta | Vline = Vphase | Iline = √3 × Iphase |
√3 ≈ 1.732. A common example: 230 V phase in a star system gives 400 V line-to-line — the standard European/Indian three-phase supply.
Phase voltage is measured across a single winding (phase to neutral in a star system); line voltage is measured between two of the three supply conductors (phase to phase).
Because the two phase voltages contributing to a line voltage are 120° apart in time, their vector sum works out to √3 times either one, not simply double.
In a delta connection each winding is connected directly between two lines, so the winding (phase) voltage is exactly the line-to-line voltage.
Each line current is the vector sum of two phase currents (120° apart) from adjacent windings, which combine to √3 times a single phase current.
230 V phase (line-to-neutral) with 400 V line-to-line is the standard European/Indian supply; 120 V/208 V is common in North America.
Star gives access to a neutral for single-phase loads and lower per-winding voltage stress; delta needs no neutral and is common in motor windings and industrial equipment.
A method that starts a motor in star (reducing voltage and starting current) then switches to delta for full running voltage — reducing inrush current and mechanical stress at start-up.
Three-phase power P = √3 × Vline × Iline × cosφ uses line quantities directly, giving the same total power regardless of star or delta connection.
Yes, using the star-delta transformation for balanced sources: the equivalent delta voltage is √3 times the star voltage, rotated 30°, with three times the impedance per branch.
They refer to the same nominal supply; 415 V was the older UK/Indian standard, later harmonised to 400 V (with 230 V phase) across most of Europe and India.
No — it is specific to balanced three-phase systems. Single-phase circuits have only one line and phase voltage, so there is no √3 factor.
Check the nameplate: it lists the rated voltage for each connection (e.g. 400/690 V for delta/star) and the wiring diagram inside the terminal box.
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