Side-by-side comparison
| Parameter | Star | Delta Network Transformation |
|---|---|---|
| Configuration | Three resistors meet at a common central node | Three resistors form a closed triangle, no central node |
| Number of Nodes | 4 (three terminals + one central neutral) | 3 (three terminals only) |
| Delta to Star (R_A) | R_A = (R_AB × R_CA) / (R_AB + R_BC + R_CA) | N/A — this is the source formula |
| Star to Delta (R_AB) | N/A — this is the source formula | R_AB = R_A + R_B + (R_A × R_B)/R_C |
| For Equal Resistors R | R_star = R_delta / 3 | R_delta = 3 × R_star |
| Phase Voltage (3-phase) | V_phase = V_line / √3 (e.g., 230 V in 400 V system) | V_phase = V_line (e.g., 400 V) |
| Phase Current (3-phase) | I_phase = I_line | I_phase = I_line / √3 |
| Typical Application | Generator windings, induction motor star-start, neutral provision | Motor running connection, delta-connected transformer secondary |
Key differences
The star-to-delta conversion multiplies the resistance: R_delta = 3 × R_star for equal resistors, so a 10 Ω star becomes a 30 Ω delta. Delta-to-star divides: R_star = R_delta / 3, so a 30 Ω delta becomes a 10 Ω star. In three-phase systems, star connection gives a 230 V phase voltage from a 400 V line (÷√3), while delta keeps the full 400 V across each winding. Induction motors start in star to reduce starting current by one-third, then switch to delta for full torque — the star-delta starter is the most common soft-starting method in Indian industry.
When to use Star
Use star configuration when you need a neutral conductor for single-phase loads or when reducing starting current in a three-phase motor — for example, a DOL star-delta starter for a 15 kW induction motor.
When to use Delta Network Transformation
Use delta configuration for the running condition of a three-phase induction motor or when connecting a transformer secondary to deliver full line voltage — for example, a 400 V, 50 Hz delta-connected motor winding.
Recommendation
For exam and GATE problems, memorize R_star = R_delta/3 for equal resistors — that single relation solves 80 percent of star-delta MCQs instantly. For unequal resistors, choose the product-over-sum form carefully and label terminals consistently to avoid sign errors.
Exam tip: Examiners frequently hide a star or delta inside a bridge circuit — recognize the inner three-terminal group, apply the transformation, and then reduce the resulting series-parallel network.
Interview tip: Interviewers at ABB, Siemens, or BHEL will ask why motors start in star and run in delta — answer: star reduces phase voltage by √3, limiting starting current to one-third of delta value, protecting supply and switchgear.