Star to Delta and Delta to Star conversions

Star to Delta and Delta to Star conversions

1. Star (Y) to Delta (Δ) Conversion Formula Chart

• Diagram of Star connection with resistances R1, R2, R3.

• Diagram of Delta connection with resistances RA, RB, RC.

• Side-by-side formulas:

$$RA = \frac{R1R2 + R2R3 + R3R1}{R3}$$ $$RB = \frac{R1R2 + R2R3 + R3R1}{R2}$$ $$RC = \frac{R1R2 + R2R3 + R3R1}{R1}$$

👉 Visual cue: “Opposite branch rule” (product of two + sum of all / opposite resistor).

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2. Delta (Δ) to Star (Y) Conversion Formula Chart

• Diagram of Delta with RA, RB, RC.

• Diagram of Star with R1, R2, R3.

• Formulas neatly highlighted:

$$R1 = \frac{RA \cdot RB}{RA + RB + RC}$$ $$R2 = \frac{RA \cdot RC}{RA + RB + RC}$$ $$R3 = \frac{RB \cdot RC}{RA + RB + RC}$$

👉 Visual cue: “Node rule” (product of two connected / sum of all).

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3. Comparison Table

Conversion	Formula Logic	Usage
Star → Delta	(Sum of products) ÷ Opposite	To simplify star networks
Delta → Star	(Product of two connected) ÷ (Sum of all)	To simplify delta networks

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4. Practical Applications Infographic

• Where Star–Delta conversions are used:

  • ✅ Three-phase power system analysis

  • ✅ Circuit simplification in resistive/impedance networks

  • ✅ Transformer winding configurations

  • ✅ Motor starting methods (Star–Delta starter)

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5. Step-by-Step Example Flowchart

• Example: Given R1 = 2Ω, R2 = 4Ω, R3 = 6Ω.

• Walk through formulas → Calculate RA, RB, RC.

• Show numerical substitution → final values.