Delta-to-Wye transformation numeric example: Rab=6Ω, Rbc=3Ω, Rca=3Ω. Compute Ra, Rb, Rc.

Delta-to-Wye transformation numeric example: Rab=6Ω, Rbc=3Ω, Rca=3Ω. Compute Ra, Rb, Rc.

• A. Ra = 1.5 Ω; Rb = 1.5 Ω; Rc = 0.75 Ω.
• B. Ra = 3 Ω; Rb = 2 Ω; Rc = 1 Ω.
• C. Ra = 0.75 Ω; Rb = 1.5 Ω; Rc = 1.5 Ω.
• D. Ra = 2 Ω; Rb = 4 Ω; Rc = 6 Ω.

Answer: (A)

In a delta-to-wye transformation, the three delta resistances Rab, Rbc, and Rca become a Y network with Ra, Rb, Rc connected to a common node. The value at each node to the neutral point is found using Ra = Rab × Rca / (Rab + Rbc + Rca), Rb = Rab × Rbc / sum, Rc = Rbc × Rca / sum, where sum = Rab + Rbc + Rca. Plugging in Rab = 6 Ω, Rbc = 3 Ω, Rca = 3 Ω gives sum = 12 Ω. Then Ra = 6 × 3 / 12 = 1.5 Ω, Rb = 6 × 3 / 12 = 1.5 Ω, Rc = 3 × 3 / 12 = 0.75 Ω. So the effective wye resistances are Ra = 1.5 Ω, Rb = 1.5 Ω, Rc = 0.75 Ω, which matches the given values.

In a delta-to-wye transformation, the three delta resistances Rab, Rbc, and Rca become a Y network with Ra, Rb, Rc connected to a common node. The value at each node to the neutral point is found using Ra = Rab × Rca / (Rab + Rbc + Rca), Rb = Rab × Rbc / sum, Rc = Rbc × Rca / sum, where sum = Rab + Rbc + Rca.

Plugging in Rab = 6 Ω, Rbc = 3 Ω, Rca = 3 Ω gives sum = 12 Ω. Then Ra = 6 × 3 / 12 = 1.5 Ω, Rb = 6 × 3 / 12 = 1.5 Ω, Rc = 3 × 3 / 12 = 0.75 Ω.

So the effective wye resistances are Ra = 1.5 Ω, Rb = 1.5 Ω, Rc = 0.75 Ω, which matches the given values.