Provide the formulas for converting a delta network Rab, Rbc, Rca to a Y network Ra, Rb, Rc.

Provide the formulas for converting a delta network Rab, Rbc, Rca to a Y network Ra, Rb, Rc.

• A. Ra = Rab*Rca/(Rab+Rbc+Rca); Rb = Rab*Rbc/(Rab+Rbc+Rca); Rc = Rbc*Rca/(Rab+Rbc+Rca).
• B. Ra = Rab+Rca; Rb = Rab+Rbc; Rc = Rbc+Rca.
• C. Ra = Rab*Rbc/( Rab+Rbc+Rca ); Rb = Rca*Rbc/(Rab+Rbc+Rca); Rc = Rab*Rca/(Rab+Rbc+Rca).
• D. Ra = Rab*Rca/(Rca+Rab+Rbc); Rb = Rab*Rbc/(Rca+Rab+Rbc); Rc = Rcb*Rca/(Rab+Rbc+Rca).

Answer: (A)

Delta-to-Y transformation preserves the same resistance between every pair of external terminals. For a delta with Rab between nodes a and b, Rbc between b and c, and Rca between c and a, the equivalent Y has legs Ra, Rb, Rc given by Ra = Rab × Rca / (Rab + Rbc + Rca) Rb = Rab × Rbc / (Rab + Rbc + Rca) Rc = Rbc × Rca / (Rab + Rbc + Rca) This arrangement ensures each Y leg is the product of the two adjacent delta resistances divided by the sum of all three delta resistances. A quick check: if all delta resistances are equal to R, each Y leg becomes R^2/(3R) = R/3, which is consistent with the transformation. Other forms would not preserve the same equivalence between node pairs.

Delta-to-Y transformation preserves the same resistance between every pair of external terminals. For a delta with Rab between nodes a and b, Rbc between b and c, and Rca between c and a, the equivalent Y has legs Ra, Rb, Rc given by

Ra = Rab × Rca / (Rab + Rbc + Rca)

Rb = Rab × Rbc / (Rab + Rbc + Rca)

Rc = Rbc × Rca / (Rab + Rbc + Rca)

This arrangement ensures each Y leg is the product of the two adjacent delta resistances divided by the sum of all three delta resistances. A quick check: if all delta resistances are equal to R, each Y leg becomes R^2/(3R) = R/3, which is consistent with the transformation. Other forms would not preserve the same equivalence between node pairs.