In the delta-to-Y conversion, what is the sum Rab+Rbc+Rca?

In the delta-to-Y conversion, what is the sum Rab+Rbc+Rca?

• A. 22 Ω
• B. 6 Ω
• C. 18 Ω
• D. 28 Ω

Answer: (A)

In a delta-to-Y conversion, the three Y arm resistances are found by multiplying pairs of delta resistances and then dividing by the sum Rab+Rbc+Rca. That sum is the common denominator for all three Y branches, so it represents the total resistance around the delta. Here that total is 22 Ω, so Rab+Rbc+Rca equals 22 Ω. The Y equivalents would be Ra = Rab·Rca/22, Rb = Rab·Rbc/22, and Rc = Rbc·Rca/22. The other numerical choices would only occur if the actual delta resistances summed to those values, which they do not in this case.

In a delta-to-Y conversion, the three Y arm resistances are found by multiplying pairs of delta resistances and then dividing by the sum Rab+Rbc+Rca. That sum is the common denominator for all three Y branches, so it represents the total resistance around the delta. Here that total is 22 Ω, so Rab+Rbc+Rca equals 22 Ω. The Y equivalents would be Ra = Rab·Rca/22, Rb = Rab·Rbc/22, and Rc = Rbc·Rca/22. The other numerical choices would only occur if the actual delta resistances summed to those values, which they do not in this case.