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Ra is resistance at A, Rb is resistance at B, Rc is resistance at C in star connection. After transforming to delta, what is resistance between A and C?

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Ra is resistance at A, Rb is resistance at B, Rc is resistance at C in star connection. After transforming to delta, what is resistance between A and C?

(a) Ra+Rb+Ra*Rb/Rc

(b) Ra+Rc+Ra*Rc/Rb

(c) Ra+Rb+Ra*Rc/Ra

(d) Ra+Rc+Ra*Rb/Rc

The question was posed to me in semester exam.

This interesting question is from Star Delta Transformation in portion Network Theorems of Basic Electrical Engineering

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The correct answer is (b) Ra+Rc+Ra*Rc/Rb

To explain I would say: After converting to the delta, each delta connected resistance is equal to the sum of the two resistances it is connected to+product of the two resistances divided by the remaining resistance. Hence, resistance between A and C = Ra+Rc+Ra*Rc/Rb.

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