Which, among the following is the right expression for converting from delta to star?

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Examoogle · Accepted Answer

R1=Ra*Rb/(Ra+Rb+Rc), R2=Rb*Rc/(Ra+Rb+Rc), R3=Rc*Ra/(Ra+Rb+Rc) Explanation: The Delta-to-Star (or $\Delta-Y$) transformation is a mathematical technique used to simplify complex resistive networks. In this transformation, each resistance in the star network is equal to the product of the two adjacent delta resistances divided by the sum of all three delta resistances. Working Principle: This principle is derived from equating the resistances measured between any two terminals of both configurations. For terminal equivalence, the star resistances ($R_1, R_2, R_3$) must satisfy the condition where the total resistance seen from any two nodes is identical in both networks, resulting in the partition rule where each branch is the product of adjacent arms over the total sum of delta arms. Key Formulas: $R_1 = \frac{R_a R_b}{R_a + R_b + R_c}$ — Star resistor connected to node 1; $R_2 = \frac{R_b R_c}{R_a + R_b + R_c}$ — Star resistor connected to node 2; $R_3 = \frac{R_c R_a}{R_a + R_b + R_c}$ — Star resistor connected to node 3 Key Points: Transformation allows simplification of bridge circuits.; Used when standard series/parallel combinations are insufficient.; The numerator is always the product of the two resistors connected to the same node in the delta network. Advantages: Simplifies circuit analysis for complex networks.; Essential for solving unbalanced Wheatstone bridge circuits. Disadvantages: Can be algebraically tedious for circuits with many meshes. Applications: Power system distribution networks.; Three-phase transformer connections.; Bridge circuit measurements. Additional Info: In $\Delta-Y$ transformation, the denominator is common for all three star resistances: $\Sigma R_{\Delta} = R_a + R_b + R_c$.. Option B is dimensionally incorrect (resistance unit mismatch).. Option C and D are mathematically incorrect formulations. Answer: A is correct — The formula correctly represents the product of the adjacent branches divided by the sum of all branches in the delta circuit. Exam Tip: Remember: for Star-to-Delta conversion, the numerator is the sum of products of pairs ($R_1R_2 + R_2R_3 + R_3R_1$), which is the reciprocal of the Delta-to-Star process.

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