What is Star to Delta Conversion?
R12 R31
We know, R1 =------------------------ ---------- (1)R12 + R23 +R31
R23 R12
R2 =---------------------------- ---------- (2)
R12 + R23 +R31
R31 R23
R3 =----------------------------- ---------- (3)
R12 + R23 +R31
From the above relations:
R12 2R23 R31
(1) X (2) => R1 R2 =--------------------------- ---------- (4)
R12 + R23 +R31
R12 R23 2 R31
(2) X (3) => R2 R3 =----------------------------- ---------- (5)
R12 + R23 +R31
R12 R23 R31 2
(3) X (1) => R3 R1 =---------------------------- ---------- (6)
R12 + R23 +R31
By adding Equation: (4) + (5) + (6)
R12 R23 R31 (R12 + R23 +R31)
R1 R2 + R2 R3+R3 R1 =--------------------------------------------
(R12 + R23 +R31)2
R12 R23 R31
=--------------------------
R12 + R23 +R31
R23 R31
R12 =--------------------------- x (R1 R2 + R2 R3+R3 R1)
R12 + R23 +R31
R1 R2 + R2 R3+R3 R1
R12 =---------------------------------------
R3
R1 R2 + R2 R3+R3 R1
R23 =-----------------------------------------
R1
R1 R2 + R2 R3+R3 R1
R31 =--------------------------------------
R2

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