Electrical Engineering ⇒ Topic : Delta-Star Transformation

Delta-Star Transformation

                                  FIGURE (1) Three-terminal Star-Delta networks

In solving certain problems, it is necessary to convert a mesh or Delta network into an equivalent star (Y) network. When the two networks shown in Figs. (1) (a) and  (b) are equivalent, then the resistance between any two terminals of the first network (Fig. 1 (a)) will be equal to the resistance between the corresponding terminals of the second network (Fig. 1 (b)), with the third terminal open circuited.

The resistance between points A and B when C is open circuited (Fig. 1 (a)) is given as R_a + R_b and is equal to R_ab(R_bc + R_ca)/(R_ab+ R_bc + R_ca) from Fig. (1)(b)).

                                    ............ (1)

Similarly, comparing the resistances between points A and C, we get

                                  .............. (2)

Similarly, comparing the resistances between points B and C, we get

                                 ............ (3)

Adding Eqs (1), (2) and (3), we get

         ........... (4)

Subtracting Eq. (3) from (4), we get

               ............... (5)

                 ................... (6)

               ................. (7)