CBSE Class 12-science Answered

The transformation is used to establish equivalence for networks with three terminals. Where three elements terminate at a common node and none are sources, the node is eliminated by transforming the impedances. For equivalence, the impedance between any pair of terminals must be the same for both networks. The equations given here are valid for complex as well as real impedances.

[edit]Equations for the transformation from Δ-load to Y-load 3-phase circuit

The general idea is to compute the impedance R_y at a terminal node of the Y circuit with impedances R', R'' to adjacent nodes in the Δ circuit by

where R_Δ are all impedances in the Δ circuit. This yields the specific formulae

[edit]Equations for the transformation from Y-load to Δ-load 3-phase circuit

The general idea is to compute an impedance R_Δ in the Δ circuit by

where R_P = R₁R₂ + R₂R₃ + R₃R₁ is the sum of the products of all pairs of impedances in the Y circuit and R_opposite is the impedance of the node in the Y circuit which is opposite the edge with R_Δ. The formula for the individual edges are thus