Introductory Electrical Engineering With Math Explained in Accessible Language

7Delta–Wye Conversions: Circuit Analysis

7.1 Introduction

In this chapter, we will examine two kinds of circuit configurations, Delta and Wye (Y), and how to convert from one to the other.¹

Converting a circuit between Delta and Y configurations and vice versa can make a circuit easier to understand and analyze.

7.2 Delta Circuit

Figures 7.1 and 7.2 show examples of Delta and Y circuit configurations.

Figure 7.1 Delta or triangle circuit.

7.3 Delta–Wye Conversion

Consider that we want to find the resistance between points A and B in the circuit shown in Figure 7.1 and that point C is not connected to anything.

If point C is not connected to anything, we can redraw the circuit into a friendlier version shown in Figure 7.3.

Thus, the resistance between A and B will be the resistance of R₁ in parallel with the sum of R₂ and R₃, because these later resistors are in series.

Figure 7.2 Y or Wye circuit.

Figure 7.3 Delta circuit modified.

Mathematically speaking,

By applying the equations for the equivalent resistance of parallel resistors,

If we want to convert the original ...