Wye-Delta Conversion

In many circuits, resistors are neither in series nor in parallel, so the rules for series or parallel circuits described in previous chapters cannot be applied. For these circuits, it may be necessary to convert from one circuit form to another to simplify the solution. Two typical circuit configurations that often have these difficulties are the wye (Y) and delta (D) circuits.

Wye to Delta



For a circuit like this (Y):

We can convert it to (D):

To obtain the value for Ra, Rb and Rc:

Ra= (R1)(R2)+(R1)(R3)+(R2)(R3)

                           R1

Rb= (R1)(R2)+(R1)(R3)+(R2)(R3)

                           R2

Rc= (R1)(R2)+(R1)(R3)+(R2)(R3)

                           R3

On the other hand, if you want to convert D to Y:

R1= (Rb)(Rc)   

       Ra+Rb+Rc

R2= (Ra)(Rc)   

       Ra+Rb+Rc

R3= (Ra)(Rb)   

       Ra+Rb+Rc

Take a look at the following example:

Find the equivalent resistance of the circuit:

Notice that the resistors are connected neither in series nor in parallel, so we can't use the rules for series or parallel connected resistors

Let's choose the delta of R₁,R₂ and R₄:and convert it to a star circuit of R_A, R_B, R_C.

Using Wye to Delta, we would get:

After this transformation, the circuit contains only resistors connected in series and parallel. Using the series and parallel resistance rules, the total resistance is: 

Souces:
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