Examples of Star (Y) to Delta (Δ) or Delta (Δ) to Star (Y) Transformation

Example: 1

Determine the equivalent resistance between the terminals A and B of network shown in fig.(a).

(a)

Solution:

A ‘ Δ ’ is substituted for the ‘Y ’ between points c, d, and e as shown in fig.(b); then unknown resistances value for Y to Δ transformation are computed below.

                                                         (b)

Next we transform ‘Δ’connected 3-terminal resistor to an equivalent ‘Y ’ connected network between points ‘A’; ‘c’ and ‘e’ (see fig.(b)) and the corresponding Y connected resistances value are obtained using the following expression. Simplified circuit after conversion is shown in fig.(c).

                                              (c)

The circuit shown in fig.(c) can further be reduced by considering two pairs of parallel branches   and the corresponding simplified circuit is shown in fig.(d).

                                                            (d)

Now one can find the equivalent resistance between the terminals ‘ A ’ and ‘ B ’ as

Example: 2

Find the value of the input resistance    of the circuit.

Solution

Y connected network formed with the terminals a-b-o is transformed into Δ connected one and its resistance values are given below.

Now Y connected network formed with the terminal ‘a-b-c’ is converted to equivalent Δ connected network.