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We got the resistances of star network from delta network as

Equation 1

Equation 2

Equation 3**Delta Network Resistances in terms of Star Network Resistances**

Let us manipulate the above equations in order to get the resistances of delta network in terms of resistances of star network.

- Multiply each set of two equations and then add.

Equation 4 - By dividing Equation 4 with Equation 2, we will get
- By dividing Equation 4 with Equation 3, we will get
- By dividing Equation 4 with Equation 1, we will get

By using the above relations, we can find the resistances of delta network from the resistances of star network. In this way, we can convert star network into delta network.

Example

Let us calculate the resistances of delta network, which are equivalent to that of star network as shown in the following figure.

Given the resistances of star network as R_{A} = 6 Î©, R_{B} = 18 Î© and R_{C} = 3 Î©.

We know the following relations of the resistances of delta network in terms of resistances of star network.

Substitute the values of R_{A}, R_{B} and R_{C} in the above equations.

So, we got the resistances of delta network as R_{1} = 10 Î©, R_{2} = 60 Î© and R_{3} = 30 Î©, which are equivalent to the resistances of the given star network.

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