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**Delta Network**

Consider the following delta network as shown in the following figure.

The following equations represent the equivalent resistance between two terminals of delta network, when the third terminal is kept open.**Star Network**

The following figure shows the equivalent star network corresponding to the above delta network.

The following equations represent the equivalent resistance between two terminals of star network, when the third terminal is kept open.

R_{AB} = R_{A} + R_{B}

R_{BC} = R_{B} + R_{C}

R_{CA} = R_{C} + R_{A}**Star Network Resistances in terms of Delta Network Resistances**

We will get the following equations by equating the right-hand side terms of the above equations for which the left-hand side terms are same.

Equation 1

Equation 2

Equation 3

By adding the above three equations, we will get

Equation 4

Subtract Equation 2 from Equation 4.

By subtracting Equation 3 from Equation 4, we will get

By subtracting Equation 1 from Equation 4, we will get

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

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

Given the resistances of delta network as R_{1} = 10 Î©, R_{2} = 60 Î© and R_{3} = 30 Î©.

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

Substitute the values of R_{1}, R_{2} and R_{3} in the above equations.

So, we got the resistances of star network as R_{A} = 6 Î©, R_{B} = 18 Î© and R_{C} = 3 Î©, which are equivalent to the resistances of the given delta network.

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