Star to Delta Conversion | Network Theory (Electric Circuits) - Electrical Engineering (EE) PDF Download

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 Ω, R_B = 18 Ω and R_C = 3 Ω.
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 R₁ = 10 Ω, R₂ = 60 Ω and R₃ = 30 Ω, which are equivalent to the resistances of the given star network.