Star to Delta Conversion Notes | Study Network Theory (Electric Circuits) - Electrical Engineering (EE)

Electrical Engineering (EE): Star to Delta Conversion Notes | Study Network Theory (Electric Circuits) - Electrical Engineering (EE)

The document Star to Delta Conversion Notes | Study Network Theory (Electric Circuits) - Electrical Engineering (EE) is a part of the Electrical Engineering (EE) Course Network Theory (Electric Circuits).
All you need of Electrical Engineering (EE) at this link: Electrical Engineering (EE)

We got the resistances of star network from delta network as
Star to Delta Conversion Notes | Study Network Theory (Electric Circuits) - Electrical Engineering (EE)  Equation 1
Star to Delta Conversion Notes | Study Network Theory (Electric Circuits) - Electrical Engineering (EE)  Equation 2
Star to Delta Conversion Notes | Study Network Theory (Electric Circuits) - Electrical Engineering (EE)  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.
    Star to Delta Conversion Notes | Study Network Theory (Electric Circuits) - Electrical Engineering (EE)
    Star to Delta Conversion Notes | Study Network Theory (Electric Circuits) - Electrical Engineering (EE)
    Star to Delta Conversion Notes | Study Network Theory (Electric Circuits) - Electrical Engineering (EE)  Equation 4
  • By dividing Equation 4 with Equation 2, we will get 
    Star to Delta Conversion Notes | Study Network Theory (Electric Circuits) - Electrical Engineering (EE)
    Star to Delta Conversion Notes | Study Network Theory (Electric Circuits) - Electrical Engineering (EE)
  • By dividing Equation 4 with Equation 3, we will get
    Star to Delta Conversion Notes | Study Network Theory (Electric Circuits) - Electrical Engineering (EE)
  • By dividing Equation 4 with Equation 1, we will get 
    Star to Delta Conversion Notes | Study Network Theory (Electric Circuits) - Electrical Engineering (EE)

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.
Star to Delta Conversion Notes | Study Network Theory (Electric Circuits) - Electrical Engineering (EE)
Given the resistances of star network as RA = 6 Ω, RB = 18 Ω and RC = 3 Ω.
We know the following relations of the resistances of delta network in terms of resistances of star network.
Star to Delta Conversion Notes | Study Network Theory (Electric Circuits) - Electrical Engineering (EE)
Star to Delta Conversion Notes | Study Network Theory (Electric Circuits) - Electrical Engineering (EE)
Star to Delta Conversion Notes | Study Network Theory (Electric Circuits) - Electrical Engineering (EE)
Substitute the values of RA, RB and RC in the above equations.
Star to Delta Conversion Notes | Study Network Theory (Electric Circuits) - Electrical Engineering (EE)
Star to Delta Conversion Notes | Study Network Theory (Electric Circuits) - Electrical Engineering (EE)
Star to Delta Conversion Notes | Study Network Theory (Electric Circuits) - Electrical Engineering (EE)
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.

The document Star to Delta Conversion Notes | Study Network Theory (Electric Circuits) - Electrical Engineering (EE) is a part of the Electrical Engineering (EE) Course Network Theory (Electric Circuits).
All you need of Electrical Engineering (EE) at this link: Electrical Engineering (EE)

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