Delta to Star Conversion | GATE Notes & Videos for Electrical Engineering - Electrical Engineering (EE) PDF Download

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

Conversion of Star Network Resistances into 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.

Solved Example

Example.1 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 R₁ = 10 Ω, R₂ = 60 Ω and R₃ = 30 Ω.
• We know the following relations of the resistances of star network in terms of resistances of delta network.
  
  
  
• Substitute the values of R₁, R₂ and R₃ in the above equations.
  
  
  
• So, we got the resistances of star network as R_A = 6 Ω, R_B = 18 Ω and R_C = 3 Ω, which are equivalent to the resistances of the given delta network.

Question for Delta to Star Conversion

Try yourself:The value of the 3 resistances when connected in star connection is ________.

• A.

  2.32ohm, 1.22ohm, 4.54ohm
• B.

  3.55ohm, 4.33ohm, 5.67ohm
• C.

  2.78ohm, 1.67ohm, 0.83ohm
• D.

  4.53ohm, 6.66ohm, 1.23ohm

Explanation

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