Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev

Network Theory (Electric Circuits)

Electrical Engineering (EE) : Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev

The document Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev is a part of the Electrical Engineering (EE) Course Network Theory (Electric Circuits).
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Delta Network

Consider the following delta network as shown in the following figure.
Delta to Star Conversion Electrical Engineering (EE) Notes | EduRevThe following equations represent the equivalent resistance between two terminals of delta network, when the third terminal is kept open.
Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev
Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev
Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev

Star Network

The following figure shows the equivalent star network corresponding to the above delta network.
Delta to Star Conversion Electrical Engineering (EE) Notes | EduRevThe following equations represent the equivalent resistance between two terminals of star network, when the third terminal is kept open.
RAB = RA + RB
RBC = RB + RC
RCA = RC + RA

Try yourself:Star connection is also known as ________.
View Solution


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.
    Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev    Equation 1
    Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev   Equation 2
    Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev    Equation 3
  • By adding the above three equations, we will get
    Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev
    Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev   Equation 4
  • Subtract Equation 2 from Equation 4.
    Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev
    Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev
  • By subtracting Equation 3 from Equation 4, we will get
    Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev
  • By subtracting Equation 1 from Equation 4, we will get
    Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev
  • 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.1 Let us calculate the resistances of star network, which are equivalent to that of delta network as shown in the following figure.
Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev

  • 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.
    Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev
    Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev
    Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev
  • Substitute the values of R1, R2 and R3 in the above equations.
    Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev
    Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev
    Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev
  • So, we got the resistances of star network as RA = 6 Ω, RB = 18 Ω and RC = 3 Ω, which are equivalent to the resistances of the given delta network.

Try yourself:The value of the 3 resistances when connected in star connection is ________.
Delta to Star Conversion Electrical Engineering (EE) Notes | EduRev
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