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

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

The document Delta to Star 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)

Delta Network

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

Star Network

The following figure shows the equivalent star network corresponding to the above delta network.
Delta to Star Conversion Notes | Study Network Theory (Electric Circuits) - Electrical Engineering (EE)The 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 Notes | Study Network Theory (Electric Circuits) - Electrical Engineering (EE)    Equation 1
    Delta to Star Conversion Notes | Study Network Theory (Electric Circuits) - Electrical Engineering (EE)   Equation 2
    Delta to Star Conversion Notes | Study Network Theory (Electric Circuits) - Electrical Engineering (EE)    Equation 3
  • By adding the above three equations, we will get
    Delta to Star Conversion Notes | Study Network Theory (Electric Circuits) - Electrical Engineering (EE)
    Delta to Star Conversion Notes | Study Network Theory (Electric Circuits) - Electrical Engineering (EE)   Equation 4
  • Subtract Equation 2 from Equation 4.
    Delta to Star Conversion Notes | Study Network Theory (Electric Circuits) - Electrical Engineering (EE)
    Delta to Star Conversion Notes | Study Network Theory (Electric Circuits) - Electrical Engineering (EE)
  • By subtracting Equation 3 from Equation 4, we will get
    Delta to Star Conversion Notes | Study Network Theory (Electric Circuits) - Electrical Engineering (EE)
  • By subtracting Equation 1 from Equation 4, we will get
    Delta to Star Conversion Notes | Study Network Theory (Electric Circuits) - Electrical Engineering (EE)
  • 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 Notes | Study Network Theory (Electric Circuits) - Electrical Engineering (EE)

  • 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 Notes | Study Network Theory (Electric Circuits) - Electrical Engineering (EE)
    Delta to Star Conversion Notes | Study Network Theory (Electric Circuits) - Electrical Engineering (EE)
    Delta to Star Conversion Notes | Study Network Theory (Electric Circuits) - Electrical Engineering (EE)
  • Substitute the values of R1, R2 and R3 in the above equations.
    Delta to Star Conversion Notes | Study Network Theory (Electric Circuits) - Electrical Engineering (EE)
    Delta to Star Conversion Notes | Study Network Theory (Electric Circuits) - Electrical Engineering (EE)
    Delta to Star Conversion Notes | Study Network Theory (Electric Circuits) - Electrical Engineering (EE)
  • 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 Notes | Study Network Theory (Electric Circuits) - Electrical Engineering (EE)
View Solution

The document Delta to Star 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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