Solved Examples Problems On Star-Delta Transformation Or Conversion

Solved Examples Problems On Star-Delta Transformation Or Conversion

Ques:- Find the equivalent resistance between A & B in the given network.

Solution:-

 For the given network, we can easily determine the value of equivalent resistance i.e, R_AB through  Star-Delta conversion.

We have

Above network can also be represent as below:-

Now, I am going to solved this network by using  delta to star conversion as shown in the figure given below:-

For the value of new star connected resistance are finding through direct formula of delta to star conversion,as shown below

So, R_AB / R_equivalent = R₁ + R₂ + R₃ = 4Ω + 3.88Ω + 1.77Ω = 9.65Ω Answer

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Delta To Star Transformation Or Delta To Star Conversion and Its Formulas

Delta To Star Transformation Or Delta To Star Conversion and Its Formulas

Fig:-

Suppose, R₁₂  , R₁₃ and R₂₃ is three resistances connecting to each other such that they forms a delta connections or star networks.

 Now, we have to convert this circuit in star for solving or simplifying given star connected circuits. Because if you are not convert may not get equivalent resistances of that given circuit.

Fig:-

So, we make a star connection by connecting pt.1, pt.2 and pt.3 to pt. O such that they form as star connection as shown in fig. It will form a new network as ‘Star connection’ as I shown through dotted diagram and hence forms a new ‘Star circuit’.

For new circuits containing new resistances is R_A  , R_B and R_C  having new value’s. For these new resistances we have direct formula’s I am going to give you because no need of derivation, kindly used direct formulas as given below:-

How to remember?

“Resistance of each arm of the star is given by the product of the resistances of the two delta sides that meet at its end divided by the sum of the three delta resistances”.

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