Consider the three resistances R

_{1 },R_{2 }and R_{3 }connected in Star as shown in Fig. 1.Fig. 1 |

Now by Star-Delta conversion. it is always possible to replace these Star connected resistances by three equivalent Delta connected resistances R

_{12 }, R_{23 }and R_{31}, between the same terminals. This is called equivalent Delta of the given Star. Now we are interested in finding out values of R

_{12 },R_{23 }and R_{31 }interms of R_{1 },R_{2 }andR_{3}. For this we can use set of equations derived in previous article. From the result of Delta-Star transformation we know that,

Substituting in above in R.H.S. we get,

**.**R^{.}._{1 }R_{2 }+R_{2 }R_{3 }+R_{3 }R_{1 }=R_{1 }R_{23 }Similarly substituting in R.H.S., remaining values, we can write relations for remaining tow resistances.

and

**Easy way to remember the result :**

**The equivalent Delta connected resistance to be connected between any tow terminals is sum of the tow resistances connected between the same tow terminals and star point respectively in star, plus the product of the same two star resistances divided by the third star resistance.**

Fig. 2 Star and equivalent Delta |

So if we want equivalent delta resistance between terminal (3) and (1), then take sum of the tow resistances connected between same tow terminals (3) and (1) and star point respectively i.e. terminal (3) to star point R

_{3 }and terminal (1) to star point i.e. R_{1}. Then to this sum of R_{1 }and R_{3}, add the term which is the product of the same tow resistances i.e. R_{1 }and R_{3 }divided by the third star resistance which is R_{2}.**.**We can write, R

^{.}._{31 }= R

_{1 }+ R

_{3 }+ (R

_{1 }R

_{3 })/R

_{2 }which is same as derived above.

**Note**: If all three resistances in a star connection are of same magnitude say R, then its equivalent Delta contains all resistances of same magnitude of,

R

_{12 }= R_{31 }= R_{23 }=R +R + ((R x R)/R) = 3 R
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