Page 206 - Basic Electrical Engineering

2.121 (d) and (e). This shows that star to delta and delta to star transformation
of resistances is advantageous in solving electrical circuit problems.

2.9.1 Transforming Relations for Delta to Star

Let us consider three resistances R , R , and R connected in delta
31
23
12
formation between the terminals A, B, and C. Let their equivalent star-
forming resistances between the same terminals be R , R , and R as shown
1
3
2
in Fig. 2.122. These two arrangements of resistances can be said to be
equivalent if the resistance measured between any two terminals is the same
in both the arrangements.

If we measure resistance between terminals A and B, from Fig. 2.122 (a)
we will get R and a series combination of R and R in parallel, i.e.,
23
31
12

From Fig. 2.122 (b) we get across terminals A and B, R and R in series,
2
1
terminal C being open and not connected. Therefore,

R AB = R + R 2
1

For the purpose of equivalence we can write

In the same way between terminals B and C, the equivalence can be
expressed as

Between terminals C and A, the equivalence can be expressed as