Star to Delta Transformation: Now we have to get the equivalent values of R1, R2 and R3 in Delta connection in terms of the
three resistances R
X
,R
Y
and R
Z
in Star connection.
Let us use the equations we got earlier i.e. R
X
,R
Y
and R
Z
in terms of R
1
,R
2
and R
3
and get the
sum of the three product pairs i.e. R
X
R
Y
+ R
Y
R
Z
+ R
Z
R
X
as :
Malla Reddy College of Engineering and Technology (MRCET)
Department of EEE ( 2017-18 )
Electrical Circuits EEE 𝑅𝑋𝑅𝑌 + 𝑅𝑌𝑅𝑍 + 𝑅𝑍𝑅𝑋 =
𝑅1
2
𝑅2𝑅3 + 𝑅2
2
𝑅1𝑅3 + 𝑅3
2
𝑅1𝑅2
(𝑅1 + 𝑅2 + 𝑅3)
2
Now let us divide this equation by R
X
to get
:
𝑅𝑌 + 𝑅𝑍 +
𝑅𝑌𝑅𝑍
𝑅𝑋
=
𝑅1𝑅2𝑅3(𝑅1 + 𝑅2 + 𝑅3)
𝑅𝑋(𝑅1 + 𝑅2 + 𝑅3)
2
=
𝑅1𝑅2𝑅3
𝑅𝑋(𝑅1 + 𝑅2 + 𝑅3)
Now substituting the value of R
X
= (R1+R2+R3) / R1.R3 from the earlier equations into the
above equation we get
:
𝑅𝑌 + 𝑅𝑍 +
𝑅𝑌𝑅𝑍
𝑅𝑋
=
𝑅1𝑅2𝑅3
(𝑅1 + 𝑅2 + 𝑅3)
×
(𝑅1 + 𝑅2 + 𝑅3)
𝑅1𝑅3
= 𝑅2
Then similarly dividing the same equation by RY and RZ we get the other two relations as:
𝑅𝑋 + 𝑅𝑍 +
𝑅𝑋𝑅𝑍
𝑅𝑌
= R3
𝑅𝑌 + 𝑅𝑋 +
𝑅𝑋𝑅𝑌
𝑅𝑍
= 𝑅1
Thus we get the three equivalent resistances R1, R2 and R3 in Delta connection in terms of the
three resistances RX, RY and RZ in Star connection as :
𝑅𝑌 + 𝑅𝑋 +
𝑅𝑋𝑅𝑌
𝑅𝑍
= 𝑅1
𝑅𝑌 + 𝑅𝑍 +
𝑅𝑌𝑅𝑍
𝑅𝑋
= 𝑅2
𝑅𝑋 + 𝑅𝑍 +
𝑅𝑋𝑅𝑍
𝑅𝑌
= R3
Malla Reddy College of Engineering and Technology (MRCET)
Department of EEE ( 2017-18 )
