‫أألسبوع الحادي والثاني عشر‬
Star delta transformation
: ‫الفئة المستھدفة‬
.‫طلبة المرحلة أألولى قسم التكييف والتبريد‬
A – The justification for the unit and objective :
It is important for students in first stage to study star delta
transformation .
B – Central ideas :
1. star delta transformation .
C – The objectives of the unit :
After your study this unit , it is expected to be able to :
1- Know how to transfer from star to delta and versa vies
١
Star delta transformation :
In solving complicated networks , it is necessary to transform from
star to delta or from delta to star as shown below .
A
Ra
Rb
Rc
B
C
star connection
delta connection
1. Convert from star to delta :
R ab
R a x Rb
= R a + R b + ------------RC
R ac
Ra x Rc
= R a + R c + -------------Rb
R bc
Rb x Rc
= R b + R c + --------------Ra
٢
2. Convert from delta to star :
Ra
R ab x R ac
= ------------------------R ab + R ac + R bc
Rb
R ab x R bc
= -----------------------R ab + R ac + R bc
Rc
R ac x R bc
= -----------------------R ab + R ac + R bc
٣
Example : For the circuit shown in fig. 1 , find the total resistance
4 ohm
4 ohm
8 ohm
3 ohn
12 ohm
2 ohm
10 v
Fig. 1
Convert star to delta
4x8
R 1 = 4 + 8 + --------- = 28 Ω
2
2x8
R 2 = 2 + 8 + --------- = 14 Ω
4
2x4
R 3 = 2 + 4 + --------- = 7 Ω
8
٤
4 Ω // 28 Ω ,
14 Ω // 12 Ω ,
4 x 28
------------ = 3.5 Ω
14 x 12
------------ = 6.5 Ω
14 + 12
3.5 + 6.5 = 10 Ω
٥
7 Ω // 10 Ω
7 x 10
-------- = 4 Ω
7 + 10
Rt=3+4=7Ω
٦