What is delta/star and star/delta change?
Hello friends In this article we will know what is delta/star and star/delta change? And learn about many facts related to it.
Delta/Star and Star/Delta Changes
There are some networks in which resistance are neither in series nor in parallel. A familiar case is a threeterminal network. Example : Delta network or Star network.
In such situations, series and parallel Circuit It is not possible to simplify the network by rules. However, converting a delta network to a star and vice versa often simplifies the network and makes it possible to implement seriesparallel circuit techniques.
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delta/star change
Three resistors R connected in delta across three terminals A, B and C as shown in Fig. 3.13 (i)_{AB} R_{BC} and R_{CA} Consider it. These three deltaconnected resistors are connected in the star with three resistors R._{A}R_{B} and R_{C} See Figure 3.13 (ii) so that the two networks are electrically equivalent.
If the resistance between any two terminals of one network is equal to the resistance between the corresponding terminals of the other network, then the two arrangements will be electrically equivalent It can be shown that R_{A}R_{B} and R_{C} The values of K are given by:
R_{A} = R_{AB}R_{CA} / (R_{AB} + RBC + R_{CA},
Similarly, R_{B} = R_{BC}R_{AB} / (R_{AB} + R_{BC} + R_{CA},
and R_{C} = R_{CA}R_{BC} / (R_{AB} + R_{BC} + R_{CA},
How to remember?
A fascinating way to remember it. Referring to Fig. 3.14, the starconnected resistance R_{A}R_{B}and R_{C} Electrically Delta Connected Resistors R_{AB}R_{BC} and R_{CA} We have seen above that:
R_{A} = R_{AB}R_{CA} / (R_{AB} + R_{BC} + R_{CA},
For example, any arm of star connection :
= product of two adjacent sides of the delta / sum of the sides of the delta
Star/Delta change
This means replacing the starconnected network in Fig. 3.13 (ii) and the equivalent deltaconnected network shown in Fig. 3.13 (i) to show that R_{BC}R_{CA} and R_{AB} The values of K are given by :
R_{BC} = RB + RC + R_{B}R_{C} / R_{A}
R_{CA} = R_{C} + R_{A} + R_{C}R_{A} / R_{B}
R_{AB} = R_{A} + R_{B} + R_{A}R_{B} / R_{C}
How to remember?
There’s an easy way to remember it. Quoting Fig. 3.15, the starconnected resistance R_{A}R_{B} and R_{C} The electrically delta connected resistors are equal to R_{AB}R_{BC} and R_{CA} We have seen above:
R_{AB} = R_{A} + R_{B} + R_{A}R_{B} / R_{C}
Resistance between two terminals of Delta = sum of the star resistances connected to those terminals plus the product of the same two resistors divided by the third star resistance.
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