Solved Example on Star to Delta Conversion
1. Given a network of 9 resistors, find the equivalent resistance between point E and F.
The connection between A, B, C is in delta connection which is converted to its equivalent star connection with the common node O
[Tex]R_{AO}=\frac{4X6}{2+4+6}=2 \Omega \newline R_{BO}=\frac{2 X 6}{2+4+6}=1\Omega \newline R_{CO}=\frac{2 X 4}{2+4+6}=\frac{2}{3}\Omega [/Tex]
The network can be further simplified by adding the resistances in series combination i.e. [Tex]R_{DO}=2+6=8 \Omega \newline R_{EO}= \frac{2}{3}+\frac{10}{3}=\frac{12}{3}=4\Omega \newline R_{FO}=7+1=8\Omega [/Tex]
Now again the star connection in the inner part of the triangle is again converted into delta connection.
[Tex]R_1=4+8+\frac{8X4}{8}=16\Omega \newline R_2=8+8+\frac{8X8}{4}=32\Omega \newline R_3=8+4+\frac{8X4}{8}=16\Omega [/Tex]
Now, we will apply parallel combination between the nodes DG and EI, EI and FH, FH and DG.
After that we will get the resistances as, [Tex]R_{DE}=8\Omega \newline R_{EF}=8\Omega \newline R_{FD}=\frac{32}{3}\Omega [/Tex]
The equivalent resistance between E and F will be
[Tex]R_{EF}=\frac{8 X(8+32/3)}{8+(8+32/3)}=\frac{8X56}{80}=5.6 \Omega [/Tex]
2. Find the current drawn from the 5v battery in the network given below.
Let us consider some points in the given network as A, B, C, D and G. If we consider the points A, B, C, D we can see that it is in star connection with common point as B.
Converting it into delta connection,
[Tex]R_1=2+2+\frac{2X2}{3}=\frac{16}{3} \Omega \newline R_2=2+3+\frac{2X3}{2}=8 \Omega \newline R_3=2+3+\frac{2X3}{2}=8 \Omega [/Tex]
Now applying the parallel combination we get resistances as[Tex]R_{AD}=\frac{8}{9}\Omega \newline R_{AC}=\frac{16}{3}\Omega \newline R_{CD}=\frac{8}{3}\Omega [/Tex]
Now we will use parallel combination and series combination to find an equivalent resistance,
[Tex]\frac{\frac{16}{3}X\frac{32}{9}}{\frac{16}{3}+\frac{32}{9}}=\frac{32}{15}\Omega \newline \frac{32}{15}+3=\frac{77}{15}\Omega [/Tex]
From the above circuit, we can calculate the value of I as [Tex]I=\frac{5}{77/15}=0.974A [/Tex]
Star to Delta Conversion
In this article we will discuss about star to delta conversion. We will first discuss about star and delta connections, current and voltage equations in these circuits. Then we will discuss about the differences between the star and delta connection. We will also discuss in detail the steps followed to derive the equations for conversion. In addition to this we will look into some solved examples that will help us understand the concept better. Later in the article we will discuss about the applications, advantages and disadvantages of this conversion.
Table of Content
- What is Start and Delta connection?
- Characteristics
- Difference between star and delta connection
- Conversion of Star to Delta
- Solved Example on Start to Delta conversion
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