## Solved Examples on Star/Delta Transformation

Q1). Determine the resistance between the terminals A&B
and hence find the current through the voltage source. Refer figure 16.1

Answer:

See figure 16.1(a)

The resistors in between point 1, 2&3 are about to
replace by a star connected system. Otherwise is difficult to find the total
resistance.

So we have to use the delta to star transformation
equations.

*R*_{1}= R_{12}R_{31}/ (R_{12}+R_{23}+R_{31})*R*60*40)/ (60+40+100)

_{1}= (

__R___{1}= 12Ω

*R*_{2}= R_{23}R_{12}/ (R_{12}+R_{23}+R_{31})
R

_{1}= (100*60)/ 200

__R___{1}= 30Ω

*R*_{3}= R_{31}R_{23}/ (R_{12}+R_{23}+R_{31})
R

_{3}= (100*40)/ 200

__R___{3}= 20Ω
So we can redraw the network as shown in figure 16.2

Now we can easily find the total resistance between A&B
terminals

R

_{total}= [(80+20)//(88+12)] + 30
R

_{total}= 50 + 30

__R___{total}= 80Ω
Applying ohm’s law to the total resistance,

I = V/R

I = 160v/80Ω

__I = 2A__
Q2) Find the total resistance between A&B terminals for
the network shown in figure 16.3

Answer:

See figure 16.3(a)

We are about to replace the delta system by star system in
between point 1, 2 &3

So we have to use the delta to star transformation
equations.

*R*_{1}= R_{12}R_{31}/ (R_{12}+R_{23}+R_{31})
R

_{1}= (3*6)/ (3+6+9)

__R___{1}= 1Ω

*R*_{2}= R_{23}R_{12}/ (R_{12}+R_{23}+R_{31})
R

_{2}= (9*3)/18

__R___{2}= 1.5Ω

*R*_{3}= R_{31}R_{23}/ (R_{12}+R_{23}+R_{31})
R

_{3}= (6*9)/18

__R___{3}= 3Ω
So now we can replace the system as shown in figure 16.4

Now we can easily find the total resistance between A&B
terminals

R

_{AB}= (7Ω+3Ω) + (8.5Ω+1.5Ω) + 1Ω

__R___{AB}= 6Ω
Q3). Find the total resistance between A&B terminals (R

_{AB}) shown in figure 16.5
Answer:

You must understand that you have to use star/delta
transformation for this problem. Unlike other problems, in this case it is not
pointed out which system of resistance you must replace. So you yourself have
to point it out.

This is very important. Though the tutorial problems guide
you to find the replaceable systems, in practical level you will have to guide
yourself manually. This means you must know how to choose the correct system to
apply delta/star transformation.

See figure 16.6

See the circled systems in the figure. You have to replace
these systems with delta systems. If you see it carefully, you’ll see that both
systems are same (one is upside down of the other). So you don’t need to find
two different sets of delta systems. See figure 16.7

This figure shows you the star to delta transformation. As
the required equation for transformation are given in my previous post, I’ve
directly put the values for the delta system shown in the above figure. Steps
for this calculation are shown below.

*R*_{12}= R_{1}+ R_{2}+ (R_{1}R_{2}/R_{3})
R

_{12}= 3 + 2 + (3*2)/2

__R___{12}= 8Ω

*R*_{23}= R_{2}+ R_{3}+ (R_{2}R_{3}/R_{1})
R

_{23}= 2 + 2 + (2*2)/3

__R___{23}= 16/3Ω

*R*_{31}= R_{3}+ R1 + (R_{3}R_{1}/R_{2})
R

_{13}= 3 + 2 + (3*2)/2

__R___{13}= 8Ω

So we can redraw the network as shown in figure 16.8

Now we can easily find the total resistance between A&B
terminals. For your better understanding I’ve simplified the network. See
figure 16.9

So now it is simple.

R

_{AB}= { [ (7+5)//8//8 ] + 5 } //8//4
R

_{AB}= (3 + 5) // 8 // 4
R

_{AB}= 4//4

__R___{AB}= 2Ω
Pabindu lakshitha

B.Sc. (Engineering Undergraduate)

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ReplyDelete16.6 couldnt underatand plz help

ReplyDeleteHow we understand that on RHS 56 is in parallel with 8

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ReplyDeleteYes... This is very helpful but in 2nd problem equivalent resistance is wronly calculated I think.. So when I was solving it I found terminal 1 +[terminal 2||terminal 3]

ReplyDeletePlease explain if I am wrong...

Yes... This is very helpful but in 2nd problem equivalent resistance is wronly calculated I think.. So when I was solving it I found terminal 1 +[terminal 2||terminal 3]

ReplyDeletePlease explain if I am wrong...

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