Monday, September 17, 2012

Star Delta Transformation (Solved Problems)



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.

R1 = R12R31 / (R12+R23+R31)

R1 = (60*40)/ (60+40+100)

R1 = 12Ω

R2 = R23R12 / (R12+R23+R31)

R1 = (100*60)/ 200

R1 = 30Ω

R3 = R31R23 / (R12+R23+R31)

R3 = (100*40)/ 200

R3 = 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

total = [(80+20)//(88+12)] + 30

Rtotal = 50 + 30

Rtotal = 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.

R1 = R12R31 / (R12+R23+R31)

R1 = (3*6)/ (3+6+9)

R1 = 1Ω

R2 = R23R12 / (R12+R23+R31)

R2 = (9*3)/18

R2 = 1.5Ω


R3 = R31R23 / (R12+R23+R31)

R3 = (6*9)/18

R3 = 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

RAB = (7Ω+3Ω) + (8.5Ω+1.5Ω) + 1Ω

RAB = 6Ω


Q3). Find the total resistance between A&B terminals (RAB) 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.

R12 = R1 + R2 + (R1R2/R3)

R12 = 3 + 2 + (3*2)/2

R12 = 8Ω

R23 = R2 + R3 + (R2R3/R1)

R23 = 2 + 2 + (2*2)/3

R23 = 16/3Ω

R31 = R3 + R1 + (R3R1/R2)

R13 = 3 + 2 + (3*2)/2

R13 = 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.

RAB = { [ (7+5)//8//8 ] + 5 } //8//4

RAB = (3 + 5) // 8 // 4

RAB = 4//4

RAB = 2Ω



Pabindu lakshitha
B.Sc. (Engineering Undergraduate)


32 comments:

  1. nice blog


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    ReplyDelete
  2. Electrical engineering is considered to deal with the problems associated with large-scale electrical systems.

    Electrical Engineering Consultant

    ReplyDelete
    Replies
    1. yes of course. you may go to the top of the page. the word "Fundamentals" is there

      Delete
  3. good and helpfull blog

    ReplyDelete
  4. Hey man, tnx for the tips, I REALLY NEED THIS IN MY BASIC EE CLASS :)

    ReplyDelete
  5. Thanks a ton mate its really helpful

    ReplyDelete
  6. its really helpful .God bless u moreee

    ReplyDelete
  7. its helpful to ee engineers

    ReplyDelete
  8. Really helpful material. I just solved another problem after getting ideas from here.
    Many thanks to the author(s).

    ReplyDelete
  9. How we understand that on RHS 56 is in parallel with 8

    ReplyDelete
  10. Really it's fantastic ...

    Thank you so much :)

    ReplyDelete
  11. Really it's fantastic ...

    Thank you so much :)

    ReplyDelete
  12. very very nice thank you so much

    ReplyDelete
  13. 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]
    Please explain if I am wrong...

    ReplyDelete
  14. 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]
    Please explain if I am wrong...

    ReplyDelete
  15. this was simple and straightforward. was much needed, thanks.!!

    ReplyDelete

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