# Delta-Star Combination Exercise

This post is regarding exersise 4-8 from the following book: Hughes Electrical And Electronics Technology 10th Ed.

Here it is: Let's focus on what I tried for solving part (b) :

Since this is an exercise under the chapter for delta-star transformations my first thought was to try and perform some such transformation. However this was a combination of both star and delta connections so I didnt really know whether the resulting resistances would be in series / parallel or neither, with the already existing ones, so I tried both series and parallel: However neither worked.

My next thought was that maybe I have understood something very badly about the resulting resistance of two points in a circuit. So after a little bit of digging I tried the following: However I again got a wrong result in regards to the given answers at the end of the book.

Conclusion:

• Which approach (if any) was correct?
• If no approach was correct, which concept do I need to understand better?

Any help/hint is very much appreciated

• I don't think any of your approaches makes sense and also you didn't explain anything how you draw these equivalent circuits Oct 3, 2020 at 17:35
• Take the delta, transform into a star. You have two start in parallel which is easy to simplify. Or take the star. transform into a delta. Two deltas in parallel. Or both, transform the final delta into a star (or vice versa) to check you get the same answer.
– user16324
Oct 3, 2020 at 18:33
• @BrianDrummond this is what it tried(first picture), i guess i made some computational error, will try again Oct 4, 2020 at 7:16
• @BrianDrummond I have concluded that i have not made any computational mistake, the resulting Resistance from A to N turn out to be 0.98 ohm with this method, which by the book is wrong, it should be 1.45 ohms Oct 5, 2020 at 9:14
• @BrianDrummond it worked for part (a) however so I am clearly doing somethiing wrong Oct 5, 2020 at 9:29

To calculate equivalent resistance between A and N one approach would be -

1.look at NCB which is in Delta connected form

2.make NCB in star connection from delta by conversion formula

after that conversion you'll get a very simlified circuit which is very easy to solve

• I see what you mean, and it worked, I posted the full solution as an answer here. Thank you so much! Oct 5, 2020 at 10:58

I figured it out, this is the answer for part(b) "Finding Equivalent resistance from A to N".

First of all, here is a nicer sketch: Now we will focus at the delta connection defined by N , B , C : And now if we go back to our original sketch and replace the converted circuit we can greatly simplify it: Finally, we are ready to compute the equivalent resistance from A to N: 