https://drive.google.com/open?id=0B3IenBvKWb4PMkdPUUd6eV94U1o0MUdCenV0SmRHVGlZVUdv
This question was asked in the admission test of a popular coaching institute.
My attempt to solve this question:
The current enters from A and divides into two branches which are parallel to each other. At C the current further divides into two branches. It gets very complicated after this and i am stuck at this point. I cannot figure out what is parallel to what and what will happen when the current from the two branches meet each other.

 

Oh, yeah! Like I am going to click on a Google drive link from an unsolicited source...

 

@djsfantasi for some reason i am unable to upload the image. The link is safe.

 

Hello,

You should be able to upload an image with the "Upload a File" button.
For now I will upload the image:


Bertus

 

Thanks @bertus

 

This question was asked in the admission test of a popular coaching institute.

what kind of coaching?

the line BC shorts all the inner resistors. so Rab = R//0.5R.

 

@dannyf, its a coaching institute that prepares students for JEE in India.
I have one doubt. In the question, there is no potential difference between C and B and I had read in my book that a potential difference is necessary for flow of charges. If there is no potential difference between two points, will current flow between them or not.

 

This is a double-trick question. @dannyf got the first trick with the B-C link shorted. The second trick is to realize the equivalent resistance will be less than R/2. The answer list has only one selection that is less than R/2. No calculation necessary!

 

...will current flow between them or not.

The answer is obviously NO, because C and B are the same point. A line on a schematic is not the same as a wire. Although one may designate a point with different names, it nevertheless remains the same point.

 

https://drive.google.com/open?id=0B3IenBvKWb4PMkdPUUd6eV94U1o0MUdCenV0SmRHVGlZVUdv
This question was asked in the admission test of a popular coaching institute.
My attempt to solve this question:
The current enters from A and divides into two branches which are parallel to each other. At C the current further divides into two branches. It gets very complicated after this and i am stuck at this point. I cannot figure out what is parallel to what and what will happen when the current from the two branches meet each other.

The approach you are trying to take is far too mechanical. It also suffers from the problem of being applied from the outside in instead of the inside out.

As others have already pointed out explicitly -- instead of dropping hints to help you discover it on your own, which means that you are far less likely to actually learn the knowledge they are spoon feeding you, so make sure you really understand why what they are telling you applies and how you should be able to spot things like it in the future -- the key is that there is a short between points C and B. A number of things stem from this. First, points C and B are at the same potential, which effectively makes the A-B path through R in parallel with the A-C path through R/2. A more mechanical approach is to note that the outside path from C to B is going through a zero ohm resistor and that the inner path from C to B is in parallel with this. The parallel combination of zero ohms and anything is zero ohms. Thus the path from C to B reduces to a zero ohm resistor which is in series with the R/2 ohm resistor from A to B. The end result is that we again have R/2 in parallel with R. Since we know that the equivalent resistance of two resistors is less than the smaller of the two, we know that the total resistance is less then R/2. In this particular case, this is enough to choose the correct answer since only one of the options is viable. But if other choices that were less than R/2 had been offered, we can narrow it further and note that the equivalent resistance has to be larger than half of the smaller resistance, so the correct answer has to be more than R/4.

It is common for at least some questions on this type of exam to be set up so that if you can spot these constraints you can answer the question in almost no time instead of spending time to come up with the answer through more brute force ways.

See if you can figure out how to answer the prior two questions using reasoning like this.

 

@WBahn , I am getiing R/2 as answer for question number 23 which is not in the options.
I noticed that the circuit divides into two branches in the middle, and the lower branch has no resistance. The effective resistance of both the branches is 0 and now only two resistors are left which are in parallel (between A and B) and so equivalent resistance=R/2.

 

@WBahn I tried solving for question number 23 in another way. I did not take the net resistance to be zero. The end points of the middle line are equipotent. So i represented them by a single point and redrew the circuit. I got 2R in parallel with 2R. The equivalent resistance comes out to be R. I cannot understand what is wrong with the first approach(in the above post).

 

If you move the bottom line to the middle it does not change the circuit, but does it change your perception of the circuit?

 

@RBR1317 , it looks to me like the previous one only. Now also the circuit divides into two branches and the equivalent resistance is zero due to a branch having zero resistance.

 

So here is another way of looking at it....

 

@RBR1317 But the zero parallel resistor still makes the equivalent resistance of the two branches zero. Doesn't it?

 

the zero parallel resistor still makes the equivalent resistance of the two branches zero. Doesn't it?

It depends on what you're finding the equivalent resistance of. What two points are you using to find Req?

 

@RBR1317 I was finding the equivalent resistance between the end points of the middle blue line.

 

equivalent resistance between the end points of the middle blue line.

In that case you are correct. However, question #23 was asking for something else.

 

@WBahn , I am getiing R/2 as answer for question number 23 which is not in the options.
I noticed that the circuit divides into two branches in the middle, and the lower branch has no resistance. The effective resistance of both the branches is 0 and now only two resistors are left which are in parallel (between A and B) and so equivalent resistance=R/2.

This is a very ambiguous description. What does, "divides into two branches in the middle" mean? Which branches are "both the branches" that are 0.

The best way to describe circuits is via schematics. If you want to use words then they must be chosen very carefully in order to convey exactly what you mean.