Dear Mate ,
To find the equivalent resistance between A and B in the situation shown :
The given circuit can be drawn as a Bridge with a resistance R in the middle.
Now we see that since the product of the diagonal resistances are equal so no current will go through the middle portion and so we can omit that resistance R in the middle.
So, the left out resistances are in series parallel combination.
Equivalent resistance in the above portion = R + R = 2R (series combination)
Equivalent resistance in the below portion = R + R = 2R (series combination)
Total Equivalent resistance = R (parallel of 2R and 2R).
Hence the total equivalent resistance will be R.
Regards~
