Calculate the equivalent resistance between A and B in the following circuits :

To evaluate the resistance between two points A and B which are called given points, we will do the questions by imagining that a battery is attached to these two points A and B and there is formation of complete circuit, so these two points would have potential difference(V) and hence resistors attached to these two points by both sides would be parallel to each other because of same potential difference across the ends.

Therefore we can’t merge these two points, we can’t merge the other points just by looking at them blindly.

We will solve the questions by diagram wise and not by writing for proper understanding.

This figure is given in the question, now we do not need to get afraid and be confuse that the wires are curved or anything, make the curved wires straight if you want to make it more easy to solve.

Now the 2 ohm resistors on upper half of circle are in series to each other and the 2 ohm resistors in the lower half of circle are in series to each other, so the net resistances in both the halves is,

2ohm + 2 ohm = 4 ohm,

So our figure resolves to,

Now both the 4 ohm resistors are in parallel to each other because of the two given points between them A and B.

R = 2 ohm.