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 is the figure given in the question, Now we are given with two sets in which there are three 3 ohm resistors in parallel combination to each other.

So let’s first name these sets, the left set is set 1 and the right set is set 2 and the middle 1 ohm resistor is in series to these two sets.

Now let’s solve these two sets first to minimize the number of resistors, so,

R = 1 ohm,

So our figure resolves to,

Now as we can see these three 1 ohm resistors are in series to each other, so they will get add up algebraically like simple numbers,

1ohm + 1ohm + 1ohm = 3 ohm.

Now our figure resolves to,

Which is our final figure.