Observe the circuit given and find the resistance across AB.

As we can see there are two sets of resistors, one is at left and the other is at right, both have 2 resistors in parallel each of 1 ohm. As the sets have parallel resistors, so, we can simplify them and make them one resistor to get the equivalent resistance of the circuit.

We will solve one set first and in the similar way the second set, we know that when resistors are parallel we add the reciprocals of the resistors and we equate it to the reciprocal of the total resistance after cross-multiplying we get the total resistance of the circuit.

Let the total resistance of the set A be R_A and the total resistance of the set B be R_B.

So,

, R_A

Similarly, R_B = , Hence as the two resistors in the sets are simplified and merged to a single resistor in each set, Therefore the resistors now left are R_A in set A and R_B in set B which are in series with each other because when we resolved the 1 ohm resistors which were in parallel they got merged and attached to the main circuit wire.

Now when resistors are in series we add them algebraically or simply like we add two integer numbers.

R = r₁ + r₂ + …………………. add all the resistors

As R_A and R_B are 0.5 ohm calculated by us, so when we add them we get 1 ohm as the answer.