Determine the value of equivalent resistance across nodes a and b.

Correct option is A

The given circuit is

here 2Ω∥2Ω

​$$\text{Total resistance} = \left( \frac{1}{2} + \frac{1}{2} \right)^{-1}$$

$$\text{So the total resistance is } 1\Omega, \text{ here } 4\Omega \parallel 4\Omega$$

$$\text{Total resistance} = \left( \frac{1}{4} + \frac{1}{4} \right)^{-1}$$​​​​

So the total resistance is 2Ω,

As we see that the above figure is a balanced wheat stone bridge and no current would flow from 3 ohms resistor.
So, the resistance across "a-b" would be equal to
R= (1+2)∥(1+2)
=1.5 ohms)