Find theh potential difference between points a and b.

Explanation

First step in such problems sloving happens to be the current dirtribution. You can see the upper branch has total reistance `1 + 2 = 3 Omega` and lower branch has total `2+1 = 3 Omega` . The means to both upper and lower braches have equal resistance , so the incoming 2 ampere current will be divding itself equally in upper and lower branch i.e., 1 ampere current will flow in each branch as follows :

Next step is to show the relative higher and lower potential ( by + and - sign) across each resistance . Remember potential along the currnet across a resistance decrease.

Now you have to move from a to b through any path on the circuit (because potenital difference depends only on the initial and final point) say left side circuit i.e., first `1Omega` and `2 Omega` . We are writting the potential of a as `V_(n)` and that of b as V.
Start from a then cross `1Omega` . You are moving - to + side on `1Omega` , so you are gaining potential by IR= 1A. `1Omega` = 1V. Now jump across `2 Omega`. You will lose potential `IR = 1A. 2Omega = 2V` and then you.ll reach potential `V_(B)` .

So , `V_(a) + 1 - 2 = V_(b)`
`therefore V_(a) - V_(b) = 1` volt
You could very well choose the right side circuit as well and you.ll get the same answer as shown below.

or `V_(a) -2 + 1 = V_(b)`
`therefore V_(a) - V_(b) = 1` volt .