Electric Potential at Points within a Circuit

Question

Consider the following circuit consisting of 2 batteries and 2 resistors.

How would I find the value of the potential at points $a$ and $b$?

In my initial attempt I assumed that the value of the current was consistent throughout the loop (which is where I think I went wrong) and tried to use Kirchoff's Loop Rule, giving, but seeing as there are no nodes I'm not sure how to go about solving it after.

Additional Info Edit: Using Kirchoff's, I thus far found:

V1 - R1*I - V2 - R2*I = 0

Solving for current:

I = (V1 - V2) / (R1 + R2)

And so the potential difference across is R1 is V = R1*I = R1*(V1 - V2) / (R1 + R2).

So the potential at a would be V1 - R1*(V1 - V2) / (R1 + R2).

Answer 1

Some comments: first off, $I$ is called "current," not "intensity." More importantly, you say the "potential difference across is V," but you don't clarify across what. And you seem to have solved for in the end the potential difference between b and a rather than the potential at a.

As a starting point, think about what it means to measure "the potential at a." Only potential differences have a physical meaning- so when we refer to "the potential at a," we really have to mean "the potential at a, relative to some point we define as having zero potential." What is the point defined to have a potential of 0? Once you figure that out, you should be able to find the potentials you're looking for.