How Do You Calculate the Potential Difference Between Two Points in a Circuit?

[abcdmichelle]

Homework Statement

For the circuit in the figure below, V = 3.56 V and R = 2.04 Ω. Find the potential difference between points a and b.

This is the link to the figure: http://i749.photobucket.com/albums/xx137/abcdmichelle/physics/26-62alt1.gif

Homework Equations

V=IR

The Attempt at a Solution

So I needed to find the current passing through R.
I said that the resistor at the top left had current I, the resistor at the top right was I(2), the resistor at the bottom left was I, the resistor at the bottom right was I(2), and the resistor R in the middle had a current of I(3).
I applied the junction rule and the loop rule to the left hand side loop, and found the current to be:

2-I-2.04I(3)-3.56+I=0
Current I(3)=0.76

So then to find the potential difference I did:
V= -(0.76)(2.04)-3.56

This is wrong, I'm not sure if I did anything right here!
Please help!

 

[tiny-tim]

welcome to pf!

hi abcdmichelle! welcome to pf!

(try using the X₂ tag just above the Reply box )

2-I-2.04I(3)-3.56+I=0
Current I(3)=0.76

no, you've canceled the potential differences for the two 1Ω resistors … the current is flowing the "same" way through them, so they will add

also, you normally need two loop-equations to solve a two-loop problem (though in this case you can get a relationship between I₁ and I₂ from symmetry)

(btw, are the 2V batteries 2 volts, or 2 times 3.56 V ? )