What is the Potential Difference between points a and b in this circuit?

[mr_coffee]

Hello everyone i have the follwoing circuit:
http://www.webassign.net/hrw/hrw7_27-34.gif I need to find the Potential Difference between a and b. I found the current of R1 and R2, and the questions says:
R1 = 130 , R2 = 75 , and the ideal batteries have emfs E1 = 6.0 V, E2 = 5.5 V, E3 = 4.0 V.

R1 current = .042A
R2 current = .0467

Im confused on what I should add u using kricofs rule? like do i just say
Va = -E2 -E3+ R1*i2 + Vb
Va -Vb = -E2 -E3+ R1*i2
But there is a resistor that looks like paraellel, but is that R1 parellel to R2?

 

[quantumdude]

But there is a resistor that looks like paraellel,

Not to me they don't!

but is that R1 parellel to R2?

Certainly not. To be in parallel they have to have the same potential difference across them no matter what the values of \mathcal{E}_1, \mathcal{E}_2, and \mathcal{E}_1 which is clearly not the case.

Also, note that R_1 is in parallel with \mathcal{E}_2, but that R_2 is not in parallel with \mathcal{E}_2. Since they are not both in parallel with \mathcal{E}_2, there is no way that they could possibly be in parallel with each other.

 

[quantumdude]

like do i just say
Va = -E2 -E3+ R1*i2 + Vb
Va -Vb = -E2 -E3+ R1*i2

That's not right. If you follow the path from a to b you do not go through R_1.