Stumped on a resistance problem

[gstatejoe]

Hello! I have tried for roughly 3 hours now with no success on this one problem. My professor assigns webassign's (homework submittal process) for just review...which isn't graded or anything and I can't seem to get this one
correct.

[I cannot imitate the emf symbol which looks like a capital script E, so I have subsituted that symbol with 'E'.]

Here is the problem:
In the figure below, the resistances are R1 = 1.3, R2 = 1.5 , and the ideal batteries have emfs E1 = 2.0 V, and E2 = E3 = 4.5 V.

http://img81.imageshack.us/img81/9648/help6nt.gif

The problem asks for the following:
1.) What is the current through battery 1, 2 and 3
2.) and What is the potential difference Va - Vb ?


My answers were:
Batteries 1, 2, 3, = .74 A, .373 A, .373 A
Potential Difference = 3.941 V

Some of the equations I manipulated to get values:
Vb - Va = E2 - IR2 = R1 + (2R1)(2I)
I = (e2 - e1 / 4R1 + R2)

I did the problem in the book which was similar except it had different numbers, and I got that one right. But this one comes out wrong.
Can you guys tell me what I am doing wrong, and if you are able to solve the problem, what values did you get, and more importantly, how did you get them?

THANKS!
Joseph
GSTATE!

 

[big man]

Can't see your image 'cause it's pending approval...is there any way you can just host it on imageshack and post up a link??

 

[gstatejoe]

Ah, sorry about that big man, I wasn't aware that it required authorization. Here you go:

http://img81.imageshack.us/img81/9648/help6nt.gif

Thanks

 

[vanesch]

The trick is to call the potential difference between a and b, V.
This leads, for each branch, to an equation:
I1 = (V - E1) / 2 R1
I2 = (V - E2) / R2
I3 = (V - E3) / 2 R1
(that's the total potential difference per branch over the total resistance over each branch).
We have one further equation (Kirchhoff): I1 + I2 + I3 = 0.
This system of 4 equations has 4 unknowns: V, I1, I2 and I3.
cheers,
Patrick.