Two battery current & EMF problem

[bcjochim07]

The question was to find I1 I2 and E. I got those parts of the question correct.
I1= 1 A
I2 = 2A
E = 15V.

But the only reason I got these right is because the arrows for I1 & I2 were given in the attached figure. The directions of the current don't make sense to me. If the EMF from the right battery is greater shouldn't the current flow from right to left, splitting at the junction with the 3 ohm resistor and the 2 ohm resistor?

 

[Hootenanny]

Whilst intuitively it may not make sense that the current flows clockwise around the left hand loop, Kirchoff's laws in fact show that this must be case - as you have seen.

The important point to note there is that when you initially 'choose' the direction of the current it doesn't matter if you 'choose' the 'wrong' direction, provided that you stick to that direction throughout the entire question. For example, if I₂ had been pointing in the opposite (i.e. anti-clockwise) you would have obtained an answer of I₂=-2A. Which would mean that the current was flowing in the direction indicated by the diagram and against your original choice.

Does that make sense?

 

[bcjochim07]

Ok, yes, that makes sense that I would know because it would turn out negative. It just seems to me that the current has to go up through one battery and down through the other of lesser EMF. That's the way it turned out in most of the other problems I have done.