Simple problem with voltages

[nickxyzt]

TL;DR: simple problem with voltages

I have a very simple problem with voltages, and I think that the answer in my book is wrong.

In the attached image, what's the voltage between A and B, expressed with E1, E2, I and r?
(The answer in the book is 2Ir + E1 - E2, but I think that is should be -2Ir + E1 - E2).

Thank you!

 

[Dale]

It looks like $V_{AB}=0$ to me since they are directly connected by a wire.

Is the triangle for $I$ just supposed to represent the direction of the current or is it supposed to be a current source?

 

[nickxyzt]

Thank you for replying. Of course V_AB = 0, but the problem is how to express it using E1, E2, I and r (it's a question from an exam).
My dilemma is if it's 2Ir + E1 - E2, or -2Ir + E1 - E2.

There is no reference about the direction of the current I, just that "the current goes through the wire", I guess it can also be negative.

 

[Baluncore]

Is the triangle for just supposed to represent the direction of the current I, or is it supposed to be a current source?

The arrow must represent a conventional current source, or there could be no potential difference between the points A and B..

 

[DaveE]

The voltage at B wrt A is $(V_B-V_A) \equiv V_{BA}=E_1-E_2-2IR=0$
The current arrow drawn is an arbitrary polarity definition, so we'll all agree about the signs in the equation. Except your instructor, apparently.

 

[nickxyzt]

Got it. Thank you!

 

[DaveE]

Perhaps a better schematic would help:

 

[Philip Nigel Wood]

I agree with both you @nickxyzt and @Dale, but consider the wording of the question very confusing – especially for an exam question. It would be clearer to ask for an equation relating E₁, E₂, r and I.