1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution Here is what I don't understand: how can this circuit exist? If you look at the V2 node, there are 3 currents going in but none going out. Isn't this a contradiction? From what I've heard, you can arbitrarily draw current arrows and if the direction of the arrows is wrong, you'll just get a negative current. But don't you have to at least be consistent in the rotation? If you look at the bottom left mesh, the currents are going clockwise and then there is a current that is going counter-clockwise.