If I have a simple, 2 loop, circuit with two voltage sources on opposite ends of the circuit, the currents meet at a node and then move down. What would be the voltage at that node, to the two different voltages from the two different currents interact with each other?

 

You need to provide a sketch of what you are talking about. It sounds like you are talking about two voltage sources that are connected directly together in what case, if they are ideal sources, the voltage will be undefined and you will have infinite current flow. But that may not be what you have in mind. Provide a sketch so that we are on the same page.

 

 

Voltage is a field. The fact that two currents meet at a node tells us absolutely nothing about the voltage at the node.

 

Okay, so there aren't any problems of the type I mentioned because the branches with the voltage sources also have resistors (or at least one of them does).

So next you need to show your best attempt to solve the problem -- it doesn't have to be correct, but we need to see how you are going about it so that we can see what you are doing right and what you are doing wrong. Also, so that we can tailor our answers to match the techniques you are using. The basic answer to your question, however, is that the voltage at the middle node will be whatever is required in order to satisfy KVL around all of the loops and KCL at all of the nodes.

 

To be honest, I don't have a problem, I am just talking about it theoretically. I think I understand this better somewhat though.

 

R3 in your diagram isn't connected. You will notice the dots on both sides of all the other devices connected to the wires.

Any analysis you ran with that did not show any current through or voltage across R3.