# Direction of resulting I through simple circuit with 2 voltage sources separated by 2 resistors in series?

I'm wondering how to find out which way the resultant current flows when you've got a really simple circuit with two voltage sources separated by 2 resistors in series. See the below circuit (the bottom part is supposed to be earthed in the original circuit, I guess this applies to any equivalent circuit for analysis). The current direction on the diagram is supposed to be the right answer: Now how does one go about it conceptually and how would one solve this specific problem for instance. In a way it seems so confusing with 2 voltage sources, and also a bit strange that the current is supposed to go from left to right, when the voltage source to the right provides a higher voltage. One would think from Ohm's law that a higher voltage would provide a higher current (easy to see since the resistors are equal in size), so the current from the right would "win" over the other. The question refers to electron current, but use the symbol I, so I would think what they are after is the way the current flows and not the electrons (since we know that the electrons physically run in the opposite direction of the current I).

According to Kirchoff we know that the sum of currents into node m is equal to 0, since there are only 2 entries into the node, it means both currents equal each other in magnitude, however they are opposite in direction. We also know that the same resultant current runs through both resistors. But the resulting current is not zero, and how can we find that one?

In the original circuit the bottom part is earthed, and I guess that of course would apply for any equivalent circuit when analyzing the situation.

• If you are trying to determine an unknown current you must assume that it flows in a certain direction. The current is then determined using nodal analysis, Kirchoff's laws, superposition, or whatever is easiest. If the current calculation results in a positive value the assumed direction is correct; if the calculation results in a negative value the actual direction is opposite to that assumed.
– Chu
Apr 27, 2015 at 12:52