What is the current in a circuit with two voltage sources in series? 
What happens? We have 2 voltage sources and 2 currents. When I2 and I3 come together (they have opposite sides), what happens?
I tried writing down the voltage relations but I'm stuck because I don't know what current should I work with (to determine positive sides): I2 or I3?
 A: Well, a net current results. 
I will write the general equation for the current, and determine all possible scenarios, keeping in mind that in writing this equation I assume the current is going clockwise (I assume the left voltage source is at a higher potential, and if this wasn't the case, my current will simply be negative and it will be flowing counter-clockwise.)



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*: my assumption is correct and the net current will flow in the clock-wise direction (going toward the right voltage source, entering the positive terminal.)

*: the net current is zero.

*: my assumption is wrong and hence the net current will flow in the counter-clockwise direction.



Notes:


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*Please stick to the scientific nomenclature. It is important because we have to be on the same page and talk the same language. What do you mean by "intensity"? Is it the electric current intensity, the electric field intensity, or what? You can call it the current, current intensity, the electric current, or the electric current intensity.

*In electrical engineering we don't usually call a voltage source of this symbol (the symbol you drawn) a generator. Yes it is correct that it generates a voltage, but this symbol is used for DC voltages (static E-field potentials) of low values, for example: batteries, whereas a generator is usually used for AC signals or DC generators of very high values (like what electricity stations produce.), so we call it a voltage source or a battery.

