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When 2 cells is connected in series of the same emf like the following: enter image description here

[just the part of the circuit that I need...]

The resultant emf will be twice as the previous identical emf.

If we reverse any of the the two cells (I mean let the negative side of one cell face the negative side of the other), what happens then? If the two cells were of different emfs then the current would have followed the magnitude and direction of the cell which has greater emf. But what if the cells are of the same emf?

Now for the parallel connection of cells, I really don't have any idea what happens except for the fact that when they are of the same emf, they behave like one cell but provides longer life of batteries. I will want to know about the following circumstances :

enter image description here

(1) What happens in this picture? (2) What happens if the emfs are not the same (in the same picture)? (3) What if the orientation of the cell's - and + sides were the same and they were of different emfs?

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$Kirchhoff's\space law$ can prove useful here.

Case 1. Consider a closed circuit with two batteries, of emf $V_1$ and $V_2$, and a resistor of resistance R (all in series). A circuit with no resistance will catch fire. The resistor is added to prevent short circuiting.

According to Kirchhoff's law,

(i) If the $+ve$ terminal of a battery is connected to the $-ve$ of the other :

$V_1 + V_2 -IR=0$

In this arrangement of batteries, their emfs will just add up. No problem encountered here.

(ii) If the $+ve$ terminal of a battery is connected to the $+ve$ of the other :

$V_1 - V_2 -IR = 0$

In this arrangement of batteries, the emfs will subtract. The battery with larger emf will decide the current's direction. The current will be directed from the $-ve$ to the $+ve$ terminal of the battery with larger emf.

If batteries of same emf are used then their emfs will simply cancel out, resulting in zero current.

Case 2. In a circuit with parallel batteries as shown by the 2nd picture in your question, you can find out the direction of the current and the net emf just like it was found in Case 1. You just have to apply Kirchhoff's law correctly. Also, do not forget to insert a resistor.

Kirchhoff's law will prove to be a very useful tool. You just have choose a closed loop and use the sign conventions appropriately.

FYI, for kirchhoff's law to work you can assume any direction of current in the closed loop, either clockwise or anti-clockwise. If you assumed the correct direction of the current, you will get a positive value of current, otherwise negative implying the current is flowing in the direction opposite to the assumed one.

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