In this picture, there are two capacitors C1 and C2 joined in series and connected to a battery. We know there are two terminals in a battery, a positive terminal and a negative terminal.
The potentials of the positive and negative terminals are +P and -P respectively. And there potential difference, in other word the voltage of the battery is V.
The plate on the left side of the capacitor C1 is directly connected to the positive terminal of the battery. So its potential will also be +P. Similarly the potential of the plate on the right side of C2 will have a -P potential.
A) I am assuming the magnitudes of the potentials of the opposite sides of the battery are same just different in signs. For the right plate of C2 to have a potential -P it takes -q amount of charge. The left plate of C1 also gives off this equal amount of charge and acquires the state +q. Since C1 and C2 are two different capacitors, why gain or loss of same amount of charge would cause them to have the same magnitude of potential?
B) If the left plate of C1 has a charge of +q and a potential +P, then C1's other plate should also have the potential -P as it has -q charge. Because two plates of the capacitor C1 are same in material and geometry. Similarly left plate of C2 has to acquire to the potential +P. If this happens then the voltage of C1 and C2 will be same V and net voltage of the two capacitors will become 2V which is wrong.
If someone could clarify this confusion it would be a big help.