My teacher told me that two batteries' emf cannot be added in a parallel circuit but can be added in a series circuit. However I can't seem to fully grasp why and I think there may be some loopholes in my understanding of emf. I've attached two photos to illustrate my argument for why I think two batteries in an emf can be added in a parallel circuit.
To exemplify my argument, I've drawn a circuit with two batteries of 9V and 3V in the first diagram. The two batteries' terminals are opposite to each other.
This diagram can then be redrawn like this (diagram 2).
From my understanding of emf of a battery, it is the energy supplied per unit positive charge, by the battery, in moving the charge from the negative terminal to the positive terminal of the battery. It can therefore be thought of as the potential difference between the two terminals. In the case of the 9V battery drawn, I can take the negative terminal of the 9V battery to have a potential of 0V and the positive terminal to have a potential of 9V, hence the PD between the two terminals will be 9V-0V=9V. This can then be similarly applied to the 3V battery where its negative terminal has a potential of 0V and its positive terminal has a potential of 3V.
As shown in diagram 2, since the 9V and 3V batteries are connected in parallel at the point of the two thick dots drawn, hence they share a common potential difference at those two points. The potential at the left thick dot will have a potential of 9V+0V (drawn in blue) due to the 9V battery's positive terminal and 3V battery's negative terminal. Similarly, the potential at the right thick dot will have a potential of 0V+3V (drawn in blue) due to the two batteries' terminals. Therefore the potential difference between the two thick dots will be 9V-3V=6V. Therefore, showing that batteries emf can be added (or subtracted in this case since the two terminals are in opposite direction).
In the end, the circuit can thus be drawn as a battery with 6V like this.