Sum of e.m.f.s

I know to get the resistance you just add the two together. But for the e.m.f I thought you would add those too? But the answer is supposed to be 6.4V, not 21.6V. Can anybody explain why? Thanks

Current (by convention) always flows from the highest +ve potential to the lowest potential.

The key is to recognise that in the case of a battery, this conventional current flow is external to the battery. i.e. it can only flow externally between the +ve and -ve terminals. (Always flows from highest to lowest potential.)

In this example the +14V charger is the highest potential and therefore acts as the supply voltage. All other voltages dropped in the current path, must sum to this voltage.

BUT: The battery potential is +7.6V and this is the lowest potential in the circuit. i.e. because the +ve terminals of the charger and battery are connected together and the charger is a higher +ve potential, no current can flow from the battery back into the charger. The electrons supplied by the charger recombine in a chemical reaction within the battery to store energy and that's where they stop

So the actual e.m.f. available to drive current in the two internal resistances is:

+14V = V_emf +7.6V

V_emf = 14V - 7.6V

= 6.4V


NB. Battery voltages only sum when they are connected in series with each other,: +ve terminal of one battery connected to the -ve terminal of the next and so on.