I've been poking around looking for an answer for this, mostly because my intuitions have been wrong.
What happens to the voltage and the resistance when 2 identical real batteries are connected in parallel or in series?
For a parallel pair, my intuition says that the voltages should stay, because they're technically capacitors in parallel, and parallel capacitors have have the same voltage. The inverse of the resistances are added together, and the inverse found because they are also in parallel, technically.
So, the voltage of the two batteries with an EMF $E$ and resistance $R$ would be $E$ and $1/(1/2R)$.
For a pair in series, I would do the usual operations for capacitors in series and resistors in series. So the equations would be $1/(1/2E)$ and $2R$.
Where am I going wrong?