I have a dilemma that I would like to share with you concerning batteries (without neglecting internal resistance), emf and resistance of a circuit. To better visualize my question you may need to check these pictures:
-First, I'm trying to grasp the concept of why and how the voltage drop at the terminals of a battery depends on the resistance of the circuit.
-Second, knowing that $$\epsilon= V_b + V_c$$ (battery and circuit, respectively), we know that $$\epsilon=I(R+r)$$ Considering the extreme cases where $R=0$ and $R=∞$, what I expected was that at $R = ∞$, the voltage would be 0, because there would be infinite resistance and zero current, and since $V=RI$, it would be $V= ∞ \times 0=0$ which makes absolutely no sense to me. Plus, an ideal voltmeter has an infinite resistance but it does not give a voltage reading of zero when its terminals are placed on the battery terminals.
What am I doing wrong, and how do the charges on the poles of the battery act in each of these cases?
I'm sorry I could not be clearer in how to propose the question but I hope that it is enough. I'm still learning so do not rely on any of my assumptions.