Does effective internal resistance of batteries depend on their size? If so how?

Question

It was asked to us by our professor- Consider the AA and AAA batteries, what do we think will happen to the internal resistance, will it increase or decrease or can we actually tell something about it? (I can see that there should be something similar in both of them to note change in other quantities and their dependence on one another, perhaps its emf of both that's same, I am not sure)

It seems to depends on so many factors like the area of electrodes, the mobility of ions, collision time of the ions(maybe), length of the battery etc..

The first argument goes like this- With increase in the size of the battery, the amount of electrolyte increases, the length of battery increases, and the area of the electrolyte increases as well, and since resistivity depends on both of them, including other factors like mobility, we go with the third option. It can't be determined!

The second argument goes like- The concentration of electrolyte will increase as well, which will decrease the collision time and hence more hindrance will occur in path of ions and this will be the dominating factor along with increase in length so overall internal resistance will increase.

I am not sure exactly how would the internal resistance change with the size of the batteries? What factors will dominate?

Please if possible also attach the respective sources.

Answer 1

I am not sure exactly how would the internal resistance change with the size of the batteries? What factors will dominate?

You should check out this EEVblog's video

He analyzes the internals of the battery (mainly the hardware part and not the chemicals) And shows how the size of the battery can be the reason of higher resistance.

After that, he shows how tesla tries to bypass that, by building a different hardware on the battery.

He shows that if you unroll a battery and check on its tabs, which are the positive and negative of the battery:

Are far apart from each other, making all this distance a 'huge' resistor.

Then, tesla does this:

Tabs all along the + side (and if I remember correctly, on the - side as well), so distance between + and - is minimized and thus, the resistance decreases.