Relationship between reaction area and internal resistance of battery
When considering the resistance of a metal, the resistance formula R=ρ L/S holds, where ρ of the material itself represents the difficulty of transmitting electricity. If the index is certain, it is proportional to the length of the metal. Material, which is inversely proportional to the cross-sectional area.
Taking this into account in the same way as the internal resistance of the battery, the internal resistance of the battery is equivalent to R, and the resistance value per unit area determined by the composition of the electrode mixture and the electrode structure is ρ, and the length in the direction of the electrode thickness is L. If the reaction area of the electrode is imagined as S, there is no problem.
A similar formula R=ρL/S applies to the internal resistance R of the battery. In other words, the internal resistance of the battery is inversely proportional to the reaction area, and the larger the reaction area, the smaller the internal resistance.
The relationship between reaction area and capacity of battery
Again, let's look at the relationship between the reaction area and the capacity of the battery. Here is how to calculate the battery capacity from the reaction area (the area of the positive and negative coated parts relative to each other) and the coating mass (battery design table). The electrode structure is certain (ρ is a constant), the length of the electrode thickness direction (determined by the coating quality and porosity) is certain (L is a constant), and the capacity of the battery is proportional to the area S.
We think it is easy to imagine that the larger the reaction area, the greater the capacity (that is, the reaction electricity). (If the reaction area is made using a laminated element that is also used in a laminated battery, etc., the reaction area will be proportional to the number of electrodes (the number of relative parts) and the number of components.)
That is to say, for any battery, the larger the reaction area (the larger the size), the greater the capacity. In the formula, capacitance =KS (K is a constant), when the internal resistance R=ρL/S is connected through S, S= capacitance /K=ρL/R, then the capacitance =K'/R can be. It can be seen that when the parameters other than S are fixed, the capacitance is inversely proportional to the internal resistance.
Using this concept, it is possible to predict the internal resistance and output of cells of different sizes (cells with different reaction regions) when using electrodes made of the same material and the same specifications (composition, porosity, etc.).