Because it is important to characterize the material, not the cell that is used in the investigation. If you prepare a twice bigger cell it will have twice larger capacitance, but the specific capacitance will remain the same.

The quantity with unit A/g is 'specific current', not current. It is the current supplied per unit mass of a battery (in case of battery measurement). Similarly, 'specific capacitance' has the units F/g and is the capacitance per unit mass of a capacitor. Naturally, using larger electrodes (i.e. more mass) in the battery/capacitor will lead to more current/capacitance. The specific current helps to evaluate the current supplying ability of a given type of battery irrespective of the actual size.

Note that specific current is often called 'current density' in battery circles, but this can cause confusion because A/m2 is the conventional definition of current density in general physics/engineering.

you mean that I must divide my current number to the mass of my capacitor, yes? for example, If my current is 2A and the mass of capacitor is 2g, so current density is 1A/g?

Dear Fatemeh Soleimani,

this specific quantity/notation for the normalized "current" (A/g) is meaningful, only, when we need to underline[1], that the charge/discharge capacity depends on (scales down with) the (high values of the) C-rate(s).

1. Highlight, unambiguously demonstrate, the (strong) character of the kinetic effects on the charge(/discharge) capacity.

for example, If my current is 2A and the mass of capacitor is 2g, so current density is 1A/g?

Yes, that is correct. However, be careful of the terminology and the valuable point made by Prof. Samaras.

I have to emphasize the importance to use the appropriate terms: "current density" is used for current divided by area (unit eg. A/cm2).

For A/g "normalized current" (a generalized term) or maybe "specific current" (just as general) might be considered appropriate.

(I'm open for suggestions for more specific terms, unless they are already occupied historically.)

I used chronopotentiometry to calculate charge-discharge measurement. the attached file is the diagram in various time. would you mind tellind me you idea about that.

You must use conventional mass of the material like 1g then your current applied is the same specific current in A or A/g. Simple trick to facilitate the work