Suppose if 1 coulomb of charge is flowing in 1 sec through a conductor of 1m², it will have 1A of current. But, if 1 coulomb of charge is flowing in 1 sec through a conductor of 10m², it will also have 1A of current. But logically, first conductor has more current than the second one. Then, how can we exclude area while calculating current?
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Area only matters when you are dealing with resistances, When we are finding out electrical current we need number of electrons and time to calculate (Charge of electrons is a constant) . Both of the conductors will have same current but different resistances and different potential differences
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