In a circuit, current is the flow of charge.
It can be measured in coulombs per second where 1 C / s = 1 amp.
The electrons actually flow from negative to positive
Current (A) = Charge (C) / time (s) I = Q / t
They are vibrating about randomly inside the metal very quickly but they drift though the wire very slowly.
Current is large cos there are a LOT of electrons flowing, not cos they travel quickly.
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