I am learning about current density in semiconductors. If you imagine a cube of silicon, drift current is defined as the amount of coulombs per time passing through a slice of area of the silicon.
This got me thinking about electric current in other contexts, like solving for currents through circuits using ohm's law. I haven't learned a very precise definition for what that current actually is. I know it's the amount of charge that enters then exits through something per time. But what is it defined as passing through? Is it some volume (3D), an area (2D), a line (1D), or a point (0D) in the conductor?
One idea I have is that the current is defined as the charge passing through the entire area of a conductor perpendicular to the direction of flow, or the charge passing through a volume of conductor with any length but with area being the entire area perpendicular to the flow. A volume sees the same current as an area because it is like a stretched area, since the charge that goes in one end, comes out the other, just like for an area with zero thickness. The amount of current going through a line and point would be zero, since for something to experience current, it would need to have a plane perpendicular to the direction of flow.