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The current that passes through a conductor is proportional to the potential difference applied across it. V=IR. In point form, J=oE The current is caused by moving charges. In metals, it's electrons that do the moving. In semiconductors it's holes and electrons. In gases and solutions, it is postitive and negative ions. But looking at solid conductors (like metals), it is the electrons that move. Due to thermal energy, these electrons are already chaotically moving around colliding with each other and atoms but since the direction is random there is no net current flow. If you then apply an electric field (ie a voltage drop across some distance), the electrons experience a net force in one direction and they accelerate in that direction. On average they travel some distance before colliding with something, they slow down and accelerate again until the next collision. The chaotic motion of electrons acquire an average velocity in opposite direction of the applied E field and this motion of charges is current. Ohm's Law arises from this model of current flow.
I'd like to build on the reply and add that the term J represents the electric current density i.e current per unit area through which the charges flow, sigma(o) represents the conductivity or the ability to offer encouragement for the charges to flow and E is the electric field intensity or the force per unit charge. Ohm's law simply says that the current in a conductor is directly proportional to the electric field in which it is placed. we know since electric field results in a potential difference, the charges tend to flow in a particular direction as opposed to the random motion when there was no electric field.
E=IR.. E stand for electromotive force, I stands for Intensity, and R stands for resistance. Electromotive force is measured in volts, Intensity is measured in Amps, and resistance is measured in Ohms. It helps to visualize the flow of electric current like the flow of water through a pipe. The amount or volume of water flowing is the intensity, the force pushing the water is the electromotive force, and the diameter of the pipe, opposing the flow of water, is the resistance.
V=IR . The details are above.