One of the confussing aspects of current is the direction in which the current flows. It is an accident of history that the current was a flow of positive charge carriers. However, in metal conductors, the positive ions are not able to move and the flow of charge is a result of negative electrons. As a result the true direction of the current flow is in the opposite direction to the conventional current. It does not matter which is used as long as you are consistent.
To make it absolutely clear:
· The conventional current flows from positive to negative.
· The electron flows from negative to positive.
Ohm’s Law is the linear proportionality between current and voltage that occurs for most conductors of electricity. A graph of voltage against current is a straight line. The gradient is the resistance.
The most well known form of Ohm’s law is V=IR, where V is the voltage, I is the current and R is the resistance. However there is another form of Ohm’s law which often used by physicists that operates on a microscopic level, relating the current density J to the conductivity σ and the electric field, E.
To see how consider, the volume of material with faces of area A a distance l apart. With an e.m.f. V across the faces of the material
· the current is proportional to the voltage V
· the current is proportional to the surface area A
· and the current is inversely proportional to the distance l.
The current is therefore,
I = VAσ/l.
R = l/Aσ
The proportionality constant σ is the conductivity of the material.
V/l = |E|, and J = I/A in the direction of E so in general we have the constitutive relation.