Picture a piece of metal wire. Within the metal, electrons are zooming around at speeds of about a MILLION m/s in random directions, colliding with other electrons and positive ions in the lattice. This constitutes charge in motion, but it doesn't constitute net movement of charge, because the electrons move randomly. If there is no net motion of charge, there's no current. However, if we were to create a potential difference between the ends of the wire, meaning if we set up an electric field, the electrons would experience an electric force, and they would start to drift through the wire. This is current. Although the electric field would travel through the wire at nearly the speed of light, the electrons themselves would still have to make their way through a crowd of atoms and other free electrons, so their drift speed, Vd, would be relatively slow, on the order of a millimeter per second.
Equation for current:
Equation for current:
Although the charge carriers that constitute the current within a metal are electrons, the direction of the current is taken to be the direction that positive charge carries would move. (This is explicitly stated on the AP Physics Exam.) So, if the conduction electrons drift to the right, we'd say the current points toward the left.
Let's say we had a copper wire and a glass fiber that had the same length and cross-sectional area, and that we hooked up the ends of the metal wire to a source of potential difference and measured the resulting current. If we were to do the same thing with the glass fiber, the current would probably be too small to measure, but why? Well, the glass provided more resistance to the flow of charge. If the potential difference is V and the current is I, then the resistance is:
This is known as Ohm's Law. Not all devices are ohmic, but many are. Notice for the same voltage if the current is large, the resistance is low, and vice versa.
The resistance of an object depends on two things: the material it's made of and its shape. For example, again think of the copper wire and glass fiber of the same length and area. They have the same shape, but their resistances are different because they're made of different materials. Glass has a much greater intrinsic resistance than copper does; it has a greater resistivity. Each material has its own characteristic resistivity, and resistance depends on how the material is shaped. For a wire of length L and cross-sectional area A made of a material with resistivity ρ, resistance is given by:
The resistivity of copper is around 10^-8 Ω m, while the resistivity of glass is MUCH greater, aro
Because current is charge per unit time, it's expressed in coulombs per second. One coulomb per second is an ampere (abbreviated A), or amp. So 1 C/s=1 A.
More commonly stated as:
One volt per amp is one ohm (Ω). So, 1V/A = 1Ω.
Resistance and Resistivity
Resistance of a wire is given by:
Resistivity depends on temperature:
Applies to any circuit element:
Applies to resistors only: