We are now moving from phenomena with fixed charges to phenomena with moving charges. Electric and electronic devices operate with moving charges. The material in this chapter is basic knowledge we will need and use in the study of electric circuits in the next chapter.
Electrons are constantly moving about inside a conductor, jiggling in all directions, with zero net motion. Electric current flows when some force acts on the electrons resulting in net motion. Note the similarity with the kinetic theory of gases.
Imagine a wire, and a surface that intersects the wire. We define the current through the wire to be the net flow of charge across the surface per second:
In a circuit, we will want to know the direction of current. Although we now know that, with few exceptions, current is due to the flow of electrons, we still define the direction of current as the direction of flow of positive charge. This is opposite the direction of electron flow.
In a particular television picture tube, the measured beam current is 60.0µA. How many electrons strike the screen every second?
The picture tube of a television or computer monitor operates by shooting a beam of electrons from an electron source (usually a hot filament) at a phosphor coated screen. The phosphor is excited by the electrons and emits light when the atom relaxes back to its ground state. The intensity of the light is proportional to the intensity of the electron beam.
A beam current of 60.0µA means that 60µC of charge strike the screen per second. This is equivalent to (60.0×10-6C)/(1.6×10-19C/e) = 37.5×1013 electrons = 3.75×1014 electrons.
It is instructive to relate macroscopic current to the microscopic properties of conductors. Typically, most of the electrons in a material are strongly bound to atoms -- these are the inner shell electrons -- and only a fraction are free to move, the outermost electrons. The free electrons we call mobile charges.
Consider a wire with cross section A.
Let n be the density of mobile charges (the number per unit volume).
The number of mobile charges in a length of wire Dx is the density times volume or nADx.
If each mobile charge has charge q (or the average is q), then the total amount of mobile charge in length Dx is
DQ = (nADx)q
if the charges move with average speed vd, then in time Dt they move a distance Dx = vdDt.
Then, the amount of charge that moves across a cross-sectional surface of the wire in time Dt is:
DQ = (nAvdDx)q.
The current due to this movement of charge equals:
This relation relates the current (a macroscopic quantity) to the density of mobile charges, their charge, their average drift speed, and the area of the wire.
A 200km long high-voltage transmission line 2.0cm in diameter carries a steady current of 1000A. If the conductor is copper with a free charge density of 8.5×1028 electrons per cubic meter, how long (in years) does it take one electron to travel the full length of the cable?
Begin by finding the drift velocity of the electrons.
vd = I / nqA = (1000A)/(8.5×1028e/m³)(1.6×10-19C/e)π(0.020m)² = 5.85×10-5m/s
Now determine how long it will take to travel 200km at this speed.
Use 1year = 3.1×107s.
t = l / vd = (2.0×105m) / (5.85×10-5m/s) = 0.34×1010s/ (3.1×107s/year) = 110 years.
An electric field is required to cause a net flow of electrons. The electrons are accelerated parallel to the field until they hit an atom in the material, at which point they transfer most of their energy to the atom, and bounce off in some other direction. The atoms tend to slow down the motion of the electrons, acting like a drag force. The macroscopic effect of this drag force is termed resistance.
We define the resistance, R, as the ratio of the applied voltage to the resulting current:
It is rather a coincidence that many materials exhibit a constant resistance over a wide range of conditions. Resistances from values of µW = 10-6W to GW = 109W are available. The fact that voltage and current are related by a constant is known as Ohm's law, normally expressed as:
All electric devices are required to have identifying plates that specify their electrical characteristics. The plate on a certain steam iron states that the iron carries a current of 6.4A when connected to a 120V source. What is the resistance of the steam iron?
Use Ohm's law:
R = DV / I = (120V)/(6.4A) = 19W