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Electricity and Magnetism
Electrical Conduction in Metals
A solid piece of metal, at room temperature, consists of metal ions arranged in a regular pattern called a crystal lattice with free electrons moving in the spaces between the ions. The motion of the free electrons is random. We say they have random thermal motion with an average speed which increases with temperature. Figure 1 represents a piece of metal which does not have current flowing through it.
The arrows represent the random thermal motion of the electrons (their average speed at room temperature is hundreds of kms-1).
If the piece of metal is part of a circuit through which a current is flowing, then another motion is added to the random thermal motion (see figure 2). This motion is more regular and results in a general "drift" of electrons through the metal. A typical drift velocity for electrons in metals is <1mms-1. The magnitude of the drift velocity depends on the current, the type of metal and the dimensions of the piece of metal.
The resistance of a piece of metal is due to collisions between the free electrons and the metal ions. The ions "get in the way" of the electrons and impede their progress through the metal.
During a collision, some of the kinetic energy possessed by the electron can be transferred to the ion thus increasing the amplitude of the lattice vibrations. Therefore, resistance to the flow of current causes the temperature to increase or in other words, resistance causes electrical energy to be converted into thermal energy (internal energy).
In figures 1 and 2, the thermal motion of the ions has been ignored. Figure 3 represents the situation a little more realistically. It is clear that as the amplitude of the lattice vibrations increases the ions will "get in the way" of the free electrons more. This suggests that the resistance of a piece of metal should increase with temperature.
This is confirmed by experiment. Not all conductors behave in this way: the resistance of semi-conductors (e.g. silicon and germanium) decreases with temperature