Due to overlapping of valence band and conduction band metal

\"Due to overlapping of valence band and conduction band, metal has positive temperature coefficient property.\" Please explain in detail why is this so? Relevant Equations would be much appreciated.

Solution

Here, the positive temperature coefficient represents the increase of resistance with temperature.

In metals (conductors), valence and conduction bands are overlapped i.e. all most all the valence electrons are free to contribute for the flow of electricity. Now, with the increase in the temperature does not cause the increase in number of electrons as already maximum number of electrons are there in the conduction band. So with the increase in temperature, the kinetic energy of conduction electrons increases and they start moving in zig-zag directions and collide with each other. Now in order to control the motion of electrons in a particular direction, first we need to loose some electric energy to stop this random motion and the remaining energy will accelerate the electrons in a certain direction that causes current. So the output current decreases with the increase in temperature. Effectively resistance increases with temperature i.e. positive temperature coefficient.