Resistivity and it’s

Temperature dependence

 

1) Resistivity (r) is dependent on temperature.



2) The temperature dependency is

 

Where




&

 





3) we know that





&

 




Therefore

 











Where

n = is the number of free electrons per unit volume

t = is average relaxation time or the average time between two successive collision of an electron.




4) When heating is applied to a metal,


n ----> the number of free electrons per unit volume does not change


t --->  as on heating velocity of electron increases. So time interval of successive collision decreases.


So,  t decreases means r or resistivity increases.

 

 


5) This is the reason why resistivity increases on increasing the temperature of the metal. For most metals how the electrical resistance depends on temperature is given in the graph below. 



For most metals 

 

 

 

 

In case of semiconductor:

6) On the other hand in case of semiconductor, on heating, n value increases, this n value increase is more than the t value decrease. this is the reason why resistivity decreases on increasing the temperature of a semiconductor.




the temperature dependence of resistance of a semiconductor is shown in the graph below. 


For semiconductors