Question

Using theory of drift velocity find the expression of ohm's law

Answer 1

Let us consider a conductor of length l.The area of cross section of the conductor is A

Let n number of electrons are present per each area of cross section.

The current flowing through this conductor will be -

                                               

 is the drift velocity of the electron.

The drift velocity of the electron is defined as -

                           

Here, m is the mas of electron and V is the potential difference across the two ends of the conductor.

t' is called as the relaxation time.

Putting the value of drift velocity in current equation we get-

                                 

                                         

                                         

                               ⇒  

                               ⇒            

Here R is the proportionality constant called resistance.

The value of

                         ⇒        

This expression is called Ohm's law i.e the current flowing through a conductor is directly proportional to the potential difference maintained across the two ends of conductor at constant temperature and pressure.