Question

obtain the expression for current in a conductor in terms of drift velocity and hence write the expressions for resistance and resistivity.​

Answer 1

In a conducting solid, an electron will suffer collisions with fixed heavy ions. After collisions,

electron will emerge with same speed, but direction changes randomly. If we consider

N number of electrons in a given volume, since directons are changed randomly due to collisions,

average velocity of N electrons will be zero.

This is expressed as .................(1)

If electrons are accelerated by electric field E, then acceleration is given by, a = -eE/m ..........(2)

 

Let us consider an ith electron in a group of N electrons at a given time t.

Let us assume after a previous collision, speed of this ith electron is vi and there is an elapsed time ti after collision. 

 

Speed Vi of this ith electron at time t is given by,

   Vi = vi - (eE/m)ti