what is relaxation time?derive an expression for resistivity of a wire in terms of member density of free electrons and relaxation time.

If Electric field is turned OFF suddenly the average velocity decreases exponentially. The decay of average velocity is given by 

v_avg =v_avge^-t/t_r  

At  t=t_r

v_avg=v_avge^-1

 

Relaxation  time can be defined as the time taken by electron to attain an average velocity which is 1/e times its value.

The average time interval between two successive collisions is called relaxation time of electrons.

 

 

The average time between successive collison of an electron is called relaxation time . During the relaxation time ,electron gain average velocity.

 

 

 

 

 

 

average time taken by electron to attain steady state from zero velocity in presence o electric field.

 

You can think it intuitively as well.Let us suppose that we have a solid metal ball or sphere and you placed a charge inside it. This charge will arrive at the surface as a surface charge. How fast this charge arrives at the surface can be calculated by using the term relaxation time.The charge we kept inside the ball repel each other to arrive at the surface. Time taken by charges to travel to the surface s represented by relaxation time.

Relaxation time : Relaxation time is actually a time constant that describes the rate of decay of charges inside the conductor.