Define relaxation time . Derive the expression for electrical conductcity of material in terms of relaxation time .

Explanation

The average time between two successive collisions of free electrons is known as relaxation time.
We know that drift velocity `V_d=(eEtau)/m`
We have `I=heAV_d` …(1)
Substitute for `V_d` in equation (1) and we get
`I=("ne"AeEtau)/m=("ne"^2AEtau)/m rArr I/A=("ne"^2Etau)/m`
`j=("ne"^2Etau)/m " " because j=I/A`
We know that `j=sigma E`
`therefore sigma cancelE=("ne"^2 cancelE tau)/m`
`sigma=("ne"^2tau)/m`.