Presentation1 fir enggs dfdfgfrfrf .pptx

engineering lectures

1. Ohm`s law

2. Ohm`s law In order to arrive at an atomic interpretation of Ohm`s law , it is formulate in the form which state that the current density J is proportional to filed strength E , the proportionality constant σ is the electrical conductivity of metal.

3. relaxation time Relaxation time is defined as the time interval between two successive collisions of electrons in a conductor when current flows through it. It is denoted by τ. Relaxation time is related with drift velocity of electrons.

4. The relaxation time is mathematically understood as follows :

5. Let the electrons in a metal have an average velocity < v x > 0 at any instant, t = 0 ; given that for t > 0 there is no external field, the electrons interact only with the lattice and ultimately the average velocity will go to zero . At any instant t(> 0), let the velocity be given by the expression

6. The subscript “ coll ” refers to collisions carried out by the electrons with the lattice.

7. The mean free path The mean free path of an electron, λ, will be defined as

8. where v is an appropriate average velocity of electron . In the case of metals, the conductivity always refers to a single total velocity, the one corresponding to  Fermi energy . We know that free electrons in a metal can accept a series of discrete energy levels . At absolute zero, all energy levels below a certain value E F  are filled, and those above E F  being empty, E F  is called the Fermi level of electrons . The magnitude of E F  is of the order of several electron volts. At any temperature T, the probability of a state corresponding to the energy E being occupied by an electron is given as Thus mean free path,