2.5 Mechanism of Electric Current Condution

 We know that metals are rich in free electrons which are in random motion.Even though the electrons are in random motion there is no current through a metal in the absence of a potential difference.Even though electrons in a metal are in motion ,due to the random nature of  motion of the net amount of electrons drifted to any direction averages to zero. In other words the net amount of electron transfer in any specified direction is zero and hence the random thermal motion of electrons does not constitute a current.
       When a potential difference is applied across  end of a conductor , an electric field is setup inside the conductor. Under the influence of the electric field , each free electron Experiences a force F=eE and get drifted towards the positive end. The electron during their flight collides with atoms or other electrons in their path and gets deviated.the time interval between different collision is non equal and the average time interval between two successive collisions of electrons is called the relaxation time.

Electric Current and Krichhoff's Rules

The current and the potential difference across a resistance can be obtained easily with the help of Ohm's Law for individual resistance or circuits which can be reduced to simple parallel or series combinations .In such circuits  the current through each resistance or potential difference across each resistors can be simply

obtained by Ohm's Law . The general term used to denote such a complex circuit is a network. In order to deal with electrical circuits with a number of resistors and cells interconnected in a complicated way , Gustav Robert Kirchhoff Have proposed two general rules.

Kirchhoff"s 1 Rule

We know that electric charge can neither can be created or nor be destroyed and in metals it cannot be accumulated at any point as the charges are free to move . Hence in any circuit total amount of electric charges reaching a point at any instant should be equal to that leaving the point at that instant.

                In the words of Kirchhoff's at any junction of several circuits elements , the sum of current entering    a junction must be equal to the sum of currents leaving the junction.General form of  Kirchhoff's Current Law is, If  the current reaching a junction is taken as positive and current leaving a point is taken as negative then Kirchhoff's current rule can be stated as "the algebraic sum of  current meeting a junction is zero"

Kirchhoff's 2 Law

  We have seen that electric field is a conservative field and hence potential difference between any two points depend only on the initial and final points. Now if the initial and final points are same , then potential difference must be zero. This fact is stated in Kirchhoff's 2nd rule .Kirchhoff's law 2 states that this fact as follows "The algebraic sum of change in potential around any closed resistor loop must be zero.