Current Electricity

Introduction

Transfer of charge across a cross-section of a conducting medium constitutes an electric current. Any conductor in 

general offers some resistance to the flow of electric current through it. This means an electric current cannot flow 

continuously all by itself in a conductor. An electric source is needed to continuously drive electric current through 

a conductor. Some work is done or energy is supplied by the source to drive the current in a conducting medium. 

In this chapter we will study the laws and phenomena that govern the flow of electric current in conductors. We 

will discuss the factors that affect the electrical properties of conductors, what constitutes an electric circuit and 

the laws of division of current in various branches of a complicated network. Electricity has indeed transformed 

our lives beyond imagination. Electric energy is used everywhere, right from the lights of our homes, our electronic 

appliances, computers, automobiles, heavy machines used in our industries, hospitals, aircrafts etc. We will mainly 

focus on direct current circuits and sources in this chapter. The techniques of circuit analysis developed in this 

chapter form the backbone of electrical and electronics science and engineering. 

ELECTRIC CURRENT 

Electric current is defined as the rate of flow of electric charge through a certain cross-section of a conductor. If there is to be an electric current through a given surface, there must be a net flow of charge through the surface. The free electrons (conduction electrons)in an isolated conductor are in random chaotic motion in all directions and on an average same number of electrons passes through each side of any imaginary surface. Thus, the net charge passing through any surface in any time interval is zero, and thus the current through the conductor is zero. However, if we connect the ends of the conductor to a battery, an electric field is applied inside the conductor from positive terminal to negative motion with a certain average velocity u opposite to the direction of electric field is superimposed on the chaotic motion of the electrons. Thus there is a net flow of negative charge opposite to the electric field, or equivalently flow of net positive charge in the direction of electric field. Thus an electric current flows through the conductor in the direction of electric field.

In general the electric current is distributed non-uniformly over the surface through which it passes. So to analyse the current through an elementary surface of infinitesimal area at any point inside the conducting medium, we introduce a current density vector j.

The magnitude of current density vector at any point P, is equal to the ratio 

of current dI through an elementary surface perpendicular to the direction of current at P to the area dS⊥ of this 

elementary surface. The direction of j

 is the same as the notion of dI at that point, or the direction of velocity 

vector u

 of the ordered motion of positive charge carriers.