Direct Current

The electric current is defined as the rate of flow of charge. If a charge Q flows through any cross section in time t, then electric current,

\begin{align*} \: I &= \frac Qt \\ \text {If small charge dQ flows in time dt, then} \\ I &= \frac {dQ}{dt} \\ \text {It is scalar quantity. The unit of electric is ampere in SI-units} \\ 1 \text {ampere} &= \frac {1\: \text {columb} } {1\: \text {second}} \\ \end{align*}

A current flowing through a conductor is said to be one ampere if 1 coloumb of charge flows through the conductor in 1 second. Smaller units of the current are milliampere (10^-3 A) and microampere (10^-6A). electric current is measured using an instrument called ammeter.

Current Carriers

Electric current carriers are the charged particles which flow in a definite direction. In metallic conductors, the current is due to the flow of free electrons in it. In electrolytes such as solution of common salt, both positive and negative charged ions move to produce an electric current. In gases, the positively charged ions electrons are current carriers while, in semiconductors, the current carriers are electrons and holes.

Direction of Current

The current in a conductor flows due to the flows of electrons in it. It was believed the current flow is caused by the motion of positive charges. Most of the earlier theories and scientific literature were based on this idea. That is why this usage isfollowedto these days and the current is known as conventional current. So the direction of the flow of conventional current is opposite to the direction of the electron flow as shown in the figure.

Electric current in a conductor may pass in different ways. In this regard, current can be divided into two types:Types of Current

1. Direct current: A current whose magnitude, as well as direction, remains constant at all the times is called a direct current.
2. Alternating current: A current whose magnitude and direction changes continuously periodically is called an alternating current. An AC generator produces an AC current.

Current Density

The current density at any point in a conductor is defined as the current flowing per unit area perpendicular to the direction of the flow. It is denoted by J.

\begin{align*} J &= \frac IA \\ \text {or,} \: I &= JA \\ \end{align*}

It is a vector quantity. In vector form, \(I = \vec J . \vec A\). Its unit is Am^-2 in SI-units. This expression shows that electric current I is the dot product of two vectors and hence it is a scalar quantity.

Mechanism of Metallic Conduction and Drift Velocity

When no external electric field is applied to a metallic conductor, the free electrons are in thermal equilibrium with the rest of the conductor and are in random motion as shown in the figure. So, the average velocity of the electron is zero, and consequently this motion does not make up a net transport of charge across any section of the conductor. Hence, there is no current in the conductor.

When an electron field is applied to the conductor by connecting a battery across it, each electron is acted by an electrostatic force, and the electrons get accelerated in an opposite direction to that of the field. Hence, the electrons gain velocity and kinetic energy. These electrons, however, collide with atoms on lattice site of metal. During the collisions, the electrons give up their energy to the atoms and their velocity decrease. However, the electrons again accelerate and make collision with atoms. Due to the repeated collisions, the average velocity opposite to the direction of the electric field. This velocity is called drift velocity which is responsible for the flow of current through the conductor.

The average velocity acquired by the free electrons in a conductor subjected to an electric field is called drift velocity.

Relation between Drift Velocity and Electric Current

Consider a conductor, such as a copper wire, of length l and cross-sectional area A as shown in the figure. Let n be the number of free electrons per unit volume in it and e be the charge of each electron. Then,

\begin{align*} \text {volume of conductor} = Al \\ \text {total number of free electrons in this volume} =nAl \\ \text {total charge in this volume, Q} = nAle \\ \end{align*}

When a battery is connected across the conductor, the charges flow through it. Let v_d be the drift velocity of electrons. When a charge, Q drifts through a length l of the conductor in time t, then the current I through the conductor is given by

\begin{align*} I &= \frac Qt = neA\times \frac lt = ne A v_d \\ \text {where} \: v_d &= \frac lt \\ \therefore I &= neAv_d \\ \text {So, the drift velocity,} \: v_d &= \frac {I}{nAe} \\ \text {and current density,} \: J &= \frac IA = nv_d e. \\ \end{align*}

Reference

Manu Kumar Khatry, Manoj Kumar Thapa, Bhesha Raj Adhikari, Arjun Kumar Gautam, Parashu Ram Poudel. Principle of Physics. Kathmandu: Ayam publication PVT LTD, 2010.

S.K. Gautam, J.M. Pradhan. A text Book of Physics. Kathmandu: Surya Publication, 2003.