Current Electricity Introduction

INTRODUCTION - CURRENT ELECTRICITY


The electric current is the flow of electric charges, the charge carriers. In solid conductors, the charge carriers are conduction electrons (free electrons), in electrolytes and gases, charge carriers are positive and negative ions and in semiconductors charge carriers are conduction electrons and valence electrons (holes). In a solid conductor there are a large number of free electrons, about 1028/m3. These electrons are in random motion just like the molecules of a gas. The average thermal speed of these electrons is about 105 ms-1 at room temperature. But, since they are in random motion due to collision (interaction) with the atoms of the conductor, the average velocity of an electron is zero. As the net charge crossing any section of the conductor is zero, there is no net flow of charge through any section of the conductor. So the electric current through the conductor is zero.

 

Consider a battery of potential difference V connected between the ends of the conductor AB of length I. An electric field of magnitude E = V/l is established in the conductor in the direction from the positive terminal to the negative terminal. This electric field E exerts a force, F = Ee, on the electrons and gives them a net motion in a direction opposite to the direction of the electric field. There is a net flow of charge through any section of the conductor. Hence an electric current flows through the conductor.

 

Strength (Intensity) of electric current (i)

 

Intensity of an electric current through a conductor is defined as the time rate of flow of charge through any section of the conductor.

 

If a net charge dq passes through any section of a conductor in a time interval dt, the strength of the current is given by,

i = dq/dt

If the current is constant in time, then, if q is the charge that flows in the interval of time t,

i = q/t

If n is the number of electrons crossing any section of the conductor in one direction in one second,

i = ne

If an electron moves along the circumference for a circle with frequency f ,

i = fe

It is to be noted that electric current i is the same for all cross-sections of a conductor, even when the cross-sectional area may be different at different sections.

 

Unit of electric current

 

The SI unit of current is ampere (A).

1 ampere (A) = 1 coulomb/second (Cs-1)

 

Direction of electric current

 

Although in a metal the charge carriers are electrons, in electrolytes and gases the charge carriers are positive and negative ions. A convention for labelling the direction of electric current is needed because the charges of opposite sign move in opposite directions in a given electric field. A positive charge moving in one direction is equivalent to a negative charge moving in the opposite direction. Hence for simplicity the following convention is followed.

The direction of electric current is the direction that positive charges would move, even if the actual charge carriers are negative. It is same as the direction opposite to the direction of flow of electrons (or negative charges). This is the direction of the conventional current.

In a solid, is the electrons are the charge carriers, it is more often convenient to take the direction of flow of electrons as the direction of the electric current. In this case, the direction of flow of electrons gives the direction of electronic current.

Even though we assign it a direction, the electric current is a scalar; not a vector because it does not obey the laws of vector addition. The direction merely indicates the direction of flow of charges.


Velocity of electric current


The velocity of electric current is nearly equal to the velocity of light in vacuum, 3 x 108 ms-1.


Current density at a point (j)


The electric current density at a point in a conductor is the electric current (i) flowing normally per unit area around the point.

If the current i is distributed uniformly across a conductor of cross-sectional area A; the magnitude of current density at all points on that cross-section is,

 j = i /A.

It is a vector whose direction at any point is in the direction that a positive charge carrier would move at that point. Its unit is ampere/ metre2 ( Am-2).

 

Different electric current sources

 

An electric circuit must have some source of energy to maintain a pd. The energy may be supplied by chemical reactions as in cells or by rotating a coil in a magnetic field as in generators or by converting light energy to electrical energy as in solar cells.

 

Drift velocity (v)

 

In the absence of an electric field, electrons in a conductor are in random motion due to the interaction with the electrons in the orbits of the atoms, just like the molecules of a gas. As in the case of collisions of gas molecules, there is a mean free path A and mean free time r. The speed of the electron is very high, about 106 ms-1, and is called thermal speed. Here the average velocity of an electron is zero.

When an electric field E is applied, the electrons modify their random motion in such a way that they drift slowly in the direction opposite to that of the field, with an average speed. This is because of the force Ee experienced by the electron in the electric field. Since all the electrons are drifted in the same direction, the electrons acquire a small average velocity opposite to the direction of the electric field, i.e., towards the positive terminal of the conductor. This drift is in addition to the random motion of the electrons.


The solid lines in the figure suggest a possible random path followed by an electron in the absence of an applied field and the dashed lines show how this same event might have occurred if an electric field had been applied. Note that the electron drifts steadily to the left ending at x’ rather than at x.


The drift velocity is defined as the average velocity with which free electrons are drifted under the influence of an electric field.


The drift velocity is very small and is of the order of 10-3ms-1. The drift velocity should not be confused with the speed of propagation of electric current along the conductor which is very nearly the speed of light. In fact the electrical impulse propagates, may be like electromagnetic waves, through the conductor with very high speed. The problem is similar to the effect of applying pressure to the end of a long tube filled with water. As soon as pressure is applied at one end, the pressure wave is transmitted rapidly along the tube and the flow of water from the other end starts instantly.

 

Relaxation time (τ)

 

When there is no external electric field, there is no drift velocity. In the presence of an external electric field E, each electron experiences an acceleration, a = F/m opposite the direction of the electric field. But this acceleration is momentary. The electrons frequently collide with vibrating atoms or ions or other electrons of the metal. After each collision each electron makes a fresh start and accelerates only to be deflected again.


The average time interval between successive collisions of electron with the atom or positive ion in the conductor is called the relaxation time.

 

Relation between drift velocity (v) and relaxation time (τ)

 

After each collision with atoms or ions, each electron makes a fresh start and accelerates from rest. The acceleration is given by,


â = — (Êe/m);

where m = mass of the electron


Negative sign shows that the electron is accelerated in a direction opposite to the direction of the external electric field. If τis the relaxation time, the velocity attained by the electron, i.e., the drift velocity of electron,


v̂ = u + at = at = — (Êe/m)τ


Negative sign shows that the drift velocity of the electron is opposite the direction of the electric field,

Therefore, v = (Ee/m)τ

 

Note: Thermal speed (rms value of thermal speed)

 

Free electrons in a metal behave like the molecules of an ideal gas. So, we can apply the kinetic theory of gases to find the rms velocity of the electron. Thus the average kinetic energy of an electron,

(KE)-vector = (3/2)kT; But KE = (1/2)mev2rms; vrms = √3kT/me

 

Relation between current and drift velocity

 

Consider a conductor AB of length l and cross sectional area a. Let n be the number of free electrons per unit volume (electron density or electron concentration) of the conductor.

When it is connected to a battery, an electric field E is set up along the conductor and charge flows along the conductor with the drift velocity v.

Consider a cross section P of the conductor perpendicular to the flow of electrons through the conductor in terminal B to the positive terminal A. Q is another cross section of the conductor at a distance v from the section P. Since v, the drift velocity, is the distance travelled by an electron in one second, all free electrons of the conductor between the sections P and Q will cross the section P in 1 second.

Total number of electrons crossing the section P is 1s = volume of the conductor between P and Q x electron density = (a x l) x n = (a x v) x n = nav

Total charge crossing the section P in 1 s, i.e., strength of the electric current through the conductor,

i = nav x e = nave

 

Mobility (µ)

 

The drift velocity v of a charge carrier is directly proportional to the electric field E.

i.e., v ∝ E,

Therefore, v = µE

Where µ is a constant known as the mobility of the charge carrier.

If v is the drift velocity of electron and µthe electron mobility, the electric current through a conductor is given by, i = nave = naµEe

The current density,

j = nµEe

Unit of mobility, µ = v/E = (ms-1)/(Vm-1) = m2s-1V-1

Sreejith Hrishikesan

Sreejith Hrishikesan is a ME post graduate and has been worked as an Assistant Professor in Electronics Department in KMP College of Engineering, Ernakulam. For Assignments and Projects, Whatsapp on 8289838099.

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