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Considering a piece of electrical wire of length L and using the principles of mechanics , we can write that L = V_d △t. We can approximate a piece of electrical wire of a certain length by a cylinder of area A and length L. So the volume of this cylinder is given by V = A L . On the other hand we can write L = V_d△t, where △t is the time interval that electrons travel L. Thus, we can relate the total number of electrons, N_e, contained in volume V, according to eq. 73-03.

And by definition, electric current is the rate of amount of charge that passes through a section of conductor per unit of time and its unit of measure is coulomb / second or ampère . In addition, we define the conventional sense of electric current as that which flows from the highest potential to the lowest potential. To determine the total charge of all electrons passing through the wire, we use the fact that Q = e N_e, where e is the charge of the electron and its value in coulomb is worth e = 1.6 x 10^{- 19}C. Then we can write that:

Making the simplifications possible, we arrive at the electric current equation:

Electricity Sense Convention

It is conventional that the direction of the electric current has the same direction as the electric field , that is, it is as if the electric current is the result of a positive charge movement. For a macroscopic theory there is no distinction whether what moves inside a conductor is negative or positive charges. Thus, once a convention is established the results will be correct.

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Another interesting quantity to study is the so-called current density, J , defined as the relation between the electric current in ampère that runs through a wire and the section area wire cross-section in square meter.

The eq. 73-06 can also be expressed in easily measurable quantities if we consider a piece of wire of length L and cross-sectional area. A. We know that the law of Ohm is given by V = R I, where V is the potential difference between the ends of the wire. But we also know that V = E L. And J = I / A. So we can relate all these equations and write:

Working algebraically at eq. 73-07, we get the following expression:

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As we saw in the previous item, the current density is given by eq. 73-06 , where its direct relation with the electron drift velocity is evident, V_d. Putting this equation together with eq. 73-02, we can write that:

Note that eq. 73-09 shows that for a given electric field intensity, the higher current density if the conducting material has a large electron density, n_e, or a long collision time. Thus, the higher the value of these variables, the better the conductive material. Then we can define conductivity, σ, from a material like:

Comparing eq. 73-08 with eq. 73-11 it is possible to relate the quantities involved with the definition of conductivity. From this definition we can rewrite eq. 73-06 as follows:

From this equation we can get some important information, such as:

It is noteworthy that the conductivity is affected by the temperature of the material, the crystalline structure and the impurities contained on it.

Another value of great practical utility is the so-called resistivity, ρ, of the material, which is defined as the inverse of conductivity.. Then:

The electrical resistivity of a material represents the difficulty that electrons have in moving within a conductor due to the application of an electric field over the material.

The more known and most commonly used unit of measurement for the resistivity é o Ω m. Since conductivity is the inverse of resistivity, so its unit of measurement is the Ω^-1 m^-1.

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Considering that the electric current is a consequence of a movement of electrons within a conductor due to the electric field between its ends, we can say that:

"The rate at which electrons exit from one end of the conductor is exactly equal to rate at which electrons enter the other end of the conductor."

This means that electric current cannot be consumed or created within a conductor. So, what is used by the circuit is the kinetic energy that the electrons have, being the same dissipated in collisions with the conductor wire mesh ions, generating as a consequence, an increase in conductor temperature. So, we conclude that:

"The current is the same everywhere in a conductor carrying an electric current."