# Electric current

**Definition of Electric current**

In a conductor such as copper, there are electrons that move randomly at high speed freely but not escape from the metal. Electrons that can move freely are called free electrons. Although the electrons move freely in all directions there is no total flow of electrons in a particular direction. This condition occurs when there is no potential difference between the two ends of the copper wire.

When the wire is connected to an electrical source, a potential difference arises between the two ends of the copper wire, so that an electric field appears within the copper wire. The existence of an electric field causes free electrons to experience the electric force F = q E = e E, where F = electric force, e = electron charge, E = electric field. This electric force causes all the electrons that are moving freely to accelerate together which is the same direction as the electric force.

The free electrons that move together are between the atoms that remain in the copper wire so that all the electrons collide with the atoms. The collision causes the direction of the free electron to change. All these electrons always experience an electric force so that all the electrons are accelerated in the same direction as the direction of the electric force. After moving for a moment, free electrons collide with atoms in copper wire. But free electrons always experience an electric force so that all electrons are accelerated again. So besides moving randomly in various directions, all free electrons also move slowly together in the direction of the electric force and in the opposite direction to the electric field. The direction of the electric field from a high electric potential to a low electric potential, while the electrons move from a low potential to a high potential. The random motion of each free electron has a very fast speed while the motion with free electrons in the direction of the electric force has very slow speeds. This motion with free electrons in the direction of the electric force is also called *drift speed*.

Electric current is defined as the flow of electric charge through a cross-section of a conductor during a certain time interval. In accordance with the agreement, the direction of the electric current is the same as the direction of the positive charge. This agreement was made before it was known that what actually moves in a conductor is the negatively charged free electrons. The direction of the movement of electrons in the conductor is opposite to the direction of the electric current. So if we discuss the current flowing in the conductor, what is meant is the flow of positive charge, which is also called conventional current because it is the result of an agreement.

**The equation of electric current**

Mathematically, electric current is expressed by the equation:

I = ΔQ / Δt

*I = electric current, ΔQ = amount of electric charge, Δt = time interval.*

**Unit of electric current**

The unit of electric charge is Coulomb, the unit of time is second, so the unit of electric current is Coulomb/second. Coulomb/second is also called Ampere, the name of the French physicist Andre Marie Ampere (1775-1836). 1 Ampere = 1 Coulomb/second (1 A = 1 C/s). In other words, an electric current of 1 Ampere is equal to an electric charge of 1 Coulomb that passes through a cross-sectional area of wire for 1 second. Besides being expressed in Amperes, electric currents are also expressed in milliamperes (1 mA = 10^{-3} A), microamperes (1 μA = 10^{-6} A), nano amperes (1 nA = 10-9 A) or picoamperes (1 pA = 10^{-12} A).

Sample problem 1:

A current of 2 Amperes flows through the wire for 8 seconds. Determine the amount of charge passing through a point and the number of electrons in that charge!

__Known:__

Electric current (I) = 1 Ampere

Time interval (t) = 2 seconds

__Wanted:__ charge (Q) and number of electrons (e)

__Solution:__

Equation of electric current:

I = Q/t

*I = electric current, Q = electric charge, t = time interval*

Electric charge :

Q = I t = (2 Ampere)(8 seconds) = 16 C.

The charge of one electron is 1.6 x 10^{-19} Coulomb so the charge of 16 Coulomb has electrons as much as 16 C / 1.6 x 10^{-19} Coulomb = 10 x 10^{19} electrons.

**Electric current, drift speed, and current density**

Review the positive charge that is moving right with the speed drifting v in the direction of the electric field E on a conductor which has a cross-sectional area A. Positive charge moves as far as s = v t during the time interval t.

If the number of charged particles per volume (density of charged particles) is n and the volume of the conductor is A s = A v t, then the number of charged particles in the volume of the conductor is n A v t. If each charged particle has a charge of q then the amount of charge passing through the end of the conductor during the interval t is Q = n q A v t. So the electric current flowing through the tip of the conductor is I = Q / t = n q A v. Whereas the current density or current per cross-sectional area A is J = I / A = n q v. It can be concluded that the current flowing in the conductor is the product of the multiplication of the density of the charged particles (n), the amount of charge for each particle (q), the area of the conductor (A) and the velocity of charged particles (v).

Study the following example questions.

Sample problem 2:

A constant current of 10 amperes flows in a copper wire with a cross-section area of 3 x 10^{-6} m^{2}. The free electron density is 8.4 x 10^{28} electrons/m^{3}. Determine the speed of free electron drift!

__Known:__

Electric current (I) = 10 Ampere

Wire cross-sectional area (A) = 3 x 10^{-6} m^{2}

Free electron density (n) = 8.4 x 10^{28 }m^{-3}

Electron charge (q) = 1.6 x 10^{-19} C

__Wanted:__ Speed of free electron drift (v)

__Solution:__

The speed of electrons is calculated using a formula that has been derived before:

*I = electric current, n = density of charged particles = electron density, q = one electron charge, A = cross-sectional area of conductor, v = velocity of electron drift*

The speed of electron drift is 0.248 x 10^{-3} meters/second = 0.248 millimeters/second.

Free electrons move together in a wire at speeds of 0.248 millimeters per second. In other words, every single second all free-electron move as far as 0.248 millimeters. This is a very slow speed. If the movement of free electrons is very slow, why does the electric light immediately turn on after the switch is turned on?

To understand this, electrons flow in the conductor like the flow of water inside the hose. If the hose is filled with water then if one end of the hose is connected to the faucet, the water immediately flows out from one end of the other hose. Likewise, there are free electrons in the copper wire and light bulb wire. When the switch is turned on, an electric field arises with speed approaching the speed of light (speed of light = 3 x 10^{8} meters/second), which causes free electrons to start moving together at that moment. There are already free electrons in the light bulb wire so that the light is on at that very moment.

**Problems and solutions**

1. A steady current of 10 A exists in a wire for 2 minutes. How much the amount of charge passes through the conductor at any location.

__Known :__

Electric current (I) = 10 A

Time interval (t) = 2 minutes = 2 x 60 seconds = 120 seconds

__Wanted :__ Charge (Q)

__Solution :__

Equation of the electric current :

I = q/t

*I = the electric current, q = the electric charge, t = the time interval*

The electric charge :

Q = I t = (10)(120) = 1200 C

2. 60 C of charge passes by a point in the circuit for 5 minutes. What is the electric current?

__Known :__

The time interval (t) = 5 minutes = 5 x 60 seconds = 300 seconds

The electric charge (Q) = 60 C

__Wanted :__ The electric current (I)

__Solution :__

The electric current :

I = Q/t

I = 60 / 300

I = 0.2 Coulombs/second

I = 0.2 Ampere

3. Unit of the electric current in SI system is…

Solution

Coulombs/seconds

Coulombs/seconds, given a special name, the Ampere.