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PowerPedia:Electric current

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Electric current is by definition the flow of electric charge. The SI unit of electric current is the ampere (A), which is equal to a flow of one coulomb of charge per second.

Table of contents
1 Introduction
2 Ampere

2.1 Definition
2.2 Explanation
2.3 Proposed future definition

2.3.1 CIPM recommendation

3 Current density
4 Electric charges drift
5 Conventional current
6 Mathematics

6.1 Ohm's law

7 Examples
8 Electrical safety
9 Related concepts
10 External articles and references
11 See also
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Introduction

In solid conductive metal, with no external forces applied, there exists a random motion of free electrons created by the thermal energy that the electrons gain from the surrounding medium. When an atom loses a free electron, it acquires a net positive charge. The free electron can move amongst these positive ions, while the positive ions can only oscillate about their mean fixed positions. The free electron is therefore the charge carrier in a typical solid conductor. Given an imaginary plane through which the wire passes, the number of electrons moving from one side to the other in any period of time is exactly equal to the number passing in the opposite direction.

When a wire is connected across the two terminals of a DC voltage source such as a battery, the source places an electric field across the conductor. The moment contact is made, the free electrons of the conductor will drift toward the positive terminal under the influence of this field. For every ampere of current, 1 coulomb of electric charge (which consists of about 6.242 × 1018 electrons) drifts every second at the same velocity through the imaginary plane through which the conductor passes.

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Ampere

Image:Ampere.png

This SI unit is named after André-Marie Ampère. As for all SI units whose names are derived from the proper name of a person, the first letter of its symbol is uppercase (A). But when an SI unit is spelled out, it should always be written in lowercase (ampere), unless it begins a sentence or is the name "degree Celsius". — Based on The International System of Units (http://www.bipm.org/en/si/si_brochure/chapter5/5-2.html), section 5.2.

The ampere (symbol: A) is the SI base unit of electric current. It is named after André-Marie Ampère, one of the main discoverers of electromagnetism.

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Definition

The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 metre apart in vacuum, would produce between these conductors a force equal to 2Template:E newton per metre of length.

Electric current is the time rate of change or displacement of electric charge. One ampere represents the rate of 1 coulomb of charge per second.

{1 \,A= 1 \,C/s} \,

The ampere is defined first (it is a base unit, along with the metre, the second, and the kilogram), without reference to the quantity of charge. The unit of charge, the coulomb, is defined to be the amount of charge displaced by a one ampere current in the time of one second.

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Explanation

Because it is a base unit, the definition of the ampere is not tied to any other electrical unit. The definition for the ampere is equivalent to fixing a value of the permeability of vacuum to μ0 = 4πTemplate:E H/m. Prior to 1948, the so-called "international ampere" was used, defined in terms of the electrolytic deposition rate of silver. The older unit is equal to 0.999 85 A.

The ampere is most accurately realized using an ampere balance, but is in practice maintained via Ohm's Law from the units of voltage and resistance, the volt and the ohm, since the latter two can be tied to physical phenomena that are relatively easy to reproduce, the Josephson junction and the quantum Hall effect, respectively.

The unit of electric charge, the coulomb, is defined in terms of the ampere: one coulomb is the amount of electric charge (formerly quantity of electricity) carried in a current of one ampere flowing for one second. Current (electricity), then, is the rate at which charge flows through a wire or surface. One ampere of current (I) is equal to a flow of one coulomb of charge (Q) per second of time (t):

{I=Q/t} \,
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Proposed future definition

Since a coulomb is approximately equal to 6.24150948Template:E elementary charges, one ampere is approximately equivalent to 6.24150948Template:E elementary charges, such as electrons, moving past a boundary in one second.

As with other SI base units, there have been proposals to redefine the kilogram in such a way as to define some presently measured physical constants to fixed values. One proposed definition of the kilogram is:

The kilogram is the mass which would be accelerated at precisely 2Template:E m/s2 if subjected to the per metre force between two straight parallel conductors of infinite length, of negligible circular cross section, placed 1 metre apart in vacuum, through which flow a constant current of exactly 6 241 509 479 607 717 888 elementary charges per second.

This redefinition of the kilogram has the effect of fixing the elementary charge to be e = 1.60217653Template:E C and would result in a functionally equivalent definition for the coulomb as being the sum of exactly 6 241 509 479 607 717 888 elementary charges and the ampere as being the electrical current of exactly 6 241 509 479 607 717 888 elementary charges per second. This is consistent with the current 2002 CODATA value for the elementary charge which is 1.60217653Template:E ± 0.00000014Template:E C.

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CIPM recommendation

International Committee for Weights and Measures (CIPM) Recommendation 1 (CI-2005): Preparative steps towards new definitions of the kilogram, the ampere, the kelvin and the mole in terms of fundamental constants

The International Committee for Weights and Measures (CIPM),

  • approve in principle the preparation of new definitions and mises en pratique of the kilogram, the ampere and the kelvin so that if the results of experimental measurements over the next few years are indeed acceptable, all having been agreed with the various Consultative Committees and other relevant bodies, the CIPM can prepare proposals to be put to Member States of the Metre Convention in time for possible adoption by the 24th CGPM in 2011;
  • give consideration to the possibility of redefining, at the same time, the mole in terms of a fixed value of the Avogadro constant;
  • prepare a Draft Resolution that may be put to the 23rd CGPM in 2007 to alert Member States to these activities;
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Current density

Current density is a measure of the density of electrical current. It is defined as a vector whose magnitude is the electric current per cross-sectional area. In SI unit, the current density is measured in amperes per square meter. Electrical current is a coarse, average quantity that tells what is happening in an entire wire. The current density is an important parameter in Ampère's law (one of Maxwell's equations), which show the direct link between current density and magnetic field strength.

Current density is an important consideration in the design of electrical and electronic systems. Most electrical conductors have a finite, positive resistance, making them dissipate power in the form of heat. The current density must be kept sufficiently low to prevent the conductor from melting or burning up, or the insulating material failing. In superconductors excessive current density may generate a strong enough magnetic field to cause spontaneous loss of the superconductive property.

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Electric charges drift

When studying electrical circuits, it is possible that the actual direction of current flow in a specific circuit element is not known at the start. Consequently, we arbitrarily assign each current variable a reference direction. After current values are solved for, some of them might display negative values. Hence, for the negative current variables, the actual current flows in the direction opposite to the reference direction which was originally selected.

The mobile charged particles within a conductor move constantly in random directions. In order for a net flow of charge to exist, the particles must also move together with an average drift rate. Electrons are the charge carriers in metals and they follow an erratic path, bouncing from atom to atom, but generally drifting in the direction of the electric field. In a copper wire of cross-section 0.5 mm², carrying a current of 5 A, the drift velocity of the electrons is of the order of a millimetre per second. To take a different example, in the near-vacuum inside a cathode ray tube, the electrons travel in near-straight lines ("ballistically") at about a tenth of the speed of light. However, we know that electrical signals are electromagnetic waves which propagate at very high speed (at the speed of light, as can be deduced from Maxwell's Equations). For example, in AC power lines, the waves of electromagnetic energy propagate rapidly through the space between the wires from a source to a distant load, even though the electrons in the wires only move back and forth over a tiny distance. Although the velocity of the flowing charges is quite low, the associated electromagnetic energy travels at the speed of light. The ratio of the signal velocity through a medium versus the speed of light in a vacuum is called the velocity factor.

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Conventional current

Conventional current was defined early in the history of electrical science as a flow of positive charge. In solid metals, like wires, the positive charges are immobile, and only the negatively charged electrons flow in the direction opposite conventional current, but this is not the case in most non-metallic conductors. In other materials, charged particles flow in both directions at the same time. Electric currents in electrolytes are flows of electrically charged atoms (ions), which exist in both positive and negative varieties. For example, an electrochemical cell may be constructed with salt water (a solution of sodium chloride) on one side of a membrane and pure water on the other. The membrane lets the positive sodium ions pass, but not the negative chlorine ions, so a net current results. Electric currents in plasma are flows of electrons as well as positive and negative ions. In ice and in certain solid electrolytes, flowing protons constitute the electric current. To simplify this situation, the original definition of conventional current still stands.

There are also instances where the electrons are the charge that is moving, but where it makes more sense to think of the current as the movement of positive "holes" (the spots that should have an electron to make the conductor neutral). This is the case in a p-type semiconductor.

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Mathematics

The magnitude of an electric current is defined as the time derivative of electric charge:

I = {dQ \over dt}

Formally this is written as:

i(t) = {dq(t) \over dt} or inversely as q(t_0) = \int_{-\infty}^{t_0} i(t)\, dt

The amount of charge Q flowing per unit of time t is I, standing for the intensity of the current. The current I in amperes "flowing" in a wire can be calculated with the following equation:

I = {Q \over t}

where

Q \!\ is the electric charge in coulombs (ampere seconds)
t \!\ is the time in seconds

It follows that:

Q=It \!\ and t = {Q \over I}

If we want to describe the distribution of the charge flow, we use the concept of the current density:

\vec{J}=nq\vec{v_d}=\rho \vec{v_d} \!\

where

\vec{J} \!\ is the current density vector (SI unit amperes per square metre)
n \!\ is the particle density in count per volume (SI unit m-3)
q \!\ is the individual particles' charge (SI unit coulombs)
\rho = nq \!\ is the charge density (SI unit coulombs per cubic metre)
\vec{v_d} \!\ is the particles' average drift velocity (SI unit meters per second)

The current flowing through a surface S can be calculated by the following relation:

I=\int_S{ \vec{J} \cdot d\vec{S}}

– where the current is in fact the integral of the dot product of the current density vector and the differential surface element d \vec{S}, i.e. the net flux of the current density vector field flowing through the surface S.

The speed at which electric charges drift can be calculated from the equation:

I=nAvQ \!\

where

I \!\ is the electric current
n \!\ is number of charged particles per unit volume
A \!\ is the cross-sectional area of the conductor
v \!\ is the drift velocity, and
Q \!\ is the charge on each particle.

Electric currents in solid matter are typically very slow flows.

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Ohm's law

Ohm's law predicts the current in an (ideal) resistor (or other ohmic device) to be applied voltage divided by electrical resistance:

I = \frac {V}{R}

where

I is the current, measured in amperes
V is the potential difference measured in volts
R is the resistance measured in ohms
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Examples

Natural examples include lightning and the solar wind, the source of the polar auroras (the aurora borealis and aurora australis). The most familiar artificial form of electric current is the flow of conduction electrons in metal wires, such as the overhead power lines that deliver electrical energy across long distances and the smaller wires within electrical and electronic equipment. In electronics, other forms of electric current include the flow of electrons through resistors or through the vacuum in a vacuum tube, the flow of ions inside a battery, and the flow of holes within a semiconductor.

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Electrical safety

The most obvious hazard is electric shock, where a current through part of the body can cause effects from a slight tingle to cardiac arrest or severe burns. It is the current that passes that determines the effect, and this depends on the nature of the contact, the condition of the body part, the current path through the body and the voltage of the source. The effect also varies considerably from individual to individual. (For approximate figures see Shock Effects under electric shock.)

Due to this and the fact that passing current cannot be easily predicted in most practical circumstances, any supply of over 50 volts should be considered a possible source of dangerous electric shock. In particular, note that 110 volts (a minimum voltage at which AC mains power is distributed in many countries) can certainly be lethal.

Electric arcs, which can occur with supplies of any voltage (for example, a typical arc welding machine has a voltage between the electrodes of just a few tens of volts), are very hot and emit ultra-violet (UV) and infra-red radiation (IR). Proximity to an electric arc can therefore cause severe thermal burns, and UV is damaging to unprotected eyes and skin.

Accidental electric heating can also be dangerous. An overloaded power cable is a frequent cause of fire. A battery as small as an AA cell placed in a pocket with metal coins can lead to a short circuit heating the battery and the coins which may inflict burns. NiCad, NiMh cells, and Lithium batteries are particularly risky because they can deliver a very high current due to their low internal resistance.

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Related concepts

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External articles and references

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