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.

1 Definition
2 Current in a metal wire
3 Current density
4 The drift speed of electric charges
5 Ohm's law
6 Conventional current
7 Examples
8 Electromagnetism
9 Reference direction
10 Electrical safety
11 See also
12 External links

[edit] Definition

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

Formally this is written as:

<math>i(t) = {dq(t) \over dt}</math> or inversely as <math>q(t) = \int_{t_0}^{t} i(t)\, dt + q(t_0)</math>

The quantity of charge Q flowing per unit of time t is I, standing for the intensity of the current.

[edit] Current in a metal wire

In solid conductive metal, with no external forces applied, there exists a random motion of "mobile" or "free" electrons created by the thermal energy which the electrons have gained from the surrounding medium. When a metal atom contributes a free electron, it acquires a net positive charge. The population of freed electrons form a "charge-gas" or "sea of charge" which remains bound to the ion lattice by attraction, while the metal as a whole remains neutral. Metal atoms typically contribute either one or two electrons to the "sea." Free electrons can move amongst these positive ions, while the positive ions can only oscillate about their mean fixed positions. Electrons move, but the net flow of charge remains zero: 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 metal 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 are forced to drift toward the positive terminal under the influence of this field. The free electron is therefore the current carrier in a typical solid conductor. For an electric current of 1 ampere rate, 1 coulomb of electric charge (which consists of about 6.242 × 10¹⁸ electrons) drifts every second through the imaginary plane through which the conductor passes.

The current I in amperes can be calculated with the following equation:

where

<math>Q \!\ </math> is the electric charge in coulombs (ampere seconds)

<math>t \!\ </math> is the time in seconds

It follows that:

[edit] Current density

Main article: 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 units, the current density is measured in amperes per square meter.

[edit] The drift speed of electric charges

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. The speed at which they drift can be calculated from the equation:

where

<math>I \!\ </math> is the electric current

<math>n \!\ </math> is number of charged particles per unit volume

<math>A \!\ </math> is the cross-sectional area of the conductor

<math>v \!\ </math> is the drift velocity, and

<math>Q \!\ </math> is the charge on each particle.

Electric currents in solid matter are typically very slow flows. For example, 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 outside the surface of the conductor (moving 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, moving 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.

The nature of these three velocities can be clarified by analogy with the three similar velocities associated with gases. The low drift velocity of charge carriers is analogous to air motions; to wind. The large signal velocity is roughly analogous to the rapid propagation of sound waves, while the large random motion of charges is analogous to heat; to the high thermal velocity of randomly vibrating gas particles.

[edit] Ohm's law

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

<math>

I = \frac {U}{R} </math>

where

I is the current, measured in amperes

U is the potential difference measured in volts

R is the resistance measured in ohms

[edit] 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 chloride 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.

[edit] 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.

[edit] Electromagnetism

Every electric current produces a magnetic field. The magnetic field can be visualized as a pattern of circular field lines surrounding the wire.

Electric current can be directly measured with a galvanometer, but this method involves breaking the circuit, which is sometimes inconvenient. Current can also be measured without breaking the circuit by detecting the magnetic field it creates. Devices used for this include Hall effect sensors, current clamps, current transformers, and Rogowski coils.

[edit] Reference direction

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.

[edit] Electrical safety

The most obvious hazard is electrical shock, where a current passing through part of the body can cause a slight tingle, to cardiac arrest, or severe burns. It is the amount of current passing through the body 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.