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FHSST Physics/Electricity/Using Ohm's Law

= Correct use of Ohm's Law =

One of the most common mistakes made by beginning electronics students in their application of Ohm's Laws is mixing the contexts of voltage, current, and resistance. In other words, a student might mistakenly use a value for I through one resistor and the value for E across a set of interconnected resistors, thinking that they'll arrive at the resistance of that one resistor. Not so! Remember this important rule: The variables used in Ohm's Law equations must be common to the same two points in the circuit under consideration. I cannot overemphasize this rule. This is especially important in series-parallel combination circuits where nearby components may have different values for both voltage drop and current.

When using Ohm's Law to calculate a variable pertaining to a single component, be sure the voltage you're referencing is solely across that single component and the current you're referencing is solely through that single component and the resistance you're referencing is solely for that single component. Likewise, when calculating a variable pertaining to a set of components in a circuit, be sure that the voltage, current, and resistance values are specific to that complete set of components only! A good way to remember this is to pay close attention to the two points terminating the component or set of components being analyzed, making sure that the voltage in question is across those two points, that the current in question is the electron flow from one of those points all the way to the other point, that the resistance in question is the equivalent of a single resistor between those two points, and that the power in question is the total power dissipated by all components between those two points.

The "table" method presented for both series and parallel circuits in this chapter is a good way to keep the context of Ohm's Law correct for any kind of circuit configuration. In a table like the one shown below, you are only allowed to apply an Ohm's Law equation for the values of a single vertical column at a time:

Deriving values horizontally across columns is allowable as per the principles of series and parallel circuits:

Not only does the "table" method simplify the management of all relevant quantities, it also facilitates cross-checking of answers by making it easy to solve for the original unknown variables through other methods, or by working backwards to solve for the initially given values from your solutions. For example, if you have just solved for all unknown voltages, currents, and resistances in a circuit, you can check your work by adding a row at the bottom for power calculations on each resistor, seeing whether or not all the individual power values add up to the total power. If not, then you must have made a mistake somewhere! While this technique of "cross-checking" your work is nothing new, using the table to arrange all the data for the cross-check(s) results in a minimum of confusion.


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FHSST Physics/Electricity/Conductor Size

= Conductor Size =

It should be common-sense knowledge that liquids flow through large-diameter pipes easier than they do through small-diameter pipes (if you would like a practical illustration, try drinking a liquid through straws of different diameters). The same general principle holds for the flow of electrons through conductors: the broader the cross-sectional area (thickness) of the conductor, the more room for electrons to flow, and consequently, the easier it is for flow to occur (less resistance).

Electrical wire is usually round in cross-section (although there are some unique exceptions to this rule), and comes in two basic varieties: solid and stranded. Solid copper wire is just as it sounds: a single, solid strand of copper the whole length of the wire. Stranded wire is composed of smaller strands of solid copper wire twisted together to form a single, larger conductor. The greatest benefit of stranded wire is its mechanical flexibility, being able to withstand repeated bending and twisting much better than solid copper (which tends to fatigue and break after time).

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


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FHSST Physics/Electricity/Fuses

= Fuses =

Normally, the ampacity rating of a conductor is a circuit design limit never to be intentionally exceeded, but there is an application where ampacity exceedence is expected: in the case of fuses.

A fuse is nothing more than a short length of wire designed to melt and separate in the event of excessive current. Fuses are always connected in series with the component(s) to be protected from overcurrent, so that when the fuse blows (opens) it will open the entire circuit and stop current through the component(s). A fuse connected in one branch of a parallel circuit, of course, would not affect current through any of the other branches.

Normally, the thin piece of fuse wire is contained within a safety sheath to minimize hazards of arc blast if the wire burns open with violent force, as can happen in the case of severe overcurrents. In the case of small automotive fuses, the sheath is transparent so that the fusible element can be visually inspected. Residential wiring used to commonly employ screw-in fuses with glass bodies and a thin, narrow metal foil strip in the middle.

title: FHSST Physics/Electricity/Fuses


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FHSST Physics/Electricity/Summary

= Important Equations and Quantities =

 * REVIEW:
 * A circuit is an unbroken loop of conductive material that allows electrons to flow through continuously without beginning or end.
 * If a circuit is "broken," that means it's conductive elements no longer form a complete path, and continuous electron flow cannot occur in it.
 * The location of a break in a circuit is irrelevant to its inability to sustain continuous electron flow. Any break, anywhere in a circuit prevents electron flow throughout the circuit.
 * REVIEW:
 * Electrons can be motivated to flow through a conductor by the same force manifested in static electricity.
 * Voltage is the measure of specific potential energy (potential energy per unit charge) between two locations. In layman's terms, it is the measure of "push" available to motivate electrons.
 * Voltage, as an expression of potential energy, is always relative between two locations, or points. Sometimes it is called a voltage "drop."
 * When a voltage source is connected to a circuit, the voltage will cause a uniform flow of electrons through that circuit called a current.
 * In a single (one loop) circuit, the amount of current at any point is the same as the amount of current at any other point.
 * If a circuit containing a voltage source is broken, the full voltage of that source will appear across the points of the break.
 * The +/- orientation a voltage drop is called the polarity. It is also relative between two points.
 * REVIEW:
 * Resistance is the measure of opposition to electric current.
 * A short circuit is an electric circuit offering little or no resistance to the flow of electrons. Short circuits are dangerous with high voltage power sources because the high currents encountered can cause large amounts of heat energy to be released.
 * An open circuit is one where the continuity has been broken by an interruption in the path for electrons to flow.
 * A closed circuit is one that is complete, with good continuity throughout.
 * A device designed to open or close a circuit under controlled conditions is called a switch.
 * The terms "open" and "closed" refer to switches as well as entire circuits. An open switch is one without continuity: electrons cannot flow through it. A closed switch is one that provides a direct (low resistance) path for electrons to flow through.
 * REVIEW:
 * Connecting wires in a circuit are assumed to have zero resistance unless otherwise stated.
 * Wires in a circuit can be shortened or lengthened without impacting the circuit's function - all that matters is that the components are attached to one another in the same sequence.
 * Points directly connected together in a circuit by zero resistance (wire) are considered to be electrically common.
 * Electrically common points, with zero resistance between them, will have zero voltage dropped between them, regardless of the magnitude of current (ideally).
 * The voltage or resistance readings referenced between sets of electrically common points will be the same.
 * These rules apply to ideal conditions, where connecting wires are assumed to possess absolutely zero resistance. In real life this will probably not be the case, but wire resistances should be low enough so that the general principles stated here still hold.
 * REVIEW:
 * Power is additive in any configuration of resistive circuit: $$P_{Total} = P_1 + P_2 + . . . P_n$$
 * REVIEW:
 * When electrons flow through a conductor, a magnetic field will be produced around that conductor.
 * The left-hand rule states that the magnetic flux lines produced by a current-carrying wire will be oriented the same direction as the curled fingers of a person's left hand (in the "hitchhiking" position), with the thumb pointing in the direction of electron flow.
 * The magnetic field force produced by a current-carrying wire can be greatly increased by shaping the wire into a coil instead of a straight line. If wound in a coil shape, the magnetic field will be oriented along the axis of the coil's length.
 * The magnetic field force produced by an electromagnet (called the magnetomotive force, or mmf), is proportional to the product (multiplication) of the current through the electromagnet and the number of complete coil "turns" formed by the wire.

title: FHSST Physics/Electricity/Summary


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FHSST Physics/Magnets and Electromagnetism

= Magnets and Electromagnetism =


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FHSST Physics/Magnets and Electromagnetism/Permanent Magnets

= Permanent magnets =

Magnetism has been known to mankind for many thousands of years. Lodestone, a magnetized form of the iron oxide mineral magnetite which has the property of attracting iron objects, is referred to in old European and Asian historical records, around 800 BC in Europe and earlier in the East, around 2600 BC. The root of the English word magnet is the Greek word magnes, thought to be derived from Magnesia in Asia Minor, once an important source of lodestone.

Lodestone was used as a navigational compass as it was found to orient itself in a north-south direction if left free to rotate by suspension on a string or on a float in water.

 A compass is a navigational instrument for finding directions. It consists of a magnetised pointer free to align itself accurately with Earth's magnetic field. A compass provides a known reference direction which is of great assistance in navigation. The cardinal points are north, south, east and west. A compass can be used in conjunction with a clock and a sextant to provide a very accurate navigation capability. This device greatly improved maritime trade by making travel safer and more efficient. A compass can be any magnetic device using a needle to indicate the direction of the magnetic north of a planet's magnetosphere. Any instrument with a magnetized bar or needle turning freely upon a pivot and pointing in a northerly and southerly direction can be considered a compass.

In 1269, Frenchmen Peter Peregrinus and Pierre de Maricourt, using a compass and a lodestone, found the magnetic force of the lodestone at its opposite ends, which they defined to be the poles of the magnet. They found that like poles repel one another whilst unlike poles attract. It was also discovered that poles always occur in pairs, so, it is impossible to isolate a single pole, or monopole. Breaking a piece of lodestone in half would result in two pieces, each with its own pair of poles.

In 1600 the English physician William Gilbert concluded that the Earth itself is a magnet and that the Earth's magnetic poles are approximately aligned along the Earth's axis of rotation.

The British scientist, John Michell, discovered in 1750 that the magnitude of forces between the poles of magnets follows an inverse square law i.e. it varies inversely as the square of the distance of separation.

Magnetic forces are a result of magnetic fields. The magnetic field is an entity produced by moving electric charges that exerts a force on other moving charges. In permanent ferromagnets the magnetic field is produced by the spin of electrons within the material being in the same direction.

By placing a magnet underneath a piece of paper and sprinkling iron filings on top one can map the magnetic field. The filings align themselves parallel to the field. Magnetic fields can be represented by magnetic field lines which are parallel to the magnetic field and whose spacing represents the relative strength of the magnetic field. The strength of the magnetic field is referred to as the magnetic flux. Magnetic field lines form closed loops. In a bar magnet magnetic field lines emerge at one pole and then curve around to the other pole with the rest of the loop being inside the magnet.

Opposite poles of a magnet attract each other and bringing them together results in their magnetic field lines converging.

Like poles of a magnet repel each other and bringing them together results in their magnetic field lines diverging.

Ferromagnetism is a phenomenon exhibited by materials like iron, nickel or cobalt. They become magnetized in an external magnetic field by aligning their electron spins with the external field. Ferromagnetic materials retain their magnetism even when the field is removed as the electron spins retain their orientation. At high enough temperatures ferromagnets lose their orientation as the heat causes the orientations of electron orbits within iron to become randomized.

Iron always magnetizes so as to be attracted to a magnet, regardless of which magnetic pole is brought toward the unmagnetized iron:

The ability of a ferromagnetic material tends to retain its magnetization after an external field is removed is called it's retentivity.

Paramagnetic materials are materials like aluminum or platinum which become magnetized in an external magnetic field in a similar way to ferromagnetic materials but lose their magnetism when the external magnetic field is removed.

Diamagnetism is exhibited by materials like copper or bismuth which become magnetized in a magnetic field with a polarity opposite to the external magnetic field. Unlike iron, they are slightly repelled by a magnet

The cause of Earth's magnetic field is not known for certain, but is possibly explained by the dynamo theory. The magnetic field extends several tens of thousands of kilometers into space. The field is approximately a magnetic dipole, with one pole near the geographic north pole and the other near the geographic south pole. An imaginary line joining the magnetic poles would be inclined by approximately 11.3 from the planet's axis of rotation. The location of the magnetic poles is not static but wanders as much as several kilometers a year. The two poles wander independently of each other and are not at exact opposite positions on the globe. Currently the south magnetic pole is further from the geographic south pole than than north magnetic pole is from the north geographic pole.

The strength of the field at the Earth's surface at this time ranges from less than 30 microteslas (0.3 gauss) in an area including most of South America and South Africa to over 60 microteslas (0.6 gauss) around the magnetic poles in northern Canada and south of Australia, and in part of Siberia. The field is similar to that of a bar magnet, but this similarity is superficial. The magnetic field of a bar magnet, or any other type of permanent magnet, is created by the coordinated motions of electrons (negatively charged particles) within iron atoms. The Earth's core, however, is hotter than 1043 K, the temperature at which the orientations of electron orbits within iron become randomized. Therefore the Earth's magnetic field is not caused by magnetised iron deposits, but mostly by electric currents (known as telluric currents). Another feature that distinguishes the Earth magnetically from a bar magnet is its magnetosphere.

A magnetosphere is the region around an astronomical object, in which phenomena are dominated by its magnetic field. Earth is surrounded by a magnetosphere, as are the magnetized planets Jupiter, Saturn, Uranus and Neptune. Mercury is magnetized, but too weakly to trap plasma. Mars has patchy surface magnetization.

The distant field of Earth is greatly modified by the solar wind, a hot outflow from the sun, consisting of solar ions (mainly hydrogen) moving at about 400 km/s. Earth's magnetic field forms an obstacle to the solar wind.

The Earth's magnetic field reverses at intervals, ranging from tens of thousands to many millions of years, with an average interval ofnbsp; 250,000 years. It is believed that this last occurred some 780,000 years ago. The mechanism responsible for geomagnetic reversals is not well understood. When the North reappears in the opposite direction, we would interpret this as a reversal, whereas turning off and returning in the same direction is called a geomagnetic excursion. At present, the overall geomagnetic field is becoming weaker at a rate which would, if it continues, cause the field to disappear, albeit temporarily, by about around 3000-4000 AD. The deterioration began roughly 150 years ago and has accelerated in the past several years. So far the strength of the Earth's field has decreased by 10 to 15 percent.


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FHSST Physics/Magnets and Electromagnetism/Electromagnetism

= Electromagnetism =

 The discovery of the relationship between magnetism and electricity was, like so many other scientific discoveries, stumbled upon almost by accident. The Danish physicist Hans Christian Oersted was lecturing one day in 1820 on the possibility of electricity and magnetism being related to one another, and in the process demonstrated it conclusively by experiment in front of his whole class! By passing an electric current through a metal wire suspended above a magnetic compass, Oersted was able to produce a definite motion of the compass needle in response to the current. What began as conjecture at the start of the class session was confirmed as fact at the end. Needless to say, Oersted had to revise his lecture notes for future classes! His serendipitous discovery paved the way for a whole new branch of science: electromagnetics.

Detailed experiments showed that the magnetic field produced by an electric current is always oriented perpendicular to the direction of flow. A simple method of showing this relationship is called the left-hand rule. Simply stated, the left-hand rule says that the magnetic flux lines produced by a current-carrying wire will be oriented the same direction as the curled fingers of a person's left hand (in the "hitchhiking" position), with the thumb pointing in the direction of electron flow:

The magnetic field encircles this straight piece of current-carrying wire, the magnetic flux lines having no definite "north" or "south' poles.

Note: Need to add wires attracting or wires repelling

While the magnetic field surrounding a current-carrying wire is indeed interesting, it is quite weak for common amounts of current, able to deflect a compass needle and not much more. To create a stronger magnetic field force (and consequently, more field flux) with the same amount of electric current, we can wrap the wire into a coil shape, where the circling magnetic fields around the wire will join to create a larger field with a definite magnetic (north and south) polarity:

The amount of magnetic field force generated by a coiled wire is proportional to the current through the wire multiplied by the number of "turns" or "wraps" of wire in the coil. This field force is called magnetomotive force (mmf), and is very much analogous to electromotive force (E) in an electric circuit.

An electromagnet is a piece of wire intended to generate a magnetic field with the passage of electric current through it. Though all current-carrying conductors produce magnetic fields, an electromagnet is usually constructed in such a way as to maximize the strength of the magnetic field it produces for a special purpose. Electromagnets find frequent application in research, industry, medical, and consumer products.

As an electrically-controllable magnet, electromagnets find application in a wide variety of "electromechanical" devices: machines that effect mechanical force or motion through electrical power. Perhaps the most obvious example of such a machine is the electric motor.

Relays can be constructed to actuate multiple switch contacts, or operate them in "reverse" (energizing the coil will open the switch contact, and unpowering the coil will allow it to spring closed again).


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FHSST Physics/Magnets and Electromagnetism/Magnetic Units of Measurement

= Magnetic units of measurement =

If the burden of two systems of measurement for common quantities (English vs. metric) throws your mind into confusion, this is not the place for you! Due to an early lack of standardization in the science of magnetism, we have been plagued with no less than three complete systems of measurement for magnetic quantities.

First, we need to become acquainted with the various quantities associated with magnetism. There are quite a few more quantities to be dealt with in magnetic systems than for electrical systems. With electricity, the basic quantities are Voltage (E), Current (I), Resistance (R), and Power (P). The first three are related to one another by Ohm's Law (E=IR ; I=E/R; R=E/I), while Power is related to voltage, current, and resistance by Joule's Law (P=IE; $$P=I^{2}R$$; $$P=\frac{E^{2}}{R}$$).

With magnetism, we have the following quantities to deal with:

Magnetomotive Force - The quantity of magnetic field force, or "push." Analogous to electric voltage (electromotive force).

Field Flux - The quantity of total field effect, or "substance" of the field. Analogous to electric current.

Field Intensity - The amount of field force (mmf) distributed over the length of the electromagnet. Sometimes referred to as Magnetizing Force.

Flux Density - The amount of magnetic field flux concentrated in a given area.

Reluctance - The opposition to magnetic field flux through a given volume of space or material. Analogous to electrical resistance.

Permeability - The specific measure of a material's acceptance of magnetic flux, analogous to the specific resistance of a conductive material ($$\rho$$), except inverse (greater permeability means easier passage of magnetic flux, whereas greater specific resistance means more difficult passage of electric current).

But wait. . . the fun is just beginning! Not only do we have more quantities to keep track of with magnetism than with electricity, but we have several different systems of unit measurement for each of these quantities. As with common quantities of length, weight, volume, and temperature, we have both English and metric systems. However, there is actually more than one metric system of units, and multiple metric systems are used in magnetic field measurements! One is called the cgs, which stands for Centimeter-Gram-Second, denoting the root measures upon which the whole system is based. The other was originally known as the mks system, which stood for Meter-Kilogram-Second, which was later revised into another system, called rmks, standing for Rationalized Meter-Kilogram-Second. This ended up being adopted as an international standard and renamed SI (Systeme International).

RIAAN Note: NEED TO INSERT TABLE HERE

And yes, the $$\mu$$ symbol is really the same as the metric prefix "micro." I find this especially confusing, using the exact same alphabetical character to symbolize both a specific quantity and a general metric prefix!

As you might have guessed already, the relationship between field force, field flux, and reluctance is much the same as that between the electrical quantities of electromotive force (E), current (I), and resistance (R). This provides something akin to an Ohm's Law for magnetic circuits:

And, given that permeability is inversely analogous to specific resistance, the equation for finding the reluctance of a magnetic material is very similar to that for finding the resistance of a conductor:

In either case, a longer piece of material provides a greater opposition, all other factors being equal. Also, a larger cross-sectional area makes for less opposition, all other factors being equal.


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FHSST Physics/Magnets and Electromagnetism/Electromagnetic Induction

= Electromagnetic induction = While Oersted's surprising discovery of electromagnetism paved the way for more practical applications of electricity, it was Michael Faraday who gave us the key to the practical generation of electricity: electromagnetic induction. Faraday discovered that a voltage would be generated across a length of wire if that wire was exposed to a perpendicular magnetic field flux of changing intensity.

An easy way to create a magnetic field of changing intensity is to move a permanent magnet next to a wire or coil of wire. Remember: the magnetic field must increase or decrease in intensity perpendicular to the wire (so that the lines of flux "cut across" the conductor), or else no voltage will be induced:

Faraday was able to mathematically relate the rate of change of the magnetic field flux with induced voltage (note the use of a lower-case letter "e" for voltage. This refers to instantaneous voltage, or voltage at a specific point in time, rather than a steady, stable voltage.):

The "d" terms are standard calculus notation, representing rate-of-change of flux over time. "N" stands for the number of turns, or wraps, in the wire coil (assuming that the wire is formed in the shape of a coil for maximum electromagnetic efficiency).

This phenomenon is put into obvious practical use in the construction of electrical generators, which use mechanical power to move a magnetic field past coils of wire to generate voltage. However, this is by no means the only practical use for this principle.

If we recall that the magnetic field produced by a current-carrying wire was always perpendicular to that wire, and that the flux intensity of that magnetic field varied with the amount of current through it, we can see that a wire is capable of inducing a voltage along its own length simply due to a change in current through it. This effect is called self-induction: a changing magnetic field produced by changes in current through a wire inducing voltage along the length of that same wire. If the magnetic field flux is enhanced by bending the wire into the shape of a coil, and/or wrapping that coil around a material of high permeability, this effect of self-induced voltage will be more intense. A device constructed to take advantage of this effect is called an inductor, and will be discussed in greater detail in the next chapter.

A device specifically designed to produce the effect of mutual inductance between two or more coils is called a transformer.

Because magnetically-induced voltage only happens when the magnetic field flux is changing in strength relative to the wire, mutual inductance between two coils can only happen with alternating (changing - AC) voltage, and not with direct (steady - DC) voltage. The only applications for mutual inductance in a DC system is where some means is available to switch power on and off to the coil (thus creating a pulsing DC voltage), the induced voltage peaking at every pulse.

A very useful property of transformers is the ability to transform voltage and current levels according to a simple ratio, determined by the ratio of input and output coil turns. If the energized coil of a transformer is energized by an AC voltage, the amount of AC voltage induced in the unpowered coil will be equal to the input voltage multiplied by the ratio of output to input wire turns in the coils. Conversely, the current through the windings of the output coil compared to the input coil will follow the opposite ratio: if the voltage is increased from input coil to output coil, the current will be decreased by the same proportion. This action of the transformer is analogous to that of mechanical gear, belt sheave, or chain sprocket ratios:

A transformer designed to output more voltage than it takes in across the input coil is called a "step-up" transformer, while one designed to do the opposite is called a "step-down," in reference to the transformation of voltage that takes place. The current through each respective coil, of course, follows the exact opposite proportion.


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FHSST Physics/Magnets and Electromagnetism/Alternating Current

= Alternating Current =

Most students of electromagnetism begin their study with what is known as direct current (DC). In a DC system, the current (the flow of charged particles) is in a constant direction. In a DC system, the voltage across each part has a constant polarity. DC is the kind of electric power made by a battery (with definite positive and negative terminals), or the kind of charge generated by rubbing certain types of materials against each other.

As useful and as easy to understand as DC is, it is not the only "kind" of electric power in use. Certain sources of electric power (most notably, rotary electro-mechanical generators) naturally produce voltages alternating in polarity, reversing positive and negative over time. Either as a voltage switching polarity or as a current switching direction back and forth, this "kind" of electric power is known as Alternating Current (AC):

Whereas the familiar battery symbol is used as a generic symbol for any DC voltage source, the circle with the wavy line inside is the generic symbol for any AC voltage source.

One might wonder why anyone would bother with such a thing as AC. It is true that in some cases AC holds no practical advantage over DC. In applications where electricity is used to dissipate energy in the form of heat, the polarity or direction of current is irrelevant, so long as there is enough voltage and current to the load to produce the desired heat (power dissipation). However, with AC it is possible to build electric generators, motors and power distribution systems that are far more efficient than DC, and so we find AC used predominately across the world in high power applications. To explain the details of why this is so, a bit of background knowledge about AC is necessary.

If a machine is constructed to rotate a magnetic field around a set of stationary wire coils with the turning of a shaft, AC voltage will be produced across the wire coils as that shaft is rotated, in accordance with Faraday's Law of electromagnetic induction. This is the basic operating principle of an AC generator, also known as an alternator:

Notice how the polarity of the voltage across the wire coils reverses as the opposite poles of the rotating magnet pass by. Connected to a load, this reversing voltage polarity will create a reversing current direction in the circuit. The faster the alternator's shaft is turned, the faster the magnet will spin, resulting in an alternating voltage and current that switches directions more often in a given amount of time.

While DC generators work on the same general principle of electromagnetic induction, their construction is not as simple as their AC counterparts. With a DC generator, the coil of wire is mounted in the shaft where the magnet is on the AC alternator, and electrical connections are made to this spinning coil via stationary carbon "brushes" contacting copper strips on the rotating shaft. All this is necessary to switch the coil's changing output polarity to the external circuit so the external circuit sees a constant polarity:

The generator shown above will produce two pulses of voltage per revolution of the shaft, both pulses in the same direction (polarity). In order for a DC generator to produce constant voltage, rather than brief pulses of voltage once every 1/2 revolution, there are multiple sets of coils making intermittent contact with the brushes. The diagram shown above is a bit more simplified than what you would see in real life.

The problems involved with making and breaking electrical contact with a moving coil should be obvious (sparking and heat), especially if the shaft of the generator is revolving at high speed. If the atmosphere surrounding the machine contains flammable or explosive vapors, the practical problems of spark-producing brush contacts are even greater. An AC generator (alternator) does not require brushes and commutators to work, and so is immune to these problems experienced by DC generators.

The benefits of AC over DC with regard to generator design is also reflected in electric motors. While DC motors require the use of brushes to make electrical contact with moving coils of wire, AC motors do not. In fact, AC and DC motor designs are very similar to their generator counterparts (identical for the sake of this tutorial), the AC motor being dependent upon the reversing magnetic field produced by alternating current through its stationary coils of wire to rotate the rotating magnet around on its shaft, and the DC motor being dependent on the brush contacts making and breaking connections to reverse current through the rotating coil every 1/2 rotation (180 degrees).

So we know that AC generators and AC motors tend to be simpler than DC generators and DC motors. This relative simplicity translates into greater reliability and lower cost of manufacture. But what else is AC good for? Surely there must be more to it than design details of generators and motors! Indeed there is. There is an effect of electromagnetism known as mutual induction, whereby two or more coils of wire placed so that the changing magnetic field created by one induces a voltage in the other. If we have two mutually inductive coils and we energize one coil with AC, we will create an AC voltage in the other coil. When used as such, this device is known as a transformer:

The fundamental significance of a transformer is its ability to step voltage up or down from the powered coil to the unpowered coil. The AC voltage induced in the unpowered ("secondary") coil is equal to the AC voltage across the powered ("primary") coil multiplied by the ratio of secondary coil turns to primary coil turns. If the secondary coil is powering a load, the current through the secondary coil is just the opposite: primary coil current multiplied by the ratio of primary to secondary turns. This relationship has a very close mechanical analogy, using torque and speed to represent voltage and current, respectively:

If the winding ratio is reversed so that the primary coil has less turns than the secondary coil, the transformer "steps up" the voltage from the source level to a higher level at the load:

The transformer's ability to step AC voltage up or down with ease gives AC an advantage unmatched by DC in the realm of power distribution. When transmitting electrical power over long distances, it is far more efficient to do so with stepped-up voltages and stepped-down currents (smaller-diameter wire with less resistive power losses), then step the voltage back down and the current back up for industry, business, or consumer use use.

Transformer technology has made long-range electric power distribution practical. Without the ability to efficiently step voltage up and down, it would be cost-prohibitive to construct power systems for anything but close-range (within a few miles at most) use.

As useful as transformers are, they only work with AC, not DC. Because the phenomenon of mutual inductance relies on changing magnetic fields, and direct current (DC) can only produce steady magnetic fields, transformers simply will not work with direct current. Of course, direct current may be interrupted (pulsed) through the primary winding of a transformer to create a changing magnetic field (as is done in automotive ignition systems to produce high-voltage spark plug power from a low-voltage DC battery), but pulsed DC is not that different from AC. Perhaps more than any other reason, this is why AC finds such widespread application in power systems.

If we were to follow the changing voltage produced by a coil in an alternator from any point on the sine wave graph to that point when the wave shape begins to repeat itself, we would have marked exactly one cycle of that wave. This is most easily shown by spanning the distance between identical peaks, but may be measured between any corresponding points on the graph. The degree marks on the horizontal axis of the graph represent the domain of the trigonometric sine function, and also the angular position of our simple two-pole alternator shaft as it rotates:

Since the horizontal axis of this graph can mark the passage of time as well as shaft position in degrees, the dimension marked for one cycle is often measured in a unit of time, most often seconds or fractions of a second. When expressed as a measurement, this is often called the period of a wave. The period of a wave in degrees is always 360, but the amount of time one period occupies depends on the rate voltage oscillates back and forth.

A more popular measure for describing the alternating rate of an AC voltage or current wave than period is the rate of that back-and-forth oscillation. This is called frequency. The modern unit for frequency is the hertz (abbreviated Hz), which represents the number of wave cycles completed during one second of time. In the United States of America, the standard power-line frequency is 60 Hz, meaning that the AC voltage oscillates at a rate of 60 complete back-and-forth cycles every second. In Europe, where the power system frequency is 50 Hz, the AC voltage only completes 50 cycles every second. A radio station transmitter broadcasting at a frequency of 100 MHz generates an AC voltage oscillating at a rate of 100 million cycles every second.

Period and frequency are mathematical reciprocals of one another. That is to say, if a wave has a period of 10 seconds, its frequency will be 0.1 Hz, or 1/10 of a cycle per second:

$$\ Frequency\ in\ hertz = \frac{1}{Period\ in\ seconds}$$

An instrument called an oscilloscope is used to display a changing voltage over time on a graphical screen. You may be familiar with the appearance of an ECG or EKG (electrocardiograph) machine, used by physicians to graph the oscillations of a patient's heart over time. The ECG is a special-purpose oscilloscope expressly designed for medical use. General-purpose oscilloscopes have the ability to display voltage from virtually any voltage source, plotted as a graph with time as the independent variable. The relationship between period and frequency is very useful to know when displaying an AC voltage or current waveform on an oscilloscope screen. By measuring the period of the wave (in seconds) on the horizontal axis of the oscilloscope screen and reciprocating that time value, you can determine the frequency in hertz.

Voltage and current are by no means the only physical variables subject to variation over time. Much more common to our everyday experience is sound, which is nothing more than the alternating compression and decompression (pressure waves) of air molecules, interpreted by our ears as a physical sensation. Because alternating current is a wave phenomenon, it shares many of the properties of other wave phenomena, like sound. For this reason, sound (especially structured music) provides an excellent analogy for relating AC concepts.

In musical terms, frequency is equivalent to pitch. Low-pitch notes such as those produced by a tuba or bassoon consist of air molecule vibrations that are relatively slow (low frequency). High-pitch notes such as those produced by a flute or whistle consist of the same type of vibrations in the air, only vibrating at a much faster rate (higher frequency). Here is a table showing the actual frequencies for a range of common musical notes:

Astute observers will notice that all notes on the table bearing the same letter designation are related by a frequency ratio of 2:1. For example, the first frequency shown (designated with the letter "A") is 220 Hz. The next highest "A" note has a frequency of 440 Hz - exactly twice as many sound wave cycles per second. The same 2:1 ratio holds true for the first A sharp (233.08 Hz) and the next A sharp (466.16 Hz), and for all note pairs found in the table.

Audibly, two notes whose frequencies are exactly double each other sound remarkably similar. This similarity in sound is musically recognized, the shortest span on a musical scale separating such note pairs being called an octave. Following this rule, the next highest "A" note (one octave above 440 Hz) will be 880 Hz, the next lowest "A" (one octave below 220 Hz) will be 110 Hz. A view of a piano keyboard helps to put this scale into perspective:

As you can see, one octave is equal to eight white keys' worth of distance on a piano keyboard. The familiar musical mnemonic (doe-ray-mee-fah-so-lah-tee-doe) - yes, the same pattern immortalized in the whimsical Rodgers and Hammerstein song sung in The Sound of Music - covers one octave from C to C.

While electromechanical alternators and many other physical phenomena naturally produce sine waves, this is not the only kind of alternating wave in existence. Other "waveforms" of AC are commonly produced within electronic circuitry. Here are but a few sample waveforms and their common designations:

These waveforms are by no means the only kinds of waveforms in existence. They're simply a few that are common enough to have been given distinct names. Even in circuits that are supposed to manifest "pure" sine, square, triangle, or sawtooth voltage/current waveforms, the real-life result is often a distorted version of the intended waveshape. Some waveforms are so complex that they defy classification as a particular "type" (including waveforms associated with many kinds of musical instruments). Generally speaking, any waveshape bearing close resemblance to a perfect sine wave is termed sinusoidal, anything different being labeled as non-sinusoidal. Being that the waveform of an AC voltage or current is crucial to its impact in a circuit, we need to be aware of the fact that AC waves come in a variety of shapes.


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FHSST Physics/Magnets and Electromagnetism/Measurements of AC Magnitude

= Measurements of AC magnitude =

So far we know that AC voltage alternates in polarity and AC current alternates in direction. We also know that AC can alternate in a variety of different ways, and by tracing the alternation over time we can plot it as a "waveform." We can measure the rate of alternation by measuring the time it takes for a wave to evolve before it repeats itself (the "period"), and express this as cycles per unit time, or "frequency." In music, frequency is the same as pitch, which is the essential property distinguishing one note from another.

However, we encounter a measurement problem if we try to express how large or small an AC quantity is. With DC, where quantities of voltage and current are generally stable, we have little trouble expressing how much voltage or current we have in any part of a circuit. But how do you grant a single measurement of magnitude to something that is constantly changing?

One way to express the intensity, or magnitude (also called the amplitude), of an AC quantity is to measure its peak height on a waveform graph. This is known as the peak or crest value of an AC waveform:

Another way is to measure the total height between opposite peaks. This is known as the peak-to-peak (P-P) value of an AC waveform:

Unfortunately, either one of these expressions of waveform amplitude can be misleading when comparing two different types of waves. For example, a square wave peaking at 10 volts is obviously a greater amount of voltage for a greater amount of time than a triangle wave peaking at 10 volts. The effects of these two AC voltages powering a load would be quite different:

One way of expressing the amplitude of different waveshapes in a more equivalent fashion is to mathematically average the values of all the points on a waveform's graph to a single, aggregate number. This amplitude measure is known simply as the average value of the waveform. If we average all the points on the waveform algebraically (that is, to consider their sign, either positive or negative), the average value for most waveforms is technically zero, because all the positive points cancel out all the negative points over a full cycle:

This, of course, will be true for any waveform having equal-area portions above and below the "zero" line of a plot. However, as a practical measure of a waveform's aggregate value, "average" is usually defined as the mathematical mean of all the points' absolute values over a cycle. In other words, we calculate the practical average value of the waveform by considering all points on the wave as positive quantities, as if the waveform looked like this:

Polarity-insensitive mechanical meter movements (meters designed to respond equally to the positive and negative half-cycles of an alternating voltage or current) register in proportion to the waveform's (practical) average value, because the inertia of the pointer against the tension of the spring naturally averages the force produced by the varying voltage/current values over time. Conversely, polarity-sensitive meter movements vibrate uselessly if exposed to AC voltage or current, their needles oscillating rapidly about the zero mark, indicating the true (algebraic) average value of zero for a symmetrical waveform. When the "average" value of a waveform is referenced in this text, it will be assumed that the "practical" definition of average is intended unless otherwise specified.

Another method of deriving an aggregate value for waveform amplitude is based on the waveform's ability to do useful work when applied to a load resistance. Unfortunately, an AC measurement based on work performed by a waveform is not the same as that waveform's "average" value, because the power dissipated by a given load (work performed per unit time) is not directly proportional to the magnitude of either the voltage or current impressed upon it. Rather, power is proportional to the square of the voltage or current applied to a resistance (P = E/R, and P = IR). Although the mathematics of such an amplitude measurement might not be straightforward, the utility of it is.

Consider a bandsaw and a jigsaw, two pieces of modern woodworking equipment. Both types of saws cut with a thin, toothed, motor-powered metal blade to cut wood. But while the bandsaw uses a continuous motion of the blade to cut, the jigsaw uses a back-and-forth motion. The comparison of alternating current (AC) to direct current (DC) may be likened to the comparison of these two saw types:

The problem of trying to describe the changing quantities of AC voltage or current in a single, aggregate measurement is also present in this saw analogy: how might we express the speed of a jigsaw blade? A bandsaw blade moves with a constant speed, similar to the way DC voltage pushes or DC current moves with a constant magnitude. A jigsaw blade, on the other hand, moves back and forth, its blade speed constantly changing. What is more, the back-and-forth motion of any two jigsaws may not be of the same type, depending on the mechanical design of the saws. One jigsaw might move its blade with a sine-wave motion, while another with a triangle-wave motion. To rate a jigsaw based on its peak blade speed would be quite misleading when comparing one jigsaw to another (or a jigsaw with a bandsaw!). Despite the fact that these different saws move their blades in different manners, they are equal in one respect: they all cut wood, and a quantitative comparison of this common function can serve as a common basis for which to rate blade speed.

Picture a jigsaw and bandsaw side-by-side, equipped with identical blades (same tooth pitch, angle, etc.), equally capable of cutting the same thickness of the same type of wood at the same rate. We might say that the two saws were equivalent or equal in their cutting capacity. Might this comparison be used to assign a "bandsaw equivalent" blade speed to the jigsaw's back-and-forth blade motion to relate the wood-cutting effectiveness of one to the other? This is the general idea used to assign a "DC equivalent" measurement to any AC voltage or current: whatever magnitude of DC voltage or current would produce the same amount of heat energy dissipation through an equal resistance:

Suppose we were to wrap a coil of insulated wire around a loop of ferromagnetic material and energize this coil with an AC voltage source:

As an inductor, we would expect this iron-core coil to oppose the applied voltage with its inductive reactance, limiting current through the coil as predicted by the equations $$X_L= 2\pi\ fL$$ and $$I=E/X$$ (or $$I=E/Z$$). For the purposes of this example, though, we need to take a more detailed look at the interactions of voltage, current, and magnetic flux in the device.

Kirchhoff's voltage law describes how the algebraic sum of all voltages in a loop must equal zero. In this example, we could apply this fundamental law of electricity to describe the respective voltages of the source and of the inductor coil. Here, as in any one-source, one-load circuit, the voltage dropped across the load must equal the voltage supplied by the source, assuming zero voltage dropped along the resistance of any connecting wires. In other words, the load (inductor coil) must produce an opposing voltage equal in magnitude to the source, in order that it may balance against the source voltage and produce an algebraic loop voltage sum of zero. From where does this opposing voltage arise? If the load were a resistor, the opposing voltage would originate from the "friction" of electrons flowing through the resistance of the resistor. With a perfect inductor (no resistance in the coil wire), the opposing voltage comes from another mechanism: the reaction to a changing magnetic flux in the iron core.

Michael Faraday discovered the mathematical relationship between magnetic flux ($$\Phi$$)and induced voltage with this equation:

The instantaneous voltage (voltage dropped at any instant in time) across a wire coil is equal to the number of turns of that coil around the core (N) multiplied by the instantaneous rate-of-change in magnetic flux (d\Phi /dt) linking with the coil. Graphed, this shows itself as a set of sine waves (assuming a sinusoidal voltage source), the flux wave $$90^\circ$$ lagging behind the voltage wave:

Magnetic flux through a ferromagnetic material is analogous to current through a conductor: it must be motivated by some force in order to occur. In electric circuits, this motivating force is voltage (a.k.a. electromotive force, or EMF). In magnetic "circuits," this motivating force is magnetomotive force, or mmf. Magnetomotive force (mmf) and magnetic flux ($$\Phi$$) are related to each other by a property of magnetic materials known as reluctance (the latter quantity symbolized by a strange-looking letter "R" ($$\Re$$)):

In our example, the mmf required to produce this changing magnetic flux ($$\Phi$$) must be supplied by a changing current through the coil. Magnetomotive force generated by an electromagnet coil is equal to the amount of current through that coil (in amps) multiplied by the number of turns of that coil around the core (the SI unit for mmf is the amp-turn). Because the mathematical relationship between magnetic flux and mmf is directly proportional, and because the mathematical relationship between mmf and current is also directly proportional (no rates-of-change present in either equation), the current through the coil will be in-phase with the flux wave:

This is why alternating current through an inductor lags the applied voltage waveform by $$90^\circ$$: because that is what is required to produce a changing magnetic flux whose rate-of-change produces an opposing voltage in-phase with the applied voltage. Due to its function in providing magnetizing force (mmf) for the core, this current is sometimes referred to as the magnetizing current.

It should be mentioned that the current through an iron-core inductor is not perfectly sinusoidal (sine-wave shaped), due to the nonlinear B/H magnetization curve of iron. In fact, if the inductor is cheaply built, using as little iron as possible, the magnetic flux density might reach high levels (approaching saturation), resulting in a magnetizing current waveform that looks something like this:

When a ferromagnetic material approaches magnetic flux saturation, disproportionately greater levels of magnetic field force (mmf) are required to deliver equal increases in magnetic field flux ($$\Phi$$). Because mmf is proportional to current through the magnetizing coil (mmf = NI, where "N" is the number of turns of wire in the coil and "I" is the current through it), the large increases of mmf required to supply the needed increases in flux results in large increases in coil current. Thus, coil current increases dramatically at the peaks in order to maintain a flux waveform that isn't distorted, accounting for the bell-shaped half-cycles of the current waveform in the above plot.

The situation is further complicated by energy losses within the iron core. The effects of hysteresis and eddy currents conspire to further distort and complicate the current waveform, making it even less sinusoidal and altering its phase to be lagging slightly less than $$90^\circ$$ behind the applied voltage waveform. This coil current resulting from the sum total of all magnetic effects in the core (d$$\Phi$$/dt magnetization plus hysteresis losses, eddy current losses, etc.) is called the exciting current. The distortion of an iron-core inductor's exciting current may be minimized if it is designed for and operated at very low flux densities. Generally speaking, this requires a core with large cross-sectional area, which tends to make the inductor bulky and expensive. For the sake of simplicity, though, we'll assume that our example core is far from saturation and free from all losses, resulting in a perfectly sinusoidal exciting current.

As we've seen already in the inductors chapter, having a current waveform $$90^\circ$$ out of phase with the voltage waveform creates a condition where power is alternately absorbed and returned to the circuit by the inductor. If the inductor is perfect (no wire resistance, no magnetic core losses, etc.), it will dissipate zero power.

Let us now consider the same inductor device, except this time with a second coil wrapped around the same iron core. The first coil will be labeled the primary coil, while the second will be labeled the secondary:

If this secondary coil experiences the same magnetic flux change as the primary (which it should, assuming perfect containment of the magnetic flux through the common core), and has the same number of turns around the core, a voltage of equal magnitude and phase to the applied voltage will be induced along its length. In the following graph, the induced voltage waveform is drawn slightly smaller than the source voltage waveform simply to distinguish one from the other:


text: Template:FHSST Physics/Atom

title: Template:FHSST Physics/Atom


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FHSST Physics/Atom

=The Atom =

Atoms are the building blocks of matter. They are the basis of all the structures and organisms in the universe. The planets, the sun, grass and trees, the air we breathe, and people are all made up of atoms.

There are approximately 100 different types of atom, although many of these exist in very small quantities. Every chemical element is one type of atom, such as hydrogen (H), aluminium (Al) and iron (Fe).

title: FHSST Physics/Atom


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FHSST Physics/Atom/Models

= Models of the Atom =

title: FHSST Physics/Atom/Models


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FHSST Physics/Atom/Structure

= Structure of the Atom =

Atoms are very small and cannot be seen with the naked eye nor can they be seen in microscopes using the eye. One million atoms fit across the width of a strand of hair.

They consist of two main parts: the positively charged nucleus at the centre and the negatively charged elementary particles called electrons which surround the nucleus in their orbitals. (Elementary particle means that the electron cannot be broken down to anything smaller and can be thought of as a point particle.) The nucleus of an atom is made up of a collection of positively charged protons and neutral particles called neutrons.

Interesting fact: the neutrons and protons are not elementary particles. They are actually made up of even smaller particles called quarks. Both protons and neutrons are made of three quarks each. There are all sorts of other particles composed of quarks which nuclear physicists study using huge detectors - you can find out more about this by reading the essay in Chapter ??

NOTE :Insert diagram of atomic structure - see lab posters

Atoms are electrically neutral which means that they have the same number of negative electrons as positive protons. The number of protons in an atom is called the atomic number which is sometimes also called Z.

NOTE :check A and Z

The atomic number is what distinguishes the different chemical elements in the Periodic table from each other. In fact, the elements are listed on the Periodic table in order of their atomic numbers. For example, the first element, hydrogen (H), has one proton whereas the sixth element, carbon (C) has 6 protons. Atoms with the same number of protons (atomic number) share physical properties and show similar chemical behaviour. The number of neutrons plus protons in the nucleus is called the atomic mass of the atom.

title: FHSST Physics/Atom/Structure


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FHSST Physics/Atom/Isotopes

= Isotopes =

Two atoms are considered to be the same element if they have the same number of protons (atomic number). However, they do not have to have the same number of neutrons or overall atomic mass. Atoms which have the same number of protons but different numbers of neutrons are called isotopes. For example, the hydrogen atom has one proton and no neutrons. Therefore its atomic number is Z=1 and atomic mass is A=1. If a neutron is added to the hydrogen nucleus, then a new atom is formed with atomic mass A=2 but atomic number is still Z=1. This atom is called deuterium and is an isotope of hydrogen.

title: FHSST Physics/Atom/Isotopes


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FHSST Physics/Atom/Energy Quantization

= Energy quantization and electron configuration =

The electrons which inhabit the space surrounding the nucleus are not able to have arbitrary energies. In fact they are restricted to a discrete set of energies while they are trapped in an atom. This discretization of energy values is known as "quantization", meaning that the allowed energies are separated by discrete energy differences, known as "quanta".

This startling behavior arises from the wavelike nature of electrons and the Schröedinger equation which governs them, both topics which should be addressed in a quantum physics course. Suffice it to say that when particles are in free space (meaning there are no potentials present), the allowed energy values are continuous. However, when they are within a potential, for instance in the potential generated by protons in the nucleus of an atom, their energy values become quantized.

The effects of this quantization are profound. Essentially all of the other natural sciences - chemistry, biology, and other derived sciences rely primarily on the atomic behavior resulting from this quantization.

These energy levels are associated with distances from the nucleus (quantum physics introduces a caveat here). That is, the higher the energy of an electron, the further it is from the nucleus. For some time between Rutherford's discovery of the nucleus-electron system within the atom and the development of quantum physics, electrons were pictured around the nucleus as planets in a solar system. In fact, an impressive body of correct predictions can be made using this classical orbit model, but eventually quantum mechanics must take over to provide the "complete" picture. It turns out that electrons exist as "wavefunctions". They can only be described by a field of probabilities for finding them at some location. These 3-D probability functions can be for visual purposes encapsulated by surfaces:

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When researchers were first beginning to understand the electrical structure of the atom, the primary tool was the spectrometer.

title: FHSST Physics/Atom/Energy Quantization


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FHSST Physics/Atom/Successive Ionization Energies

= Successive ionization energies to provide evidence for arrangement of electrons into core and valence =

[Brink and Jones sections: de Broglie - matter shows particle and wave characteristics, proved by Davisson and Germer. Shroedinger and Heisenberg developed this model into quantum mechanics]

The nucleus (atomic nucleus) is the center of an atom. It is composed of one or more protons and usually some neutrons as well. The number of protons in an atom's nucleus is called the atomic number, and determines which element the atom is (for example hydrogen, carbon, oxygen, etc.).

Though the positively charged protons exert a repulsive electromagnetic force on each other, the distances between nuclear particles are small enough that the strong interaction (which is stronger than the electromagnetic force but decreases more rapidly with distance) predominates. (The gravitational attraction is negligible, being a factor 1036 weaker than this electromagnetic repulsion.)

The discovery of the electron was the first indication that the atom had internal structure. This structure was initially imagined according to the "raisin cookie" or "plum pudding" model, in which the small, negatively charged electrons were embedded in a large sphere containing all the positive charge. Ernest Rutherford and Marsden, however, discovered in 1911 that alpha particles from a radium source were sometimes scattered backwards from a gold foil, indicating that there must be a dense concentration of positive charge at the center of the atom. This discovery led to the acceptance of a planetary model, in which the electrons orbited a tiny nucleus in the same way that the planets orbit the sun.

Interesting Fact: The word atom is derived from the Greek atomos, indivisible, from a-, not, and tomos, a cut.

An atom is the smallest portion into which a chemical element can be divided while still retaining its properties. Atoms are the basic constituents of molecules and ordinary matter. Atoms are composed of subatomic particles.

Atoms are composed mostly of empty space, but also of smaller subatomic particles. At the center of the atom is a tiny positive nucleus composed of nucleons (protons and neutrons). The rest of the atom contains only the fairly flexible electron shells. Usually atoms are electrically neutral with as many electrons as protons.

Atoms are generally classified by their atomic number, which corresponds to the number of protons in the atom. For example, carbon atoms are those atoms containing 6 protons. All atoms with the same atomic number share a wide variety of physical properties and exhibit the same chemical behavior. The various kinds of atoms are listed in the Periodic table. Atoms having the same atomic number, but different atomic masses (due to their different numbers of neutrons), are called isotopes.

The simplest atom is the hydrogen atom, having atomic number 1 and consisting of one proton and one electron. It has been the subject of much interest in science, particularly in the early development of quantum theory.

The chemical behavior of atoms is largely due to interactions between the electrons. In particular the electrons in the outermost shell, called the valence electrons, have the greatest influence on chemical behavior. Core electrons (those not in the outer shell) play a role, but it is usually in terms of a secondary effect due to screening of the positive charge in the atomic nucleus.

There is a strong tendency for atoms to completely fill (or empty) the outer electron shell, which in hydrogen and helium has space for two electrons, and in all other atoms has space for eight. This is achieved either by sharing electrons with neighboring atoms or by completely removing electrons from other atoms. When electrons are shared a covalent bond is formed between the two atoms. Covalent bonds are the strongest type of atomic bond.

When one or more electrons are completely removed from one atom by another, ions are formed. Ions are atoms that possess a net charge due to an imbalance in the number of protons and electrons. The ion that stole the electron(s) is called an anion and is negatively charged. The atom that lost the electron(s) is called a cation and is positively charged. Cations and anions are attracted to each other due to coulombic forces between the positive and negative charges. This attraction is called ionic bonding and is weaker than covalent bonding.

As mentioned above covalent bonding implies a state in which electrons are shared equally between atoms, while ionic bonding implies that the electrons are completely confined to the anion. Except for a limited number of extreme cases, neither of these pictures is completely accurate. In most cases of covalent bonding, the electron is unequally shared, spending more time around the more electronegative atom, resulting in the covalent bond having some ionic character. Similarly, in ionic bonding the electrons often spend a small fraction of time around the more electropositive atom, resulting in some covalent character for the ionic bond.

Models of the atom

 * Democritus' shaped-atom model (for want of a better name)
 * The plum pudding model
 * Cubical atom
 * The Bohr model
 * The quantum mechanical model

The Plum pudding model of the atom was made after the discovery of the electron but before the discovery of the proton or neutron. In it, the atom is envisioned as electrons surrounded by a soup of positive charge, like plums surrounded by pudding. This model was disproved by an experiment by Ernest Rutherford when he discovered the nucleus of the atom.

The Bohr Model is a physical model that depicts the atom as a small positively charged nucleus with electrons in orbit at different levels, similar in structure to the solar system. Because of its simplicity, the Bohr model is still commonly used and taught today.

In the early part of the 20th century, experiments by Ernest Rutherford and others had established that atoms consisted of a small dense positively charged nucleus surrounded by orbiting negatively charged electrons. However, theoretical predictions and experimental evidence quickly began to cast doubt on the classical orbital model.

The simplest possible atom is hydrogen, which consists of a positively charged proton and a negatively charged orbiting electron. According to the orbital model of the atom, since the nucleus (the proton) and the electron are oppositely charged they will attract one another by coulomb force, in the same way that the Sun attracts the Earth with the gravitational force. However, if the electron orbits the nucleus in a classical orbit, it is undergoing a central acceleration, and ought to emit electromagnetic radiation (light) according to well established theories of electromagnetism. If the orbiting electron radiates as it orbits, it must lose energy and therefore spiral into the nucleus in a very short time, which clearly does not occur.

Also, it was well known at the time that atoms emit light only at certain frequencies - the frequencies at which an atom can radiate are known as the spectra of the atom. It was clear that the emission of light by atoms was due to electrons radiating. However, if the electrons are simply orbiting the nucleus classically like planets, there is no reason for the spectra - one would expect the electrons to emit radiation in a continuous frequency spectrum. It soon became clear that something was very wrong with the orbital description of the atom.

These difficulties were resolved in 1913 by Niels Bohr who proposed that:

 * (1) The orbiting electrons existed in orbits that had discrete quantized energies. That is, not every orbit is possible but only certain specific ones. The exact energies of the allowed orbits depends on the atom in question.
 * (2) The laws of classical mechanics do not apply when electrons make the jump from one allowed orbit to another.
 * (3) When an electron makes a jump from one orbit to another the energy difference is carried off (or supplied) by a single quantum of light (called a photon) which has a frequency that directly depends on the energy difference between the two orbitals.

$$f = E / h $$

where f is the frequency of the photon, E the energy difference, and h is a constant of proportionality known as Planck's constant. Defining we can write

where ?? is the angular frequency of the photon.

 * (4) The allowed orbits depend on quantized (discrete) values of orbital angular momentum, L according to the equation

Where n = 1,2,3, and is called the angular momentum quantum number.

These assumptions explained many of the observations seen at the time, such as why spectra consist of discrete lines. Assumption 4) states that the lowest value of n is 1. This corresponds to a smallest possible radius (for the mathematics see Ohanian-principles of physics or any of the large, usually American, college introductory physics textbooks) of 0.0529 nm. This is known as the Bohr radius, and explains why atoms are stable. Once an electron is in the lowest orbit, it can go no further. It cannot emit any more light because it would need to go into a lower orbit, but it can't do that if it is already in the lowest allowed orbit.

The Bohr model is sometimes known as the semiclassical model because although it does include some ideas of quantum mechanics it is not a full quantum mechanical description of the atom. Assumption 2) states that the laws of classical mechanics don't apply during a quantum jump but doesn't state what laws should replace classical mechanics. Assumption 4) states that angular momentum is quantised but does not explain why.

In order to fully describe an atom we need to use the full theory of quantum mechanics, which was worked out by a number of people in the years following the Bohr model. This theory treats the electrons as waves, which create 3D standing wave patterns in the atom. (This is why quantum mechanics is sometimes called wave mechanics.) This theory considers that idea of electrons as being little billiard ball like particles that travel round in orbits as absurdly wrong instead electrons form probability clouds. You might find the electron here with a certain probability; you might find it over there with a different probability. However it is interesting to note that if you work out the average radius of an electron in the lowest possible energy state it turns out to be exactly equal to the Bohr radius (although it takes many more pages of mathematics to work it out).

The full quantum mechanics theory is a beautiful theory that has been experimentally tested and found to be incredibly accurate, however it is mathematically much more advanced, and often using the much simpler Bohr model will get you the results with much less hassle. The thing to remember is that it is only a model, an aid to understanding. Atoms are not really little solar systems.

 * See also: Hydrogen atom, quantum mechanics, Schr&ouml dinger equation, Niels Bohr.
 * An interactive demonstration http://webphysics.davidson.edu/faculty/dmb/hydrogen/ of the probability clouds of electron in Hydrogen atom according to the full QM solution.


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FHSST Physics/Atom/Bohr Orbits

= Bohr orbits =

Brink and Jones sections: Standing waves (quantization). Atom seen as positive nucleus with vibrating electron waves surrounding it. Schrödinger's equation calculates the energy of these waves and their shape and position- most probable region of movement of electrons called orbitals (talk about n=1,2 energy levels and spdf orbitals).

title: FHSST Physics/Atom/Bohr Orbits


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FHSST Physics/Atom/Heisenberg Uncertainty Principle

= Heisenberg Uncertainty Principle =

Quantum mechanics is a physical theory that describes the behavior of physical systems at short distances. Quantum mechanics provides a mathematical framework derived from a small set of basic principles capable of producing experimental predictions for three types of phenomena that classical mechanics and classical electrodynamics cannot account for: quantization, wave-particle duality, and quantum entanglement. The related terms quantum physics and quantum theory are sometimes used as synonyms of quantum mechanics, but also to denote a superset of theories, including pre-quantum mechanics old quantum theory, or, when the term quantum mechanics is used in a more restricted sense, to include theories like quantum field theory.

Quantum mechanics is the underlying theory of many fields of physics and chemistry, including condensed matter physics, quantum chemistry, and particle physics.


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FHSST Physics/Atom/Pauli Exclusion Principle

= Pauli exclusion principle =

The Pauli exclusion principle is a quantum mechanical principle which states that no two identical fermions may occupy the same quantum state. Formulated by Wolfgang Pauli in 1925, it is also referred to as the "exclusion principle" or "Pauli principle."

The Pauli principle only applies to fermions, particles which form antisymmetric quantum states and have half-integer spin. Fermions include protons, neutrons, and electrons, the three types of elementary particles which constitute ordinary matter. The Pauli exclusion principle governs many of the distinctive characteristics of matter. Particles like the photon and graviton do not obey the Pauli exclusion principle, because they are bosons (i.e. they form symmetric quantum states and have integer spin) rather than fermions.

The Pauli exclusion principle plays a role in a huge number of physical phenomena. One of the most important, and the one for which it was originally formulated, is the electron shell structure of atoms. An electrically neutral atom contains bound electrons equal in number to the protons in the nucleus. Since electrons are fermions, the Pauli exclusion principle forbids them from occupying the same quantum state. For example, consider a neutral helium atom, which has two bound electrons. Both of these electrons can occupy the lowest-energy (1s) states by acquiring opposite spin. This does not violate the Pauli principle because spin is part of the quantum state of the electron, so the two electrons are occupying different quantum states. However, the spin can take only two different values (or eigenvalues.) In a lithium atom, which contains three bound electrons, the third electron cannot fit into a 1s state, and has to occupy one of the higher-energy 2s states instead. Similarly, successive elements produce successively higher-energy shells. The chemical properties of an element largely depends on the number of electrons in the outermost shell, which gives rise to the periodic table of the elements.

The Pauli principle is also responsible for the large-scale stability of matter. Molecules cannot be pushed arbitrarily close together, because the bound electrons in each molecule are forbidden from entering the same state as the electrons in the other molecules - this is the reason for the repulsive r-12 term in the Lennard-Jones potential. The Pauli principle is the reason you do not fall through the floor.

Astronomy provides the most spectacular demonstrations of this effect, in the form of white dwarf stars and neutron stars. In both types of objects, the usual atomic structures are disrupted by large gravitational forces, leaving the constituents supported only by a "degeneracy pressure" produced by the Pauli exclusion principle. This exotic form of matter is known as degenerate matter. In white dwarfs, the atoms are held apart by the degeneracy pressure of the electrons. In neutron stars, which exhibit even larger gravitational forces, the electrons have merged with the protons to form neutrons, which produce a larger degeneracy pressure.

Another physical phenomenon for which the Pauli principle is responsible is ferromagnetic, in which the exclusion effect implies an exchange energy that induces neighboring electron spins to align (whereas classically they would anti-align).


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FHSST Physics/Atom/Ionization Energy

= Ionization Energy =

(first, second etc.)

title: FHSST Physics/Atom/Ionization Energy


text:
FHSST Physics/Atom/Electron Configuration

= Electron configuration =

i.e. filling the orbitals starting from 1s..... Aufbau principle unpaired and paired electrons Hund's rule: 1 e- in each orbital before pairing in p orbitals shorthand: $$ 1s^2\ 2s^2\ 2p^2$$ etc.


text:
FHSST Physics/Atom/Valency

= Valency =

Capacity for bonding
Covalent bonding is a form of chemical bonding characterized by the sharing of one or more pairs of electrons, by two atoms. In order to produce a mutual attraction atoms tend to share electrons, so as to fill their outer electron shells. Such bonds are always stronger than the intermolecular hydrogen bond and similar in strength or stronger than the ionic bond. Commonly covalent bond implies the sharing of just a single pair of electrons. The sharing of two pairs is called a double bond and three pairs is called a triple bond. Aromatic rings of atoms and other resonant structures are held together by covalent bonds that are intermediate between single and double. The triple bond is relatively rare in nature, and two atoms are not observed to bond more than triply.

Covalent bonding most frequently occurs between atoms with similar electronegativities, where neither atom can provide sufficient energy to completely remove an electron from the other atom. Covalent bonds are more common between non-metals, whereas ionic bonding is more common between two metal atoms or a metal and a non-metal atom.

Covalent bonding tends to be stronger than other types of bonding, such as ionic bonding. In addition unlike ionic bonding, where ions are held together by a non-directional coulombic attraction, covalent bonds are highly directional. As a result, covalently bonded molecules tend to form in a relatively small number of characteristic shapes, exhibiting specific bonding angles.

title: FHSST Physics/Atom/Valency


text:
Wikibooks:Book of the month/May 2005

The book of the month for May is How To Build A Computer.

How To Build A Computer teaches you how to build your own computer, starting from choosing the right parts, assembling them, and choosing and installing the right software. You can learn more about computer hardware by building a computer than you can by reading every computer hardware textbook ever written. Aside from that, you get a totally personalized computer that no OEM (Original Equipment Manufacturer) could match, and the opportunity to save a lot of money in the process.

Vote for June - Book of the month

title: Wikibooks:Book of the month/May 2005


text:
Wikibooks:Book of the month/June 2005

The book of the month for June is FHSST Physics, a Wikibook for High School Students Studying Physics.

Vote for July - Book of the month

title: Wikibooks:Book of the month/June 2005


text:
Wikibooks:Book of the month/May 2005 voting

The voting for the Book of the month for May 2005 is open from 1 - 30 April, 2005, and will close on April 30, 2005, 00:00 UTC. The book of the month will be featured on the main page of Wikibooks.

'''Closed. Any votes added will be reverted.'''

Physics Study Guide (1)
(Automatically nominated with 4 votes in March)

Votes:
 * 1) Lemontea 09:58, 14 Apr 2005 (UTC)

Comments:

The Unicyclopedia (3)
(Automatically nominated with 4 votes in March)

Votes:
 * 1) Gentgeen 21:36, 2 Apr 2005 (UTC)
 * 2) Andreas 07:50, 19 Apr 2005 (UTC)
 * 3) Reub2000 23:04, 19 Apr 2005 (UTC)

Comments:
 * Nice guide, almost makes me want to start unicycling.Reub2000 23:04, 19 Apr 2005 (UTC)

How To Build A Computer (9)
(Automatically nominated with 4 votes in March)

Votes: Comments:
 * 1) --Hyperlink 03:39, 1 Apr 2005 (UTC)
 * 2) --Noogz 01:20, 2 Apr 2005 (UTC)
 * 3) --Gentgeen 21:36, 2 Apr 2005 (UTC)
 * 4) --Andrewcool 06:33, 4 Apr 2005 (UTC)
 * 5) -- marsh 17:15, 5 Apr 2005 (UTC)
 * 6) --Yayyak 10:27, 14 Apr 2005 (UTC)
 * 7) --Reub2000 00:59, 17 Apr 2005 (UTC)
 * 8) --Naryathegreat|(talk) 01:13, 19 Apr 2005 (UTC)
 * 9) --Eyu100 23:26, 27 Apr 2005 (UTC)
 * Pictures and a little more flesh will really help, but the story looks pretty complete and easy to read - marsh
 * Needs work on trouble shooting sections, more pictures. Hopefully being Book of the Month will bring more people to complete these tasks. Reub2000
 * I agree with the above comments, but this is without a doubt the best book on the list.--Naryathegreat|(talk) 01:13, 19 Apr 2005 (UTC)

Mandarin Chinese (1)
(Automatically nominated with 3 votes in March)

Votes:
 * 1) --EuropracBHIT 05:58, 1 Apr 2005 (UTC).

Comments:

FHSST Physics:Index (5)

 * 1) Check out this book, it has a whole team of people working on it to use in schools in South Africa. It is not ready for the spotlight yet but this books looks like it might become a WikiBooks poster child of how to organize a collaborative team.--Karl Wick 20:02, 18 Apr 2005 (UTC)
 * 2) Constantijn 17:05, 24 Apr 2004 (UTC)
 * 3) Gentgeen 21:18, 24 Apr 2005 (UTC)
 * 4) Marknewlyn 03:41, 28 Apr 2005 (UTC)
 * 5) Moldi 05:37, 28 Apr 2005 (UTC)


text:
User:Riaan

Hi

My name is Riaan, I live in Cape Town, South Africa. I have been asked to Wikify material that has been developed around the South African School Curriculum.

I am not the author of the material, see the specific pages for details about the different authors.

The material I have wikified can be found here.

=How I wikified the textbooks=

Some of the material was given to me in PDF format! I used ... I will continue with this later :)

title: User:Riaan


text:
User:Kesara

Visit my home page for more information. Kesara's Home Page

title: User:Kesara


text:
Ada Programming/Ada 95

Ada 95 is the second revision of the language, preceded by Ada 83. It was standardized by the ISO in 1995. The Technical Corrigendum 1 was published in June 2001.

New language features
Main additions:
 * Object Orientation
 * Protected Objects
 * Hierarchical libraries

Character set

 * Latin-1 (8-bit) character set for identifiers
 * Type Character expanded to the 256 values of Latin-1 (8 bits)
 * New type Wide_Character (16-bit character type, UCS-2 encoding) and Wide_String

Specialized Needs Annexes

 * Annex C, "Systems Programming"
 * Annex D, "Real-Time Systems"
 * Annex E, "Distributed Systems"
 * Annex F, "Information Systems"
 * Annex G, "Numerics"
 * Annex H, "Safety and Security" (in Ada 2005 renamed to "High Integrity Systems")

Other language additions

 * Modular types
 * General access types
 * Access to subprograms
 * 'delay until' statement
 * 'use type' clause

New keywords
Ada 95 has 6 new keywords with respect to Ada 83 (69 keywords in total):

New pragmas
Added 29 pragmas, removed 5 (38 total):

New attributes
Added 52 attributes, removed 7 (85 total):

Wikibook

 * Ada Programming/Ada 83
 * Ada Programming/Ada 2005
 * Ada Programming/Ada 2012
 * Ada Programming/Keywords
 * Ada Programming/Attributes
 * Ada Programming/Pragmas

title: Ada Programming/Ada 95


text:
Ada Programming/Ada 83

Ada 83 is the first version of the Ada programming language. It was based in the so called Ada 80, a preliminary version of the language formally known as MIL-STD-1815 (published in December 1980). This standard was refined and standardized by the DoD and ANSI as ANSI/MIL-STD-1815A in February 1983 (note the additional 'A' at the end), which was later adopted by International Organization for Standardization as ISO/IEC 8652:1987.

Character set

 * Identifiers in ASCII (7-Bit)

Keywords
Ada 83 has 63 keywords:

Pragmas
Has 14 pragmas:
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)

Attributes
Has 40 attributes:
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)
 * (obsolescent since Ada 95)

Wikibook

 * Ada Programming/Ada 95
 * Ada Programming/Ada 2005
 * Ada Programming/Ada 2012
 * Ada Programming/Keywords
 * Ada Programming/Attributes
 * Ada Programming/Pragmas

title: Ada Programming/Ada 83


text:
Robotics/Computer Control/The Interface/Computers

Personal computers (PC) have a large number of ports to which you could add your own hardware to control your robot. Some of these are very easy to use, while others are nearly impossible without special (expensive) ICs. Not all of these interfaces are available on all computers. This section gives an overview of some of the best known ports on a PC. These ports and their uses are well document all over the internet.

External Ports
These are all the ports that are available on the outside of a PC. Most computer users are familiar with them (or at least know them by name and looks).

Serial Port
The serial port is one of the two easiest to use ports on a PC. This port consist of 2 wires to transfer your data (one for each direction) and a number of signal wires. This port is reasonably sturdy, and if you know some digital electronics or use a microcontroller, is pretty easy to use too. It is limited on speed and can only connect two devices directly. By using special ICs you can connect the serial port to a RS-485 network and connect it to multiple devices.

 * Serial Programming/RS-232
 * This site contains a lot information on serial ports (among others).

Parallel Port
The parallel port is the second of the easiest to use ports on a PC. This port uses 8 lines to transfer data and has several signal lines. Modern parallel ports can send and receive data. This port is easier to use, but less sturdy than the serial port. Since it operates on TTL voltage levels (0 and 5V) it can connect directly to microcontrollers and TTL logic.

This page covers parallel ports and the differend modes of operation.

USB
USB is the successor of the serial port. It's faster and allows connecting devices without turning off the PC. Some modern microcontrollers have built in USB support.

 * Everything you'd need to know about USB.
 * Serial Programming:USB Technical Manual
 * Embedded Systems/Particular Microprocessors

IEEE 1394: Firewire, i.link, Lynx
IEEE 1394 also known as FireWire, i.link or lynx is a (much) faster port, similar to the USB port. It reaches speeds up to 400Mbit/s.

 * The Connector
 * Article about IEEE 1394.
 * Linux FireWire wiki

Keyboard Connector
Keyboards use TTL level signals to transfer button presses and releases to the PC. A keyboard sends a code when a button is pressed and sends another one when the button is released. This port could be used for some purposes.

See this site for a in depth explanation and example of how to interface the keyboard. (menu: miscellaneous -> interfacing the AT keyboard) Covers both how to replace the keyboard as how to use the keyboard for other purposes.

Ethernet
Ethernet can be used to connect other devices to a PC. Complete webserver-on-a-chip are available these days, and an ethernet network can be a way to connect multiple devices in a robot (and even hook it up to the internet and let people control the robot from all over the world).

Internal Ports
These are the connectors inside the PC, generally these are used with special PCBs (called cards). Although harder to use, they offer great speed.

ISA
ISA was the (8-, later 16-bit) bus where you plugged your video, sound, IDE and network card in the old days. You'll find these on PC up to (some) early Pentium II (the latter usually has only 1 E-ISA socket, if any). This bus is pretty easy to use for your own projects and well documented on the internet.

ISA bus connector More indepth explanation of the ISA bus

PCI
PCI is the successor of the ISA bus. It's a faster 32bit bus. Since it support plug and play, a PCI device needs a few registers which identify the component and manufacturer. This page covers most of the basics of the PCI bus.

AGP
The Accelerated Graphics Port is aimed at 3D graphic cards. It's a fast bus, but optimized for graphics.

PCI Express
PCI Express replaces both PCI and AGP. It's quite different from all the other busses, as it uses serial communication, rather than parallel. Its speed depend on the number of "lanes" (serial connections) used PCI Express support 1, 2, 4, 8 and 16 lanes.

Wireless
These are "ports" too as they can be used to connect other devices to the PC.

IRDA
IRDA is an infrared communication port. Modern versions reach speeds up to 4Mbit/s. IRDA may be a good alternative to wires for table top robots. Since it's an Infrared port it needs a line of sight to work reliable and its range is limited to 1m. Note that this port works at a much higher speed than remote controls and therefor standard remote control repeaters may not work reliable for IRDA.

This site covers the basics of IRDA. Here is a pinout of the mainboard IRDA connector.

WiFi / WLAN / 802.11 / Wireless Ethernet
All the names in the headline are synonyms for the same technology. WLANs are commonly used in PCs (especially laptops) as data networks. The bandwidth available is in the order of several megabits per second or more, far more than normally is necessary in any robotics project. A WLAN typically reaches about 100m, but with special directional antennas far more is possible (in a specific direction).

A WLAN is the obvious choice if your robot has an inbuilt PC or perhaps even PDA for control. Also, when you have ethernet connectivity in your controller (reasonably low cost but not a standard feature except in certain kits), there are low cost (~€50) WLAN bridges available, such as the D-Link DWL-810+ and DWL-G810.

If you only have a serial port available, a wireless device server could be used. The cost of one of them is, however, over €100.

Bluetooth
Bluetooth is a low bandwidth protocol most commonly found in cellular phones. It is increasingly being deployed in laptops, and there are separate USB "sticks" available as well. Bluetooth can be used for making a serial connection wireless - there are Bluetooth serial ports available on the market, which can be used as converters. Total bandwidth in the system is about a megabit per second, with range up to about ten meters (standard Bluetooth, 2.5 mW), or about hundred meters (industrial Bluetooth, 100 mW). There are limitations on scaling with Bluetooth - it is mostly deployed in 1:1 links even though the standard includes networks with up to 8 active nodes (and even more passive ones). This means that if you plan on building large numbers of robots with a common communication network, Bluetooth might be less well suited.

 * Bluetooth resources

ZigBee
ZigBee is a protocol stack based on the 802.15.4 wireless network communication standard. It is low-cost, low-power and all-in-all perfectly suited for low-bandwidth communication needs. The bandwidth is on the order of tens to hundreds kilobits per second, and the range is up to about a kilometer, depending on equipment.

Interesting solutions are XBee from Maxstream, which basically provide a wireless serial link. There also is a list of other vendors at ZigBee.

Cellular networks
A possibility is to use standard cellular networks (mobile phones). It is only a viable solution for large-scale geostationary outdoor applications with low communication needs though, because of cost, latency and bandwidth limitations.

Radio modems
Radio modems are normally older proprietary solutions for wireless linking of serial ports. Proprietary solutions probably shouldn't be considered for new designs.

Using a PC or laptop in a robot
PCs have the benefit of abundance of memory, program space and processing power. Additionally they provide the best debug I/O (screen, keyboard and mouse) you could wish for. But they do have a few flaws that limit their usefulness in a mobile robot.

 * First of all their size. Even the smallest PC, a laptop, is quite bulky and forces you to use a rather large frame.
 * Secondly, except for a laptop, power consumption is large and provide AC-power on a mobile unit is bulky as you need heavy batteries and an inverter.
 * Lastly Pcs are lousy when it comes to getting a reliable accurate timing from the outside world.

The first two points basically shape most of your robot's frame and other than using a different controller not much you can do about it. Picking the best hardware you can find is pretty much all that can make these points a little less troublesome.

The last point is quite easy to get around. Most PCs have a serial port. Most microcontrollers have a serial port as well. Use a level converter to connect the TTL level serial port of the microcontroller with the RS232 level computer serial port and use a little program that handles the accurate timing in the microcontroller and transfers this information to the computer through the serial connection. This is a very powerful setup that combines the strengths of both the PC and the microcontroller.

See this site for example interfacing hardware for the serial port. Covers an I/O module and RS232 to TTL level converter for use with robotics or microcontroller based projects.

Some microcontrollers provide USB or Ethernet ports, which can be used in pretty much the same way, although the software would be a bit harder to implement.