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done in automotive ignition systems to produce high-voltage spark plug power from a low-voltage DC battery), but pulsed DC is not that diﬁerent from AC. Perhaps more than any other reason, this is why AC ﬂnds such widespread application in power systems. If we were to follow the changing voltage produced by a coil in ...
constitutes a step backward in clarity. A similar change occurred when the unit of "Celsius" replaced that of "Centigrade" for metric temperature measurement. The name Centigrade was based on a 100-count ("Centi-") scale ("-grade") representing the melting and boiling points of H2O, respectively. The name Celsius, on ...
by a ute 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: Note A A sharp (or B flat) B C (middle) C sharp (or D flat) D D sharp (or E flat) E F F sharp (or G flat) G...
-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...
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: Peak Time 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 wavef...
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 cu...
same type, depending on the mechanical design 309 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 fac...
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 ...
around the core (the SI unit for mmf is the amp-turn). Because the mathematical relationship between magnetic ux 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 coi...
(d'/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 ux densities. Generally speaking, this requires a core with large cross-sectional area, whic...
eld, by accumulating an internal imbalance of electric charge. It is made of two conductors separated by a dielectric (insulator). The problem of two parallel plates with a uniform electric ﬂeld between them is a capacitor. When voltage exists one end of the capacitor is getting drained and the other end is getting ﬂll...
iron/steel or ferrite. Important qualities of an inductor There are several important properties for an inductor. * Current carrying capacity is determined by wire thickness. * Q, or quality, is determined by the uniformity of the windings, as well as the core material and how thoroughly it surrounds the coil. * Last ...
conducting current, there is a small voltage dropped across it, leaving most of the battery voltage dropped across the lamp. When the battery’s polarity is reversed and the diode becomes reverse-biased, it drops all of the battery’s voltage and leaves none for the lamp. If we consider the diode to be a sort of self-ac...
erent. Typically, LEDs have much larger forward voltage drops than rectifying diodes, anywhere from about 1.6 volts to over 3 volts, depending on the color. Typical operating current for a standard-sized LED is around 20 mA. When operating an LED from a DC voltage source greater than the LED’s forward voltage, a series...
. A typical LED might only be rated at 5 volts in reverse-bias mode. Therefore, when using alternating current to power an LED, you should connect a protective rectifying diode in series with the LED to prevent reverse breakdown every other half-cycle: 320 Light emission The wavelength of the light emitted, and therefo...
red and infrared gallium arsenide/phosphide (GaAsP): red, orange-red, orange, and yellow gallium nitride (GaN): green, pure green (or emerald green), and blue gallium phosphide (GaP): red, yellow and green zinc selenide (ZnSe): blue † † † † † 321 indium gallium nitride (InGaN): bluish-green and blue silicon carbide (S...
The newest method used to produce white light LEDs uses no phosphors at all and is based on homoepitaxially grown zinc selenide (ZnSe) on a ZnSe substrate which simultaneously emits blue light from its active region and yellow light from the substrate. Other colors Recent color developments include pink and purple. Th...
a polymer. Polymer materials can be exible; such LEDs are known as PLEDs or FLEDs. Compared with regular LEDs, OLEDs are lighter and polymer LEDs can have the added beneﬂt of being exible. Some possible future applications of OLEDs could be: Light sources Wall decorations Luminous cloth † † † LED applications Here is ...
. Since an individual device is smaller than a centimetre in length, LED-based light sources used for illumination and outdoor signals are built using clusters of tens of devices. Because they are monochromatic, LED lights have great power advantages over white lights where a speciﬂc color is required. Unlike the white...
the current directions and voltage polarities for each type of transistor are exactly opposite each other. Bipolar transistors work as current-controlled current regulators. In other words, they restrict the amount of current that can go through them according to a smaller, controlling current. The main current that i...
the transistor in modern society is its ability to be produced in huge numbers using simple techniques, resulting in vanishingly small prices. Computer "chips" consist of millions of transistors and sell for rands, with per-transistor costs in the thousandths-of-cents. The low cost has meant that the transistor has be...
are now. We must also make sure that the lamp’s current will move against the direction of the emitter arrow symbol to ensure that the transistor’s junction bias will be correct: 327 In this example I happened to choose an NPN transistor. A PNP transistor could also have been chosen for the job, and its application wo...
current is necessary to turn the transistor on, while the transistor itself handles the majority of the lamp’s current. This may be an important advantage if the switch has a low current rating: a small switch may be used to control a relatively high-current load. Perhaps more importantly, though, is the fact that the...
O2) glass. This is why an alternative name for the FET is ’unipolar transistor.’ When a potential diﬁerence (of the proper polarity) is impressed across gate and source, charge carriers are introduced to the channel, making it conductive. The amount of this current can be modulated, or (nearly) completely turned oﬁ, by...
ETs (for Insulated Gate Field-Eﬁect Transistor) can be depletion-mode, enhancement-mode, or mixed-mode, but are almost always enhancement mode in modern commercial practice. This means that, with the source and gate tied together (thus equipotential) the channel will be oﬁ (high impedance or non-conducting). The n-chan...
users had to settle for relatively poor (horizontal) P-type FET devices. This is no longer the case and allows for quieter and faster analog circuits. A clever variant of the FET is the dual-gate device. This allows for two opportunities to turn the device oﬁ, as opposed to the dual-base (bipolar) transistor which pre...
of chip, to reduce size and power consumption still further, the bipolar transistors were replaced with complementary ﬂeld-eﬁect transistors (MOSFETs), resulting in complementary metal-oxide-semiconductor (CMOS) logic. For small-scale logic, designers now use prefabricated logic gates from families of devices such as ...
of the individual delays, an eﬁect which can become a problem in high-speed circuits. The US symbol for an AND gate is: AND symbol and the IEC symbol is AND symbol. The US circuit symbol for an OR gate is: OR symbol and the IEC symbol is: OR symbol. 332 The US circuit symbol for a NOT gate is: NOT symbol and the IEC s...
adder produces a sum and carry value, which are both binary digits. Sum = (A xor B) xor Cin Cot = (A nand B) nand (Cin nand (A xor B)) Full adder circuit diagram Full adder circuit diagram 333 A B Cin Sum Cot Quantity Symbol Unit S.I. Units Direction Units or Table 16.1: Units used in Electronics 334 Chapter 17 The At...
3 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 diﬁerent numbers of neutrons are called isotopes. For example, the hyd...
isible, 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 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...
and spiral into the nucleus, so why do atoms even exist? What’s more, the spectra of atoms show that the orbiting electrons can emit light but only at certain frequencies. This made no sense at all to the scientists of the time. These di–culties were resolved in 1913 by Niels Bohr who proposed that: * (1) The orbiting...
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 tr...
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 ﬂeld theory. Quantum mech...
the periodic table of the elements. 339 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 r...
atoms are not observed to bond more than triply. Covalent bonding most frequently occurs between atoms with similar electronegativities, where neither atom can provide su–cient energy to completely remove an electron from the other atom. Covalent bonds are more common between non-metals, whereas ionic bonding is more ...
only that side of his personality. So to you, he is just a good cricketer. You do not see his golﬂng side, for example. Only when he is playing golf, will that side be revealed to you. The same applies to light. Now, we consider light to behave not as a wave, but as particles. But what do we call a ’particle’ of light...
to the energy of the photon minus the work function,?, i.e. Ek = h? -? The electrons emerge with a range of velocities from zero up to a maximum vmax. The maximum kinetic energy, (1/2)mvmax2, depends (linearly) on the frequency of the radiation, and is independent of its intensity. For incident radiation of a given fr...
�s equation in their argument. The Planck constant h is extremely small and that explains why we don’t perceive a wave-like quality of everyday objects: their wavelengths are exceedingly small. The fact that matter can have very short wavelengths is exploited in electron microscopy. In quantum mechanics, the wave-parti...
terms of quantum states that are characterized by probability distributions of various observable quantities. For example, an electron in the atom is not moving along a certain trajectory but rather along all imaginable trajectories with diﬁerent probabilities. If we were trying to catch this electron, after many such...
light particle. Its mass is negligible as compared to the total mass of the atom. For example, in the lightest of all atoms, hydrogen, the electron constitutes only 0.054% of the atomic mass. In the silicon atoms that are the main component of the rocks around us, all 14 electrons make up only 0.027% of the mass. Thus...
suggests that it must be something else inside nuclei in addition to protons. These additional particles that kind of \glue" the protons and make up the nuclear mass, apparently, are electrically neutral. They were therefore called neutrons. Rutherford predicted the existence of the neutron in 1920. Twelve years later...
the diﬁerence N = A should not cause any confusion). Chemical symbol is inseparably linked with Z. This is why the lower index is sometimes omitted and you may encounter the simpliﬂed notation like 56Fe. ¡ If we add or remove a few neutrons from a nucleus, the chemical properties of the atom remain the same because it...
correct. Nuclear force has rather unusual properties. Firstly, it is charge independent. This means 10¡13 cm, that in all pairs nn, pp, and np nuclear forces are the same. Secondly, at distances 100 times stronger than the electromagnetic the nuclear force is attractive and very strong, » repulsion. Thirdly, the nucle...
:225 MeV : The simplicity of the numbers is not the only advantage of using the unit MeV. Another, more important advantage, comes from the fact that most of experiments in nuclear physics are collision experiments, where particles are accelerated by electric ﬂeld and collide with other particles. From the above value ...
it the energy, some part of which makes up the lost mass. Albert Einstein came to the idea of the equivalence between the mass and energy long before any experimental evidences were found. In his theory of relativity, he showed that total energy E of a moving body with mass m is ; v2 c2 mc2 E = 1 ¡ r 350 (19.1) where ...
and hence A = 10 N £ 0:1 m = 1 J ; ¢m = 1 J (299792458 m=s)2 … 10¡17 kg: 1:1 £ This is very small value for measuring with a scale, but huge as compared to typical masses of atoms and nuclei. 19.4.4 Nuclear masses Apparently, an individual nucleus cannot be put on a scale to measure its mass. Then how can nuclear mass...
of proton and neutron, given in the second and third rows of Table 19.1, and subtracting the mass of 2 1H, we obtain the binding energy 2.225 MeV of the deuteron without further ado. One more advantage comes from particle physics. In collisions of very fast moving particles new particles (like electrons) can be create...
a magnetic ﬂeld and therefore must consist of charged particles. For his discovery of radioactivity, Becquerel was awarded the 1903 Nobel Prize for physics. 19.5.2 Nuclear ﬁ, ﬂ, and rays Classical experiment that revealed complex content of the nuclear radiation, was done as follows. The radium crystals (another radio...
Imagine thousands of tiny tiny bullets passing through your body and making destruction on their way. Although people do not feel any pain when exposed to nuclear radiation, it harms the cells of the body and thus can make people sick or even kill them. Illness can strike people years after their exposure to nuclear r...
��c" situation, there is a strict order in all this. Atomic nuclei, being microscopic objects, are ruled by quantum probabilistic laws. Although we cannot predict the exact moment of its decay, we can calculate the probability that a nucleus will decay within this or that time interval. Nuclei decay because of their in...
to be in equilibrium with the atmosphere, taking in carbon dioxide from the air for photosynthesis. Cosmic ray protons blast nuclei in the upper atmosphere, producing neutrons which in turn bombard nitrogen, the major constituent of the atmosphere. This neutron bombardment produces the radioactive isotope 14 6C. The r...
T1=2 on the curve 19.2, i.e. period. According to the Table 19.2), this means that the tree, from which this piece of wood was made, was cut approximately 5730 years ago. This is how physicists help archaeologists to assign dates to various organic materials. 19.6 Nuclear reactions Those of you who studied chemistry, ...
states of the reaction. To make the checking of nucleon number and charge conservation easier, sometimes the proton and neutron are denoted with superscripts and subscripts as well, 357 namely, 1 subscripts are the same on both sides of the equation. 1p and 1 0n. In this case, all we need is to check that sum of super...
dating back to Becquerel, is the nuclear photographic emulsion. Passage of charged particles is recorded in the emulsion in the same way that ordinary black and white photographic ﬂlm records a picture. The only diﬁerence is that nuclear photoemulsion is made rather thick in order to catch a signiﬂcant part of the par...
aesthetically most appealing visualization of subnuclear collisions. 19.7.6 Spark chamber Spark chamber is a historic device using electric discharges over a gap between two electrodes with large potential diﬁerence, to render passing particles visible. Sparks occurred where the gas had been ionized. Most often, multi...
8 6 4 2 0 \| {z } "fusion % \| {z } - ˆ ﬂssion \| {z }. ˆ 10 8 6 4 2 0 0 50 100 150 200 250 number of nucleons, A Figure 19.3: Binding energy per nucleon. In ﬂssion processes, which were discovered and used ﬂrst, a heavy nucleus like, for example, uranium or plutonium, splits up in two fragments which are both positively...
19.4) » that released 185 MeV of energy as well as two neutrons which could cause similar reactions on surrounding nuclei. The fact that instead of one initial neutron, in the reaction (19.4) we obtain two neutrons, is crucial. This gives us the possibility to make the so-called chain reaction schematically shown in Fi...
) can move up and down in between the fuel rods. When totally in, the control rods absorb so many neutrons, that the reactor is shut down. To start the reactor, operator gradually moves the control rods up. In an emergency situation they are dropped down automatically. To collect the energy, water ows through the react...
neutrons in the reactor, usually it is brought to a heat exchanger, where it heats another gas, or steam. The primary advantage of pebble-bed reactors is that they can be designed to be inherently safe. When a pebble-bed reactor gets hotter, the more rapid motion of the atoms in the fuel increases the probability of n...
PBMR plants on South Africa’s seacoast. Eskom also wants to export up to 20 PBMR plants per year. The estimated export revenue is 8 billion rand a year, and could employ about 57000 people. 19.8.2 Fusion energy For a given mass of fuel, a fusion reaction like 1H + 3 2 1H ¡! 4 2He + n + 17:59 MeV : (19.5) yield several...
plasma. Thus the initial energy \investment" pays oﬁ. The typical temperature needed to ignite the reaction of the type (19.5) is extremely high. In fact, it is the same temperature that our sun has in its center, namely, 15 million degrees. This is why the reactions (19.3), (19.5), and the like are called thermonucle...
the temperature. However, there is another way based on the quantum laws. » As you remember, when discussing the motion of the electron inside an atom (see Sec. 19.1), we said that it formed a \cloud" of probability around the nucleus. The density of this cloud diminishes at very short and very long distances but neve...
we make a muonic atom of hydrogen, that is a bound state of a proton and a muon? Due to its large mass the muon would be very close to the proton and the size of such atom would be 200 times smaller than that of an ordinary atom. This is clearly seen from the formula for the atomic Bohr radius where the mass is in the...
second it makes 1011 attempts to jump 10¡7. Therefore, during through it. The calculations show that the penetration probability is 1 microsecond nuclei can penetrate through the barrier 10000 times and fusion can happen much faster than the decay rate of the muon. » » Cold fusion via the formation of muonic molecules ...
. 367 19.9.1 ﬂ decay Among the three types of radioactivity, the ﬁ and rays were easily explained. The emission of ﬁ particle is kind of ﬂssion reaction, when an initial nucleus spontaneously decays in two fragments one of which is the nucleus 4 2He (i.e. ﬁ particle). The rays are just electromagnetic quanta emitted by...
, 234 90Th ¡! 234 91Pa + e¡ + „” : (19.6) This additional particle was called neutrino (in Italian the word \neutrino" means small neutron). The neutrino is electrically neutral, has extremely small mass (maybe even zero, which is still a question in 2004) and very weakly interacts with matter. This is why it was not d...
of quanta. For example, if an electron collides with a positron, the following reaction may take place e¡ + e+ + ; ¡! (19.7) where two photons are needed to conserve the total momentum of the system. In principle, stable antimatter can exist. For example, the pair of „p and e+ can form an atom of anti-hydrogen with ex...
¡ The golden age of particle physics began in 1950-s with the advent of particle accelerators, the machines that produced beams of electrons or protons with high kinetic energy. Having such beams available, experimentalists can plan the experiment and repeat it, while with the cosmic rays they were at the mercy of cha...
ons (light particles, like electron), mesons divided in four groups according to their mass: (intermediate mass, like pion), baryons (heavy particles, like proton or neutron), and hyperons 370 (very heavy particles). Then it was realized that it would be more logical to divide the particles in three families according ...
arks for Mister Mark..." appeared in that fanciful book (in German, the word \quark" means cottage cheese). He needed a name for three particles and this was the answer. Thus the term quark was coined. Later, the theory was generalized to include all known particles, which required six types of quarks. Modern theories ...
so-called strong forces. An10¡15 m), other name for these forces is nuclear forces. They are very strong at short distances ( and very quickly vanish when the distance between the particles increases. All these particles are called hadrons. The protons and neutrons are examples of hadrons. » As you remember, we learne...
meson and proton, (19.8) would suggest (if naively interpreted) that either K 0 or ⁄0 is a constituent part of the nucleon while the pion is incorporated into the other \fragment". On the other hand, the same collision can knock out diﬁerent \fragments" from the same proton. For example, ¡! …¡ + p K 0 + ⁄0 ; which lea...
not immediately. And due to this annihilation, the lifetime of … 0 is 100 million times shorter than the lifetime of …§ (see Table 19.3). 373 …¡ ‰ p ( d „u u u d d „s s u d K 0 ⁄0 ) Figure 19.8: Quark-ow diagram for the reaction …¡ + p K 0 + ⁄0. ¡! …¡ ‰ p ( „u d u u d „u u d u d …0 n ) Figure 19.9: Quark-ow diagram fo...
. In contrast to all other systems, the attraction between quarks grows with the distance separating them. It is like a rubber cord connecting two balls. When the balls are close to each other, the cord is not stretched and the balls do not feel any force. If, however, you try to separate the balls, the cord pulls them...
are either of gravitational or electromagnetic nature. As we also know, in the microworld there are two other types of forces: The strong (nuclear) forces that act between all hadrons, and the weak forces that are responsible for changing the quark avors. Therefore, all interactions in the Universe are governed by onl...
, and Glashow, who developed a uniﬂed theory of electromagnetic and weak interactions. According to that theory, the electromagnetic and weak forces converge to one electro-weak interaction at very high collision energies. The theory also predicted the existence of heavy particles, the W and Z, with masses around 80000...
the end of science. The ultimate theory of everything would provide an unshakable pillar of coherence forever assuring us that the universe is a comprehensible place. 19.10 Origin of the universe Looking deep inside microscopic particles, physicists need to collide them with high kinetic energies. The smaller parts of...
validity of our theories. Nowadays, the most popular theory, describing the history of the universe, is the so{called Big-Bang model. The diagram given in Fig. 19.11, shows the sequence of events which led to the creation of matter in its present form. Nobody knows what was before the Big Bang and why it happened, but...
�35sec ¡10sec 1 sec 10 sec 500 sec »? 15 £ 109years time Figure 19.11: Schematic \history" of the universe. and neutrons combined very rapidly to form deuterium and then helium. During the very ﬂrst seconds there were too many very energetic photons around which destroyed these nuclei immediately after their formation....
. 19.12 for 2H and 4He. The temperature and the density, however, continued to decrease. After a few minutes the temperature dropped to such a level that the fusion practically stopped because the kinetic energy of the nuclei was not su–cient to overcome the electric repulsion between nuclei anymore. Therefore the abun...
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Hence, l.")708 radians = 90°, or 1 radian = 57°.2958 = 57° 17' 45".? / An angle has a sign as well as a numerical value. Thus, if OA be chosen as a fixed direction, there is a difference between the angles (AOB) and (y40(7), although they are numeric- ally equal. The latter corresponds °' to a rotation like that of th...
process of "addition of vectors" is defined as follows: move one vector parallel to itself until one of its ends meets that end of the other which causes the arrows to indicate continuous ad- vance from the free end of one vector to that of the other, and then join the former free end to the latter by a straight line....
where.1 // and f'/>aiv any two vectors such that, when added, their initial and final points are A and D: the vector AD is said to be "resolved into components." The case when the two components are at right angles is the most important. Let* AD be any vector and (JT any straight line; drop 28 INTRODUCTION perpendicul...
2 = rav aa = ra2 = rzav etc. It is seen that a2 = Vd^ag. So, in gen- eral, the " geometric mean " of two similar quantities a and b is defined to be MECHANICS AND PROPERTIES OF MATTER INTRODUCTION \\'E have recognized three so-called fundamental proper- «»f matter: inertia, weight, and tin- one which includes the varie...
to bodies, unless the contrary is expressly noted. If the motion of any actual body is observed (for instance, a stick thrown at random in the air, a moving baseball, the wheel of a moving wagon), it is seen that there are two types of motion involved : the object moves as a whole, and it also turns. These motions are...
a knowledge of tin anurle l>etwern these lines and of its changes in value. It should l»e noted that this is a special case of rotation, because tin- axis does imt ci. position, as it does in general. To describe the most complicated motion, tin -i must consider it resolved into two parts, a translation and a rotation...
the point 0. If, as the displace- ment becomes very small, its length is represented by Aa?, and the corresponding interval of time by A£, the ratio — in the limit is called the " linear velocity " at the point 0 with reference to the fixed figure ; that is, it is the " rate of change" of the displacement. It is evide...
38 MECHANICS if the train were at rest ; if a boat is rowed across a river, the actual velocity with reference to the earth is the geometrical sum of that of the water of the river and of that due to the oars ; the velocity of a raindrop with reference to the window pane of a moving carriage as it strikes it is the ge...
difference between the vectors PS and PQ; that is, it is the vector s v. Linear Acceleration. - - To Fio.J_6. — Uniform motion In » circle. PQ and PS are the velocities of the point at A and B. return to the original problem, that of describing the general case of the motion of a point in a curved path, ire have defin...

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