very basics of electronics

8/12/2019 Very Basics of Electronics

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Chapter 1

Basics of Electricity

1 . 1 Static Electricity. Atoms and Electrons

You have probably all noted some of the peculiar phenomena - cracklingand hair on end -

which may occur when dry hair is combed. Such phenomena were noticed centuries ago

(before plastic combs were invented), for example when amber was rubbed with a cloth.

The Greek word for amber was electron - and hence words were coined such as electric

and electronic to describe these and related phenomena. For much of the time until the last

century, it was considered that electricity was some kind of fluid. Observations such as

transfer of electricity from one object to another seemed to support this idea, It was also

thought that this fluid could be present in arbitrarily small quantities. Likewise it was

thought that all substances can be divided into arbitrarily small parts.

It turned out that there is a limit to this division and so the atomic theory was conceived.

Atomic theory - which says thatmatter is made up of very small objects called atoms- also

provides insight into the nature of electricity. We will review here its key concepts.

Atomic theory (at its simplest) describes atomsas made up of three different components.

In the centreof an atom there is a small and dense nucleus, made up of protonsand

neutrons. There is normally quite a few of them, and the number of protons is roughly

similar to that of neutrons. Substances are made up of various atoms, which differ in their

number of protons1. An important point for us is that the proton has a special property

called charge. Charge is a basic quantity underpinning all electrical phenomena. Chargein a proton is conventionally denoted as positive, and as a result the nucleus is positively

charged.

In addition to protons and neutrons, an atom has electrons. The number of electrons in

atoms is equal to the number of protons2. Electrons are lighter than protons, and also

have the property of charge, which is negative and equal to that of a proton. Electrons

hover near the atomic nucleus, being attracted to positive charge (Figure 1.1). They remain

quite close to the nucleus, so that a typical atom is about 10-10m across and, as a whole,

has a net charge of zero. This is because the number of protons is equal to the number of

electrons, and they have opposite charge.

1Protons and neutrons are small, they have the same mass, about 1.7 x 10-27kg, and

their size is about 10-15 m .

2The numbers of protons and electrons in atoms are equal if atoms have not been

tampered with. Later we describe how to make these numbers unequal.

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We know now that in many substances, such as for example amber, plastics or metals, it is

possible to make some electrons either part with their parent atoms for good, or at least

move to a considerable distance. This can be done by friction (very effective for amber,

synthetic fibres etc.), or exposing atoms to light (practically used in photocopying

machine), or attaching the ends to a battery. In all these cases electrons are made to go

away, or move, thus leading to movement of charge. Positively charged nuclei in atoms

are heavier, and firmly stuck in the substance, and they do not move. As a result we have a

net separation of charge - negative electrons go one way, leaving positive charge behind.

At this point we notice that electrical phenomena start to set in. Usually some electrons

leave the substance or the object, while an equal amount of electrons flows to the object

from the other end, so the object retain its net zero charge. Movement of charges is very

important in technology; later we will call this movement a current.

We now reiterate what we just learned. Electricity has to do with electrons, which are all

identical and have a property called electron charge that is, by definition, negative. Larger

bodies can also have charge, either negative or positive. Negatively charged bodies have

an excess of electrons compared to uncharged bodies. These electrons could have been

transferred intentionally from another charged body, or in the process of a natural

phenomenon, such as lightning strike, friction etc. Objects can also be positively charged,

in which case some of their electrons are missing. This once again can arise throughfriction, charge transfer, etc. Negative charges are capable of cancelling or neutralising

positive charges, if present in adequate numbers (and the other way round).

The degree to which a body is charged can be specified by giving the number of excess (or

missing) electrons. This is not a very convenient quantity, as a single electron charge is

very small. The charge of a single electron qeis

qe= 1.6 x10-19C (Coulomb)

Since the discovery of electricity, a number of useful devices and appliances have beeninvented that changed our lives forever. They mostly involve moving charges (currents).

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Applications of static charges remain quite rare; the most familiar one is in the

photocopying machine. Inside, a special drum made of the element selenium acquires a

pattern of positive charge that corresponds to the original pattern - by being exposed to light

reflected off the original document. Then it has negatively charged black particles (the

toner) poured over it. The positive spots on the drum attract negatively charged toner.

Now the resulting black pattern is rolled on to a sheet of paper. The paper is heated to fix

the pattern and a copy is then produced.

1 . 2 Conductors, Insulators ...

We distinguish two basic types of substances, which differ in the way their electrons are

allowed to move around. The substances in which electrons can move or less freely are

called conductors, those in which electrons cannot move are called insulators. This is

just a rough division, becausethere are many substances in which electrons have some

degree of freedom of movement, so they are sort of in-between. There are also materials

where only a few electrons are allowed to move freely. These are very important inelectronics because semiconductorsbelong to this group.

It is important to be able to distinguish conductors from insulators in practice. A typical

conductor is a metal, such as for example aluminium, gold, copper, steel (although steel is

not such a good conductor as copper)and many others (see Table 1.1). Metals all have a

characteristic property that they are shiny when polished; this feature is also related to the

presence of electrons. So, if you see an unknown substance and it is shiny, it is very likely

to be a good conductor. A typical insulator is a compound substance, and good examples

are most plastics, rubber and glass. The ability to identify good insulators is important and

may be lifesaving. We will now spend some time talking about these issues.

________________________________________________

Metal Resistance (Ohms)

________________________________________________

Silver 2.02

Copper 2.16

Gold 3.11

Aluminium 3.59

Tungsten 7.13

Iron 12.7

Nichrome 191________________________________________________

Table 1.1 The resistance of 100-metre long wires with a diameter of 1 millimetre.

First of all we concentrate on water and other liquids. Chemically pure water is an

insulator,which is practically irrelevant, because most of the water in our environment -tap

water, rain water, sweat etc.is NOT chemically pure and conducts electricity quite easily

due to dissolved salts. We should then always assume that water is essentially a

conductor3. On the other hand organic liquids such as petrol are insulators - but it needs

3Therefore you should NEVER use a hairdryer, or other electrical appliances, in abathtub.

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to be noted that many are flammable and special safety requirements apply if these are to be

used near electrical appliances or devices, like a car.

Any object which is moist conducts electricity, and many everyday objects do. Wood often

may contain moisture, so a fresh branch can also conduct electricity. Dry wood, however,can be considered as an insulator. Air can also be quite humid, and may conduct electricity

too. This can easily be noticed, as on a humid day static electricity generated when

combing hair disperses quickly. On the other hand, when humidity is low, many of us are

having notorious bad-hair days, as charges cling on to hair for ages. The ground contains

some moisture too and can conduct electricity quite well.

Finally, all substances, even perfect insulators, will conduct electricity if they are

sufficiently thin. An example is a lightning passing through air, which is essentially an

insulator. In a thunderstorm a huge amount of charge is accumulated in the cloud and,

despite a large distance to the ground, the charge alters the air along a path, making a

conductive track - and then rushes to the ground. Similar effects may occur in a high-voltage cable. If the plastic shielding on a high-voltage cable is worn out and too thin,

electric discharge from this cable will take place. This is why electricians use pliers and

other tools which are specially rated. These tools are covered in thick plastic which

prevents electric shock.

Exercise 1.1 Which of the following everyday objects may potentially be used to

rescue someone from a live electrical wire. Remember that bare hands may not be

used.

- a damp bathroom towel,

- a painted metal chair,

- a wooden chair,

- a branch found in the garden.

1. 3 Current and Voltage

1.3.1 Currents

The most popular way of producing a flow of electrons or currentis to make the right-

hand end of a wire attract electrons and the left-hand end repel them, thus causing an

overall drift of electrons to the right. For historical reasons a drift of electrons to the rightis described as current flowing to the left. This is summarised in saying that the

conventional direction of currents is opposite to the movement of electrons. So, the

current - by tradition - is regarded as motion of positive charges,although modern science

knows very well that this is not true.

We could measure currents in units of electrons per second. The accepted unit is the

ampere (A), where

1 ampere = 1 coulomb/sec.

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________________________________________________

Power station 1000 A

Starter of a car 100 A

Light bulb 1 A

Small radio 10 mA = 10 x10-3AWristwatch 1 A = 1 x10-6A

________________________________________________

Table 1.2 Typical values of currents.

You should remember that current measures the rate of flow of electrons through a

conductor. However it does not indicate how hard it was to make electrons move - there is

another quantity (voltage) to describe this.

1.3.2 Electric Potential - Voltage

Many issues discussed in electronics are fairly abstract. Even the concept of electricity at

the very beginning of your studies may feel a bit unreal. Electricity is hard to see; we can

observe some of its effects - such as lightning - but generally cannot sense it, unless a

current is passing through our body. This inability to see electricity makes it difficult to

develop an intuitive understanding. To facilitate this intuitive understanding we will use

models. One in particular will be quite important, namely thewatermodel of electricity.

We all know how water flows in a hose and what happens if the hose is pinched at one

point. We know that water generally flows downwards - to carry it upwards we need

water pumps. The water model is not perfect, but illustrates a number of features of

electricity.

Consider two water tanks, connected by a pipe (Figure 1.2). If we place the two tanks on

a table for a while, we would have the situation (at the left) where both tanks have the same

water level, and there is no flow of water in the pipe. If we lifted one tank up in the air,

water would flow from it into the lower reservoir. The greater is the difference in height,

the greater would be the flow.

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Similarly, we can increase the flow of electricity in a wire by changing the conditions at its

end, in a way similar to lifting one tank, which leads to difference in height and hence in

water pressure. This changed condition is referred to as creating a difference in electrical

potential between the ends of a wire. If there is no potential difference, then current wouldnot flow. For a small potential difference,the currentwould be small. A large potential

differenceleads to a large current flow. Also currents flow from the higher to the lower

potential. Water in our tanks behaves in exactly the same way as current in electric circuits.

We emphasis here that the water analogy describes the conventional direction of currents,

i.e. currents regarded as the motion of positive charges,

Potential difference, often simply referred to as voltagedifference, is measured in units

called volts.

Note that the term voltage difference refers to measurements between one end of the

conductor and the other; we talk then of the voltage across the conductor. Occasionally wespeak of the voltage at a point. This colloquial expression means the potential difference

between that point and some standard reference point.

Remember: current flows through conductors, while voltage is measured

across conductors.

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Chapter 2

Electronic Components and Circuit Diagrams

2 . 1 General Comments

Electronics is concerned with various electronic components joined togetherin a particular

way to form an electronic circuit. It provides methods to calculate currentsin particular

sections of such circuits, and voltages across various components of the circuit. The

components are joined by conductors; in particular these are just pieces of wireof various

kinds. Simple circuits may contain the following electronic elements:

a) Batteriesor voltage sourceswhich make electrons move around the circuit.

They have two metal buttons, or two metal stripes (terminals) which generate a certain

voltage difference. One terminal is usually referred to as negative and the other as

positive. When a battery is connected to the circuit, the currentin this circuit is made toflow from the positive to negative terminal1. We will discuss voltage sources in more

detail later on.

b) Switches, which allow us to control whether the current flows or not. When the

switch is open current cannot flow- as it cannot jump from one side of the switch to the

other in normal circumstances. When the switch is closedit behaves as a piece of wire and

current flowsunimpeded. There is no general rule as to what they look like (often there are

two metal strips on the two sides, and we put them in the circuit by joining circuit wires to

these strips). There are also more sophisticated switches, such as 3-way and 4-way ones.

c) Resistorsare essentially conductors, but not extremely good ones, and the current

does flow through them, but not too easily. A measure of how hardit is for current to flow

through a given resistor is called its resistance. Resistance is measured in units called

ohms. If the resistance is large, then the current flows with great difficulty. If it is small,

then the current flows very easily and it may reach very large values.

Resistors often look like tiny painted cans with two wires, one at each end. The two wires

are identical and it does not matter which way they are connected in the circuit. The

simplest resistors are carbon film, which is a thin layer of carbon on a ceramic rod, or metal

film/metal oxide on glass rods. Wire-wound resistorsare used where the resistor has to

dissipate a lot of heat. Some resistors are designed to change value when heated. They arecalled thermistorsand are used in temperature-measuring circuits. Some resistors change

in value when exposed to light. They are called light-dependent resistors. Variable

resistorsare also available. These can be operated by means of a knob or a slider on the

control panel2.

1The current flowing from the positive to the negative terminal is this historically

accepted movement of positive charges.2More about resistors later in this chapter.

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d) Inductors and capacitors3. Simple inductorsare made up of tightly wrapped

multiple wire loops. For constant currents (called DCfor direct currents) they behave

like ordinary conductors, or - with plenty of fine wire in the loops - rather like resistors.

Real differences arise when the currents through them vary in time. Capacitorsare made of

two conductive plates separated by a very thin insulating film. Constant current is unableto flow through them, but charge can be stored on the metal plates. Capacitors start to

behave in an interesting way when the voltage applied to the plates varies with time. This

actually makes current flow through a capacitor.

e) Various electronic devices and integrated circuits. Electronic catalogues

are full of them. For information purposes only we list here a couple of names, such as

diodes, bipolar junction transistors, FETs (field-effect transistors), diode lasers,

photodiodes... the list is almost endless. What they all have in common are thin metal

wires or strips attached to them, called terminals. These terminals are meant to be

connected to wires or conductive paths in circuits. Sometimes we have two terminals(in

diodes, laser diodes, photodiodes), sometimes we have three(in transistors), sometimeseight or more(in complicated electronic components called operational amplifiers) and in

very complicated electronic chipsin a computers, such as the Pentium chip, there may be

many more. It is a job of an electronics technician to know what should be connected to

these terminals. The recipes are sometimes quite complicated. Some devices, for example

diodes, may be connected only one way round and not the other in a particular circuit.

Some others, such as operational amplifiers, must have a special power supply connected

to two particular terminals, and resistors must be connected between two others.

We will not be dealing with what is inside of these electronic components. This approach,

whereby we learn what to do with component terminals, and do not bother about its

insides, treating devices as black boxes, will be our main approach in this unit.

We can also connect meters in a circuit to learn what happens in the circuit when it

operates. Various meters can be used, most importantly ammeters which measure

currents and voltmeters to measure voltages. One can also measure resistance using

ohmmeters. Sometimes these three functions are combined together in one instrument

called a multimeter. The meters may be placed intentionally in various parts of the circuit

in order to monitor currents, voltages or resistances. The meters are quite complicated and

large instruments, compared with other electronic components. A multimeter can be say 5

cm by 10 cm by 2 cm. More about these in the following sections.

The arrangement of all the components a) - e) can be shown on a layer diagram, which is

like a photograph of the actual circuit. However it is easier to see how the circuit works on

the circuit diagram. A circuit diagram represents components as symbols and shows

connections as lines. Every circuit component is conventionally assigned a certain symbol,

as shown in Figure 2.1. The way the components may be joined together is presented in

Figure 2.2. Circuit diagrams are useful for designers and of use for servicing work,

although an additional layout diagram is very handy - but rarely available.

3Capacitors and inductors will also be discussed in detail later. Their key role in

circuits will also be given.

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Some important ways of joining components are illustrated in Figure 2.3 a) which shows

components joined in series and in Figure 2.3 b) which shows components joined in

parallel. The choice of elements does not matter, it is just their arrangement which is

relevant. To make matters more difficult, mixedkinds of circuits are also possible; these

do not have special names. One is shown in Figure 2.4.

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Exercise 2.1 Draw an electronic circuit in which two resistors are joined in

parallel with a capacity, and all this in series with a voltage source and a diode.

Exercise 2.2A capacitor and an inductor are connected in parallel and the two are

connected in series with a constant voltage source. Will current flow through the

circuit?

2 . 2 Electrical Quantities and Measurements

So far we have learned that there are three electrical quantities: current measured in

amperes, voltagesmeasured in volts, and resistancesmeasured in ohms. These can be

measured by instruments called ammeters, voltmeters and ohmmeters, respectively. They

used to be manufactured as separate instruments, but nowadays they are often combined

into one instrument called a multimeter. A multimeter is portable and usually battery-

operated4.

4Batteries need replacement from time to time.

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cause a small current flow through the components. Then this current is measured and the

resistance obtained, by comparing with the current for zero ohms. Typically a moving-coil

ohmmeter has zero ohms on the right-hand end of the scale, unlike the voltmeter and

ammeter, which have zero on the left. Nowadays many multimeters are digital, rather than

analogue. They are more accurate than traditional analogue multimeters, which have a scale

and a needle.

2 . 3 Simple Circuits

In this section we will learn - or revise for those of you who studied this in high school -

how to calculate various electrical quantities in simple electronic circuit. These simple

circuit will contain only:

a) batteries,

b) resistors,

c) connecting wires.

The name circuit is appropriate, because there must be a complete return path for current

which leaves the positive terminal of the battery to return to the negative one5. The

battery does not take on any overall charge. The wires have sufficiently low resistance that

it can be ignored for all practical purposes. In practice, batteries may be replaced by larger

instruments called power supplies, connected to a power point. The calculations are

based on a few simple rules and we will go through them one by one.

2.3.1 Rule I - Ohms Law

For a large variety of metallic conductors, the relationship between the current throughagiven conductor and the voltage acrossit (with certain restrictions) is very simple, and

called Ohms law. Ohm used a circuit rather like that in Figure 2.6. He applied a series

of voltages, measured the resulting currents and found a simple linearrelationshipthat the

currentIis proportional to the voltage V. This is normally written as:

V=IR

where R= V/Iis called the resistance of the load. This is quite a good name, asR

measures to what extent the resistor resiststhe flow of electrons. Ohms law is only an

approximate rule; there are various deviations, exceptions etc. Some materials and devices,such as for example diodes, have a completely different relationship between Iand V,

sometimes very nonlinear. But Ohms law applies - with constraints - to a large variety of

conductors, and particularly well to commercial resistors, but also to most wires. This is

why it is so useful.

5Current is historically understood as a motion of positive charge. This was anunfortunate choice.

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It is to be remembered that

1 ohm = 1 volt / 1 ampere

Students seldom get Ohms law V=I R wrong, but they often apply it wrongly,

forgetting that Vmust be the voltage ACROSSR.

2.3.2 Rule II - Kirchhoffs First Law

This law says that the total current flowing into a junction is zero.

i1+ i2+ ... + in= 0

Note that each current has an arrow to indicate its direction. If the current value is positive,

then current flows in the direction of the arrow and if it is negative then it flows in the

opposite direction to the arrow. Thus in Figure 2.7, for the top junction in the gray circle,

we would write:

-I1+I2+I3= 0

where we write -I1because the current out of the junction isI1, so the current in is -I1.

The first law simply results from the observation that, if the current into a point were not

zero, this point would then steadily accumulate electrons, which is not possible. Note that

water in a network of connecting tubes would behavein exactly the same way. The total

flow of water flowing into a junction of pipesmust be equal to the total flow of water

flowing out of the junction.

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2.3.3 Rule III - Kirchhoffs Second Law

This law says that the total voltage difference around any circuit loop (Figure 2.9) is zero.

V1+ V2+ ... + Vn= 0

The second law implies that if we imagine an electron going around the loop, then, when it

gets back to its point of origin, it has gained no energy. A good analogy is to imagine a

circuit loop to behave like an artificial waterfall with a re-circulating system(and therefore a

water pump). The water fallsdown the waterfall and this downward fall corresponds to a

potential difference across the resistor. The potential at point B is smaller than at point A.

Similarly the height at the bottom of the waterfall is smaller than at the top. Then waterflows horizontally and turns back to the pump. This part corresponds to the current

flowing through the wire - there is practically no potential difference across the wire. Then

the water gets to the pump andis raisedto the top of the waterfall. In an electrical circuit

this function is fulfilled by the battery. One should be aware that the water pump needs to

have power provided so we have to plug it into the mains. In the case of a battery the extra

energy needed to raise electrons to higher potential is provided by chemical reactions6.

Finally the water gets to the top of the waterfall and the process is repeated (Figure 2.8).

6Because of these chemicals we should dispose of batteries in a responsible way.

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When we look at this waterfall and its re-circulating system, we see that the water is lifted

up by exactly the same distance as it falls down. So the sum of the two height

DIFFERENCES is zero. Kirchhoffs second law tell that the sum of the voltage

differences around the circuit loop is zero, in complete analogy.

In the circuit with one resistor of valueRABand the battery with the voltage difference of

Eas in Fig. 2.8 the current I, the resistance RAB and the battery voltage Eare related

through:

E-IxRAB = 0.

Now we apply this rule to the circuit shown in Figure 2.7. For the left-hand loop, we

would write:

E1-R3I3-R1I1= 0

and

E2-R2I2-R1I1= 0

for the right-hand loop.

It is useful to keep in mind that currents flow very much like water. Ohms law and thebehaviour of various resistors can be understood by the analogy of resistors and thin and

thick tubes. Large resistors behave like very thin and long tubes, or pinched tubes which

do not allow large currents of water. Small resistors behaves like very wide tubes, where

large water currents can flow easily.

Although the water model is useful, it is important to realise its limitations. A break in an

electric circuit causes the electricity to stop flowing; it does not spill out of the end of the

wire like water would from a broken pipe. An electric circuit is NOT analogous to a

sprinkler system used to water lawns. Similarly to a valve which blocks a flow of water, a

switchputs a gap in the conducting path to stop the flowof electricity.

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2 . 4 Potential Divider (Voltage Divider)

A potential divideris often used to get a desired voltage from an available larger one. As

this requirement is common in practical circuits, potential dividers are used very often. The

voltage divider circuit is presented in Figure 2.10.

The way the potential divider works is as follows. A common currentIflows through

R1andR2. Clearly

VI= Vo+ Vs, (2.1)

VS=IxR1, (2.2)VO=IxR2 (2.3)

VI=IxR2+IxR1 (2.4)

From equations 2.2 and 2.3

VO/ VS=R2/R1. (2.5)

That is, the input voltage is divided into two parts (Vo, Vs), each proportional to the

resistance across which they appear. Also,

VO=IxR2= VIxR2/(R2+R1), (2.6)

which is obtained from equation 2.4. That is, the output voltage Vois a fraction of the

input voltage VI. The fraction is equal to the resistance connected across the output

divided by the sum of the two resistances. You are expected to remember equation 2.6 and

the meaning of its symbols.

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likewise for four, five, etc.

Example 2.2Now we show how to use the above rules to simplify a complicated

arrangement of resistors as in Figure 2.13a. The object of our calculation is the valueof the combined (equivalent) resistance between the points A and B. This is how to

do it. You are requested to perform and verify all calculations.

First we calculate the resistors that will substitute for the two parallel connections

marked by the circles. The upper one turns out to be 800 , and the lower one 1200

.

Then we replace the circled connections with the calculated resistors as in Figure

2.13b.

Now we circle the series connection in the upper branch and in the lower branch and

calculate the equivalent resistors. We come up with 2000 and 3000 .

We are left with two resistors in parallel only as in Figure 2.13c. We calculate the

combined (equivalent) resistance which is 1200 (Figure 2.13d).

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2. 6 Equivalent Circuits

In the two previous sections we learned how to replace arrangements of resistors by a

sequence of equivalentcircuits. If a circuit is replaced by an equivalent circuit then ALL

measurements performed on the external terminals of the circuit give exactly the same

VALUES as those on the corresponding terminals of the original circuit. In most cases we

measure the voltage and the current. So if the circuit is enclosed in a black box, we would

not be able to distinguish the original circuit from its equivalent just by testing the

terminals. However in the last two sections we learned only how to build equivalent

circuits for circuits made of resistors only. In this section we will take one step further; we

will show you the way to find equivalent circuits for circuits with resistors and voltage

sources arranged in a variety of ways. Such circuits have their own name of Thevenin

equivalent circuits. We will learn a simple recipe how these circuitS may be

determined.

A Thevenin equivalent circuit is a way to simplify any connection of DC voltage

sources and resistors which are connected to two terminals A and B to become a single

voltage and a single resistor (Figure 2.14). It makes no difference in which order the two

components are placed in series. If either of these circuitS were placed in a box with two

terminals labelled A and B, then no measurement or test using those terminals would be

able to distinguish between the two circuits.

To specify the Thevenin equivalent circuit we need to give the value of the Thevenin

resistor RThand the Thevenin voltage VTh. We can find these values in one of two

ways.

In the first, measurement, approachwe need to have access to the actual circuit and not

only to its circuit diagram. First, we connect a voltmeter across the output, that is between

terminal A and terminal B, to findthe open-circuit voltageVoc. Then we connect an

ammeter to findthe short-circuit currentIsc. The voltmeter provides the open-circuit

conditions, because its very large resistance should not allow current to flow. The ammeterprovides the short-circuit current because its very small resistance means we should not

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have a voltage difference across its terminals. Once we have these two measurements, we

can find the Thevenin voltage VThand the Thevenin resistance RTh . VTh is simply

equal tothe open-circuit voltageVoc andRTh = Voc /Isc. This method is easy to

apply if we have a real circuit to measure (provided that it can withstand a short circuit)..

In the second methodthe desired quantities, VocandIsc, have to be calculated from the

circuit diagram. Then the same relationships are used: VTh= Voc,RTh = Voc/Isc.

This can be done as in the following example.

Example 2.3Derive the Thevenin equivalent for the circuit shown in Figure 2.15

left. The equivalent is actually shown in Figure 2.15 on the right.

The open-circuit voltage is just equal to the sum of the two voltages V1and V2 and

is thus:

VTh= V1+ V2.

To find RTh, we have to divide VThby Isc, the current which flows when we connect

a resistanceless wire from A to B. Application of Kirchhoffs laws and Ohms law

gives the equation:

V1- IscR1+ V2- IscR2= 0,

Isc= (V1+ V2) / (R1+R2)

Then

RTh= VTh/Isc=R1+R2.

2. 7 Real Voltage Sources

There are several ways of generating a voltage, but only two are of importance for

everyday purposes. Batteriesare the most familiar method, and the invention of the first

battery by Alessandro Volta in 1799 made it possible to study comparatively large currents

at voltage levels from 3 V to several hundred volts. A battery is, strictly speaking, a stack

of cells, each cell converting chemical action into electrical voltage. In the course of this, a

metal is dissolved into a metal salt, enabling a current flow. A cross-section through a

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battery is snown in Figure 2.16.

Some types of cells are rechargeable, so that we can pass an appropriate current through

such a battery in the reverse direction and convert the metal salt back to metal. This process

uses more energy than is received out of the cell. As always, no energy is created out of

nowhere.

Another way of generating a steady voltage was discovered by Michael Faraday in 1817.

He demonstrated the first dynamo, which worked by rotating a metal disc between the

poles of a magnet, using the energy of whatever was turningthe disc(Faradays hand first,

and later a steam engine) intoan electrical voltagethat could provide current (Figure 2.17).This principle is now widely used in steam- and petrol-powered generators,

hydroelectricity and electricity generated by wind.

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If we need to generate higher voltages then our options are twofold. First, one can

connect voltage sources in series. The resulting voltage is then a sum of the individual

voltages of the voltage sources. Secondly, in the case of time-varying voltages, such as

these provided by dynamos/generators, a component called a transformercan be used.

Transformers are built of two different coils of wire wrapped around an iron core as inFigure 2.18. They step up/downthe voltage in proportion to the ratio of wire loops on the

two arms. All consumer electronics contains inside a small transformer which steps down

the mains voltage of 230 V into lower voltages, more useful for providing power to

electronic circuits. Some appliances, such as TV sets, have a step-up transformer. In

colour TV the voltage is stepped up to about 2,500 V which is very high8.

Another factor that needs to be considered in the context of real voltage sources is how

much current we can draw from them. We will concentrate here on the example of a simple

battery. Even if we join the two terminals of a battery with an ideal conductor of zero

resistance, we would not be able to draw an arbitrarily large current. All batteries are

known to have internal resistance, which we should imagine as a small resistor sitting

somewhere inside of a battery and not able to be separated from it. So, in a circuit we have

to replace the battery with this resistance in series with a voltage source. The maximum

current drawn is then

Imax= Vbattery/Rinternal.

8This voltage causes the TV set to collect charged dust particles.

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Example 2.4 What to do if we need to draw more current from a battery than this

maximum value, Imax?

This may happen for example when one tries to start a car after a freezing night. The

cold engine needs then more current than usual to get started. If your existing batterydoes not suffice, then we can take a second battery with the same voltage and

connect it in parallel. We will get twice as much current as from a single battery.

2 . 8 Power

A useful aspect of electricity is that we can make it do a large variety of useful jobs for us.

This is possible thanks to a quantity called electric power. Electric motors allow us for

example to drill, lift, and drive vehicles. Power is measured in units called watts (W)and

is best visualised when thinking of lifting heavy objects. About 10 watts is the amount of

power needed to lift 1 kilogram by 1 metre in one second. If the lifted weight were 30 kg,

still lifted by 1 m in one second, the power used would be 300 W. If the lifting occurredslowly, say 30 kg by 1 m in 10 second, then the power would only be 30 W.

Light globes used in your house are likely to use 60 - 100 watts. Note that, if you were to

generate that much power yourself, you would have to keep on lifting 6 - 10 kg weights by

one metre in one second, which look like quite a heavy workout. The electrical power P

is calculated as:

P= VxI

where Vis the voltage across the load andIis the current through the load. If the voltage

varies in time, the current would also vary and the power would vary as well. This applies

to the power used in the house by light globes and other electrical appliances. In this case it

is useful to talk about an average power9.

2 . 9 Conversion of Power to heat

If a constant voltage is applied across a resistorRwe have

I= V/R

because of Ohms law. The power generated in the resistor is then

P= VxI= V2/R=I2xR.

This power is dissipated in the form of heat. This effect may sometimes be useful, but

more often than not for electronics it is a real nuisance. Useful applications include electric

kettles, hot plates, irons, and dryers etc10. In electronics, if parts of a circuit are getting

too hot, the components may malfunction. Precautions need to be then taken so that the

heat is properly taken away to the environment, for example by cooling fans. Some electric

9Average power is discussed later in Chapter 3.

10Light globes get hot too, which, has to be kept in mind when changing them.

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components, which use high currents, have special metal plates attached and these are

joined to large strange-looking metal objects called heat sinkswhich can be found inside

many instruments. Electronic components in particular are extremely susceptible to excess

heat and may stop working if their temperature is too high. This poses some problems in

laptops - which have no cooling fans - and major problems in supercomputers.

We cannot avoid generation of heat in electrical circuits, but in most circumstances it is

undesirable and we want to minimise it. For example in an electrical motor, designed to do

mechanical work, we would like as much electricity as possible to produce mechanical

power, and not be wasted on heating the surroundings. This ability is numerically

expressed as the efficiency. Efficiency is the ratio of useful power to the total

electricalpower delivered tothe instrument/device. This useful power is the difference

between the total delivered power and the heat, Q, generated in the device11.

= Puseful

/ Ptotal

= (Ptotal

- Q) / Ptotal

A good device, which does not waste electricity, has a high efficiency, close to one. Low

efficiency means a device will generate proportionally large amounts of heat.

It is interesting to compare the efficiencies of everyday objects, for example different light

sources. In light sources the useful part of the electrical power is converted to light power;

heat is of course unwanted. The most popular and one of the oldest light sources is the

incandescent light globe, invented by Thomas Edison back in the 19th century. Not much

progress has been made in this area since then, and the efficiency of the standard globes is

about 3 - 5%. (The remaining electrical power is wasted on warming the ceiling.)

Fluorescent lamps are quite a bit better, with efficiencies approaching 10 %. Light emittingdiodes - the little indicator lights, red, yellow, and green, that you might have seen on

stereos, videos, TVs and other consumer electronics - have efficiencies approaching 20%.

Now researchers are working on replacing all lights with light emitting diodes, hoping to

greatly improve energy savings. This example shows that energy can often be more

efficiently used through technological progress.

2 . 1 0 FAQ

Students often ask: Surely we cannot be expected to know all this material; what are the

important things we really must know? Another (related) complaint is that there are too

many equations to learn.

If you regard every sentence of your notes as isolated fact which must be memorised you

are certainly in real trouble. However, the number of truly independent facts and principles

is quite small, enough to be manageable. Most of the content of these notes is a logical

development of these few starting points. These few points need to be memorised, and the

11Heat is measured in watts, the same unit as power, but is not as easily measured. To

measure heat you would need to enclose the device in a thermally insulating box,

measure temperature increase, measure how heavy is the device and work out what it is

made of and do a couple of calculations. This cumbersome task we normally leave to themanufacturer and then we look at the device efficiency provided in their specification.

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restof the development can easily be reproduced.

1) It is vital to understand the distinction between voltage and current. Current flows

throughcomponents but voltage appears across them. The analogy of current with

water flow and voltage with height or water pressure may be helpful.

2) Ohms law needs to be remembered: V=I R, where Iis the current through R

and Vis the voltage ACROSSR.

The difference between voltage at a point (between this point and an arbitrary reference)

and the voltage difference across a component must be understood.

Other Laws of Circuits:

a) the sum of currents into a junction is zero, and

b) the sum of voltage differences is zero

should be memorised. They are easy to apply, but the sign convention may sometimes

leave students confused. Hence once again the water analogy is useful.

Resistors in seriesand resistors in parallel- expressions for combined resistance must be

memorised.

The potential dividercircuit and its function needs to be remembered and understood. The

potential divider often appears amidst other circuitry.

Voltmetersand ammetersand what they do are an essential part of this unit of study. You

will need to know how to connect themcorrectly in the circuits.

An equivalent circuit cannot be distinguished from the original by measuring the current

through and the voltage between the terminals. For Thevenin equivalent circuitswe need to

know the open-circuit voltage VThand the short-circuit Isc; these divided give the value

of the Thevenin resistanceRTh.

Power P = VxI.

very basics of electronics

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