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CHAPTER 1

VOLTAGE, CURRENT AND RESISTANCE

LEARNING OUTCOME

Upon completing this chapter, students will be able to:

1. Define voltage, current and resistance and discuss the

characteristics of each. (PLO1-C1)

2. Recognize and discuss various types and values of resistors.

(PLO4-A2)

3. Describe a basic electric circuit. (PLO4-C1)

CONTENTS

1.1 Atomic Structure

All matter is made of atoms; and all atoms are made of electrons,

protons, and neutrons. An atom is the smallest particle of elements that

retains the characteristics of that element.

According to the Classic Bohr model:

Atoms have a planetary type of structure that consists of a

central nucleus surrounded by orbiting electrons, as

illustrated in Figure 1.1.

The nucleus consists of positively charged particles called

protons and uncharged particles called neutrons. The

basic particles of negative charge are called electrons.

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Figure 1.1 The Bohr model of an atom showing electrons in

orbits around the nucleus. The “tails” on the electrons

indicate they are moving.

For example:

The simplest atom is that of hydrogen, which has one

proton and one electron, as pictured in Figure 1.2(a).

The helium atom, shown in Figure 1.2(b), has two protons

and two neutrons in the nucleus and two electrons orbiting

the nucleus.

(a) Hydrogen atom (b) Helium atom

Figure 1.2 The two simplest atoms, hydrogen and helium.

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1.1.1 Atomic Number

All elements are arranged in the periodic table of the elements in order

according to their atomic number.

The atomic number equals the number of protons in the nucleus, which is

the same as the number of electrons in an electrically balanced (neutral)

atom.

For example:

Hydrogen has an atomic number of 1.

Helium has an atomic number of 2.

In their normal (or neutral) state, all atoms of a given element have the

same number of electrons as protons; the positive charges cancel the

negative charges, and the atom has a net charge of zero.

1.1.2 Electron Shells and Orbits

Electrons orbit the nucleus of an atom at certain distances from the

nucleus. Electrons near the nucleus have less energy than those in more

distant orbits.

It is known that only discrete (separate and distinct) values of electron

energies exist within atomic structure. Therefore, electrons must orbit only

at discrete distances from the nucleus.

1.1.2.1 Energy Levels

Each discrete distance (orbit) from the nucleus corresponds to a

certain energy level. In an atom, the orbits are grouped into energy

bands known as shells. A given atom has a fixed number of shells.

Each shell has a fixed maximum number of electrons at

permissible energy levels (orbits). The differences in energy levels

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within a shell are much smaller than the difference in energy

between shells.

The shells are designated 1, 2, 3, and so on, with 1 being closest to

the nucleus. This energy band concept is illustrated in Figure 1.3:

The 1st shell with one energy level and

2nd shell with two energy levels. Additional shells may

exist in other types of atoms, depending on the

element.

Figure 1.3 Energy level increase as the distance from the nucleus

increases.

1.1.3 Valence Electrons

Electrons that are in orbits further from the nucleus have higher energy

and are less tightly bound to the atom than those closer to the nucleus.

This is because the force of attraction between the positively charged

nucleus and the negatively charged electron decreases with increasing

distance from the nucleus.

Electrons with the highest energy levels exist in the outermost shell of an

atom and are relatively loosely bound to the atom.

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This outermost shell is known as the valence shell and electrons in this

shell are called valence electrons. These valence electrons contribute to

chemical reactions and bonding within the structure of a material and

determine its electrical properties.

1.1.4 Ionization

When an atom absorbs energy from a heat source or from light, for

example, the energy levels of the electrons are raised. The valence

electrons possess more energy and are more loosely bound to the atom

than inner electrons, so they can easily jump to higher orbits within

valence shell when external energy is absorbed.

If a valence electron acquires a sufficient amount of energy, it can actually

escape from the outer shell and the atom’s influence. The departure of a

valence electron leaves a previously neutral atom with an excess of

positive charge (more protons than electrons).

The process of losing a valence electron is known as ionization, and the

resulting positively charged atom is called a positive ion. For example, the

chemical symbol for hydrogen is H. When a neutral hydrogen atom loses

its valence electron and becomes a positive ion, it is designated H+.

The escaped valence electron is called a free electron. When a free

electron loses energy and falls into the outer shell of a neutral hydrogen

atom, the atom becomes negatively charged (more electrons than

protons) and is called a negative ion, designated H-.

1.1.5 The Copper Atom

Because copper is the most commonly used metal in electrical

applications, let’s examine its atomic structure. The copper atom has 29

electrons that orbit the nucleus in four shells. The number of electrons in

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each shell follows a predictable pattern according to the formula, 2N2,

where N is the number of the shell. The first shell of any atom can have

up to 2 electrons, the second shell up to 8 electrons, the third shell up to

18 electrons, and the fourth shell up to 32 electrons.

A copper atom is represented in Figure 1.4. Notice that the fourth or

outermost shell, the valence shell, has only 1 valence electron. When the

valence electron in the outer shell of the copper atom gains sufficient

energy from the surrounding medium, it can break away from the parent

atom and become a free electron.

The free electrons in the copper material are capable of moving from one

atom to another in the material. In other words, they drift randomly from

atom to atom within the copper. Free electrons make electric current

possible.

Figure 1.4 The copper atom

1.1.6 Categories of Materials

Three categories of materials are used in electronics: conductors,

semiconductors, and insulators.

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a. Conductors

Conductors are materials that readily allow current. Have a

large number of free electrons and are characterized by one to

three valence electrons in their structure. Most metals are good

conductors.

Silver is the best conductor and copper is next. Copper is the

most widely used conductive material because it is less

expensive than silver. Copper wire is commonly used as a

conductor.

b. Semiconductors

Semiconductors are classed below the conductors in their

ability to carry current because they have fewer free electrons

than do conductors. Have four valence electrons in their atomic

structures. Certain semiconductor materials are the basis for

modern electronic devices such as the diode, transistor, and

integrated circuit. Silicon and germanium are common semi

conductive materials.

c. Insulators

Insulating materials are poor conductors of electric current.

Used to prevent current where it is not wanted. Compared to

conductive materials, insulators have very few free electrons

and are characterized by more than four valence electrons in

their atomic structures.

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1.2 Electrical Charge

The charge of an electron and that of a proton are equal in magnitude.

The electron is the smallest particle that exhibits negative electrical

charge. When an excess of electrons exists in a material, there is a net

negative electrical charge. When a deficiency of electrons exists, there is

a net positive electrical charge.

Electrical charge is symbolized by Q. Static electricity is the presence of a

net positive or negative charge in a material. Materials with charges of

opposite polarity are attracted to each other, and materials with charges of

the same polarity are repelled, as indicated in Figure 1.5.

A force acts between charges, as evidenced by the attraction or repulsion.

This force, called an electric field, consists of invisible lines of force, as

shown in Figure 1.6.

Figure 1.5 Attraction and repulsion of electrical charges.

Figure 1.6 Electric field between oppositely charged surfaces.

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1.2.1 Coulomb: The Unit of Charge

Electrical charge (Q) is measured in Coulombs, abbreviated C. One

coulomb is the total charge possessed by 6.25 X 1018 electrons. A single

electron has a charge of 1.6 x 10-19C. The total charge in a given number

of electrons is stated in the following formula:

number of electrons

Q = ---------------------------------- (1.1)

6.25 x 1018 electrons/C

1.2.2 Positive and Negative Charge

Consider a neutral atom that is, one that has the same number of

electrons and protons and thus has no net charge. If a valence electron is

pulled away from the atom by the application of energy, the atom is left

with a net positive charge (more protons than electrons) and becomes a

positive ion.

If an atom acquires an extra electron in its outer shell, It has a net

negative charge and becomes a negative ion. The amount of energy

required to free a valence electron is related to the number of electrons in

the outer shell. An atom can have up to eight valence electrons. The more

complete the outer shell, the more stable the atom and thus the more

energy is required to release an electron.

Figure 1.7(a), (b) and (c) illustrates the creation of a positive and a

negative ion when a hydrogen atom gives up its single valence electron to

a chloride atom, forming gaseous hydrogen chloride (HCI). When the

gaseous HCI is dissolved in water, hydrochloric acid is formed.

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Figure 1.7(a) The neutral hydrogen atom has a single valence electron.

Figure 1.7(b) The atoms combine to form gaseous hydrogen chloride

(HCI).

Figure 1.7(c) When dissolved in water, hydrogen chloride gas

separates into positives hydrogen ions and negative

chloride ions.

Example 1.1

How many coulombs do 93.75 x l016 electrons represent?

Solution

number of electrons

Q = ------------------------------

6.25 x 1018 electrons/C

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93.75 x l016 electrons

= ------------------------------

6.25 x 1018 electrons/C

= 15 x 10-2 C

= 0.15 C

1.3 Voltage

Voltage is defined energy per unit of charge V= W/Q, where

V = voltage in volts (V)

W = energy in joules (J)

Q = charge in coulomb (C)

1.3.1 Volt: The Unit of Voltage

The unit of voltage is the volt, symbolized by V. One volt is the potential

difference (voltage) between two points when one joule of energy is used

to move one coulomb of charge from one point to the other.

Example 1.2

If 50 J of energy are available for every 10 C of charge, what is the

voltage?

Solution

V = W/Q

= 50J/10C

= 5V

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1.3.2 Sources of Voltage

a. Batteries

A battery is a type of voltage source that converts chemical

energy into electrical energy. A cell consists of positive

electrode, negative electrode, electrolyte and porous separator,

see Figure 1.8.

Battery is divided into two major classes, primary and

secondary. Primary batteries are used once and discarded

because their chemical reactions are irreversible. Secondary

batteries can be recharged and reused many times because

they are characterized by reversible chemical reactions.

Figure 1.8 Diagram of a battery cell.

b. Solar Cells

The operation of solar cells is based on the photovoltaic effect,

which is the process whereby light energy is converted directly

into electrical energy, see Figure 1.9.

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Figure 1.9 Construction of a basic solar cell.

c. Electrical Generator

Electrical generators convert mechanical energy into electrical

energy using a principle called electromagnetic induction. A

conductor is rotated through a magnetic field, and a voltage is

produced across the conductor. A typical generator is pictured

in Figure 1.10.

Figure 1.10 Cutaway view of a dc generator.

d. The Electronic Power Supply

Electronic power supplies convert the ac voltage from the wall

outlet to a constant (dc) voltage that is available across two

terminals, as indicated in Figure 1.11(a). Typical commercial

power supplies are shown in Figure 1.11(b).

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Figure 1.11(a) Electronic power supply.

Figure 1.11(b) Typical commercial power supplies.

1.4 Current

Voltage provides energy to electrons which allows them to move through

a circuit. This movement of free electrons from negative end of a material

to the positive end is the electrical current (I).

Current in a conductive material is determined by the number of electrons

(amount of charge, Q) that flow past a point in a unit of time.

I = Q/t

where I = current in amperes.

Q = the charge of the electrons in coulombs.

t = the time in seconds.

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Figure 1.12(a) Random motion of free electrons in a material.

Figure 1.12(b) Electrons flow from negative to positive when a voltage

is applied across a conductive or semi conductive

material.

1.4.1 Ampere: The Unit of Current

Current is measured in a unit called the ampere or amp for short,

symbolized by A.

One ampere (1 A) is the amount of current that exists when a number of

electrons having a total charge of one coulomb (1 C) move through a

given cross-sectional area in one second (1 s).

See Figure 1.13. Remember, one coulomb is the charge carried by 6.25 x

1018 electrons.

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Figure 1.13 Illustration of one ampere of current in a material.

Example 1.3

Ten coulombs of charge flow past a given point in a wire in 2 s. What is

the current in amperes?

Solution

I = Q/t

= 10C/2s

= 5A

1.5 Resistance

When there is current in a conductive material, the free electrons move

through the material and occasionally collide with atoms. These collisions

cause the electrons to lose some of their energy, and thus their movement

is restricted.

The more collisions, the more the flow of electrons is restricted. This

restriction varies and is determined by the type of material. The property

of a material that restricts the flow of electrons is called resistance. The

schematic symbol for resistance is shown in Figure 1.14.

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Figure 1.14: Resistance symbol.

When there is current through any material that has resistance, heat is

produced by the collisions of free electrons and atoms. Therefore, wire,

which typically has a very small resistance, becomes warm when there is

sufficient current through it.

1.5.1 Ohm: The Unit of Resistance

One ohm (1 Ω) of resistance exists if there is one ampere (1 A) of current

in a material when one volt (1 V) is applied across the material.

a. Conductance

The reciprocal of resistance is conductance, symbolized by G. It

is a measure of the ease with which current is established. The

unit of conductance is the siemens (S). The formula:

G = 1/R

For example, the conductance of a 22kΩ resistor is G =

1/22kΩ= 45.5μS.

1.5.2 Resistors

Components that are specifically designed to have a certain amount of

resistance are called resistors. The principal applications of resistors are:

to limit current,

to divide voltage, and, in certain cases,

to generate heat.

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Although a variety of different types of resistors come in many shapes and

sizes. Two main categories:

fixed or

variable.

a. Resistor Color Codes

Fixed resistors with value tolerances of 5%, 10%, or 20% are

color coded with four bands to indicate the resistance value and

the tolerance.

This color- code band system is shown in Figure 1.15, and the

color code is listed in Table 1.1.

Figure 1.15 Color code bands on a resistor.

Table 1.1 Resistor color code.

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The color code is read as follows:

a. Start with the band closest to one end of the resistor. The

first band is the first digit of the resistance value. If it is not

clear which is the banded end, start from the end that does

not begin with a gold or silver band.

b. The second band is the second digit of the resistance value.

c. The third band is the number of zeros following the second

digit, or multiplier.

d. The fourth band indicates the tolerance and is usually gold

or silver.

1.5.3 Variable Resistors

Variable resistors are designed so that their resistance values can be

changed easily with a manual or an automatic adjustment.

Two basic uses for variable resistors are:

to divide voltage (potentiometer)

to control current (rheostat)

Schematic symbols for these types are shown in Figure 1.16(a), 1.16(b),

1.16(c). The potentiometer is a three-terminal device, as shown in figure

1.16(d). Some typical potentiometers are pictured in Figure 1.17.

Figure 1.16(a) Potentiometer.

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Figure 1.16(b) Rheostat.

Figure 1.16(c) Potentiometer connected as a rheostat.

Figure 1.16(d) Basic construction.

Figure 1.17 Typical potentiometers.

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1.6 The Electric Circuit

A basic electric circuit is an arrangement of physical components that use

voltage, current, and resistance to perform some useful function.

1.6.1 The Basic Circuit

Basically, an electric circuit consists of a voltage source, a load and a path

for current between the source and the load. Figure 1.18 shows an

example of a simple electric circuit:

Figure 1.18 A simple electric circuit.

A battery connected to a lamp with two conductors (wires). The battery is

the voltage source. The lamp is the load on the battery because it draws

current from the battery. The two wires provide the current path from the

positive terminal of the battery to the lamp and back to the negative

terminal of the battery.

Current goes through the filament of the lamp (which has a resistance),

causing it to emit visible light. Current through the battery occurs by

chemical action. In many practical cases, one terminal of the battery is

connected to a common or ground point.

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1.6.2 The Electric Circuit Schematic

An electric circuit can be represented by a schematic using standard

symbols for each element as shown in Figure 1.19 for the simple circuit in

Figure 1.18. The purpose of a schematic is to show in an organized

manner how the various components in a given circuit are interconnected

so that the operation of the circuit can be determined.

Figure 1.19 Schematic for the circuit in Figure 1.18.

1.6.3 Closed and Open Circuits

The example circuit in Figure 1.18 illustrated a closed circuit, a circuit in

which the current has a complete path. When the current path is broken,

the circuit is called an open circuit.

1.6.4 Switches

Switches are commonly used for controlling the opening or closing of

circuits by either mechanical or electronic means. For example, a switch is

used to turn a lamp on or off as illustrated in Figure 1.20. The type of

switch indicated is a single-pole-single-throw (SPST) toggle switch.

Figure 1.21 shows a somewhat more complicated circuit using a single-

pole- double-throw (SPDT) type of switch to control the current to two

different lamps. When one lamp is on, the other is off, and vice versa, as

illustrated by the two schematics in parts (b) and (c), which represent

each of the switch positions. The term pole refers to the movable arm in a

switch, and the term throw indicates the number of contacts that are

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affected (either opened or closed) by a single switch action (a single

movement of a pole).

Figure 1.20 Basic closed and open circuits using an SPST switch for

control.

Figure 1.21 An example of an SPDT switch controlling two lamps.

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In addition to the SPST and the SPDT switches (symbols are shown in

Figure 1.22(a) and (b)), the following other types are important:

a. Double-pole--single throw (DPST).

The DPST switch permits simultaneous opening or closing of

two sets of contacts. The symbol is shown in Figure 1.22(c).

The dashed line indicates that the contact arms are

mechanically linked so that both move with a single switch

action.

b. Double-pole--double-throw (DPDT).

The DPDT switch provides connection from one set of contacts

to either of two other sets. The schematic symbol is shown in

Figure 1.22(d).

c. Push-button (PB).

In the normally open push-button switch (NOPB), shown in

Figure 1.22(e), connection is made between two contacts when

the button is depressed, and connection is broken when the

button is released.

In the normally closed push-button switch (NCPB), shown in

Figure 1.22(f), connection between the two contacts is broken

when the button is depressed.

d. Rotary.

In a rotary switch, a knob is turned to make connection between

one contact and any one of several others. A symbol for a

simple six-position rotary switch is shown in Figure 1.22(g).

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Figure 1.22 Switch symbols.

1.7 Basic Circuit Measurements

An electronics technician cannot function without knowing how to

measure voltage, current, and resistance.

1.7.1 Voltage, Current and Resistance Measurements

Are commonly required in electronics work. Special types of instruments

are used to measure these basic electrical quantities. The instrument

used to measure voltage is a voltmeter. The instrument used to measure

current is an ammeter and the instrument used to measure resistance is

an ohmmeter.

Commonly, all three instruments are combined into a single instrument

such as a multimeter or a VOM (volt-ohm-milliammeter), which can

choose what specific quantity to measure by selecting the switch setting.

Figure 1.23(a) shows an analog meter with a needle pointer and Figure

1.23(b) shows a digital multimeter (DMM), which provides a digital readout

of the measured quantity plus graphing capability.

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Figure 1.23 Typical portable multimeters.

1.7.2 Measuring Current with an Ammeter

Figure 1.24(a) shows the simple circuit in which the current through the

resistor is to be measured. First, make sure the range setting of the

ammeter is greater than the expected current and then connect the

ammeter in the current path by first opening the circuit, as shown in Figure

1.24(b). Then insert the meter as shown in Figure 1.24(c). Such a

connection is a series connection. The polarity of the meter must be such

that the current is in at the positive terminal and out at the negative

terminal.

Figure 1.24(a) Circuit in which the current is to be measured.

Figure 1.24(b) Open the circuit either between the resistor and the

positive terminal or between the resistor and the negative

terminal of source.

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Figure 1.24(c) Install the ammeter in the current path with polarity as

shown.

1.7.3 Measuring Voltage with a Voltmeter

To measure voltage, connect the voltmeter across the component for

which the voltage is to be found. Such a connection is a parallel

connection.

The negative terminal of the meter must be connected to the negative

side of the circuit, and the positive terminal of the meter must be

connected to the positive side of the circuit. Figure 1.25 shows a voltmeter

connected to measure the voltage across the resistor.

Figure 1.25 Example of a voltmeter connection in a simple circuit to

measure voltage.

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1.7.4 Measuring Resistance with an Ohmmeter

To measure resistance, first turn off the power and disconnect one end or

both ends of the resistor from the circuit; then connect the ohmmeter

across the resistor. This procedure is shown in Figure 1.26.

Figure 1.26 Example of using an ohmmeter to measure resistance.

1.7.5 Reading Analog Multimeters

A representation of a typical analog multimeter is shown in Figure 1.27(a),

(b) and (c). This particular instrument can be used to measure direct

current (dc) and alternating current (ac) quantities as well as resistance

values.

It has four selectable functions: dc volts (dc volts) dc milliamperes (dc

mA), ac volts (ac volts), and ohms. Most analog multimeters are similar to

this one.

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(a) (b) (c)

Figure 1.27 Analog multimeter display.

Activity (Questions)

1. How many coulombs of charge do 50 x 1031 electron possess?

2. How many electrons does it take to make 80 µC of charge?

3. Five hundred joules of energy are used to move 100 C of charge

through a resistor. What is the voltage across the resistor?

4. If a resistor with a current 0f 2 A through it converts 1000 J of

electrical energy into heat energy in 15 s, what is the voltage

across the resistors?

5. 5.74 x 1017 electrons flow through a wire in 250 ms. What is the

current in amperes?

6. A certain current source provides 100 mA to 1 kΩ load. If the

resistance is decreased to 500 Ω, what the current in the load?

7. Determine the resistance values and the tolerance for the following

4-band resistors:

(a) Red, violet, orange, gold

(b) Brown, gray, red, silver

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8. Determine the color bands for each of the following 4-band

resistors. Assume each has a 5% tolerance.

(a) 0.47 Ω (b) 270 kΩ (c) 5.1 MΩ

9. What resistance is indicated by 4K7?

10. Show the placement of an ammeter and a voltmeter to measure

the current and the source voltage in Figure 1.28.

Figure 1.28

REFERENCES

1. Principles of Electric Circuits Conventional Current Version Seventh

Edition; Thomas L.Floyd; Prentice Hall; 2003.

2. Electric Circuit Fundamentals Sixth Edition; Thomas L.Floyd; Pearson

Prentice Hall; 2004.

3. Fundamentals of Electric Circuits; Alexander, C. K.; Sadiku, M.N.O.;

McGraw-Hill International Editions; 2000.