Basic electronics college algebra course manual

Introduction to
Electronics

CHAPTER

Section 1.1 Electronics Safety

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1-1 Electronics Safety

Safety is everyone’s responsibility. Everyone must cooperate to
create the safest possible working conditions. Where your personal
life and good health are concerned, safety becomes your
responsibility whether you step in front of a speeding truck, or
expose yourself to a lethal shock, are matters over which you, as an
individual have more control than anyone else.

1-2 Applications of
Electronics
1-3 Digital Number Systems
1-4 Representing Binary
Quantities

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Safety is simply a matter of applying common sense precautions.
The rules of safety are concerned with the prevention of accidental
injuries sustained when an accident occurs.
The general rules for shop safety apply equally to the electricalelectronics laboratory. The following important shop rules should be
observed at all times.

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Chapter 1

Introduction to Electronics

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2.
3.
4.
5.
6.
7.
8.
9.
10.

Don’t clown around or engage in horseplay. Many painful injuries are caused by the
carelessness and thoughtless antics of the clown.
Get your teacher’s approval before starting your work. This will save your time and
help prevent accidents. Remember your teacher is there to help you.
Report all injuries at once, even the slightest. A small cut can develop serious
complications if not properly treated.
Wear safety glasses- when grinding or working in areas where sparks or chips of
metals are flying. Remember that your eyes is a priceless possession.
Keep the floors around your work area clean and free of litter which might cause
someone to slip or stumble.
Use tools correctly and do not use them if they are not in proper working condition.
Observe the proper methods of handling and lifting objects. Get help to lift heavy
objects.
Do not talk nor disturb a fellow student when he is operating a machine.
Never leave the machine while it is running down. Stay with it until it stops
completely.
Obtain permission before you use power tools.

Students and teachers who work with electricity face hazard of electrical shock and should make
every effort to understand the danger.
Electricity can cause fatal burns or cause vital organs to malfunction. In general, a current of 5 mA or
less will cause a sensation of shock, but rarely any damage. Larger currents can cause hand muscles
to contract. Currents on the order of 100 mA are often fatal if they pass through the body for even a
few seconds.
The Electronics Workshop is primarily concerned with low-voltage electronics. The chance of injury
due to electric shock is very, very, low. Experiments for younger students have been designed to be
easily completed without the use of soldering.
Nonetheless, as in all laboratory situations, there are safety rules that must be followed.
The two most important safety rules are:
1. Always have a knowledgeable adult to supervise work.

Ask a teacher or parent to help you.
2. Always use common sense and pay attention to the job you are working on.
Doing so can prevent most laboratory accidents.

Electricity-electronics is a tremendous field and most of us do well to understand small segments of it.
Ask questions when in doubt. Be humble!
Every possible precaution has been taken to ensure the safety of experiments and the correctness of
information.
The study of electronics is interesting and exciting. Enjoy yourself and be safe.

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Introduction to Electronics

Section 1.2 Applications of Electronics
In addition to use in radio and television, Electronics is used to almost all industries for control
functions, automation, and computing. There are so many applications that the broad field of
electronics must be considered in smaller areas. Three logical groupings of electronics applications
are defined here. Also included is a brief description of some important divisions with some typical job
titles for working in the electronic business.
Communications Electronics. This field includes AM and FM radio with stereo, and television with
color. The equipment is divided between transmitters and receivers. Also, transmitters can be divided
between radio frequency equipment to produce the carrier wave radiated from the antenna and the
audio and video equipment in the studio that supplies the modulating signal with the desired
information.

High-fidelity audio equipment can be considered with radio receivers. The receiver itself has audio
amplifiers to drive the loudspeaker that reproduce the sound.
Satellite communications is also a transmit-receive system using electro-magnetic radio waves. The
satellite just happens to be orbiting around the earth at a height of about 22,300 miles order to
maintain a stationary position relative to the earth. Actually, the satellite is a relay station for
transmitter and receiver earth stations.
Electric Power. These applications are in the generation and distribution if 60-Hz AC power, as the
source of energy for electrical equipment. Included are lighting, heating, motors, and generators.
Electronics plays an important role in the control and monitoring of electrical equipments.
Digital Electronics. We see the digits 0 to 9 on an electronic calculator or digital watch, but digital
electronics has a much broader meaning. The circuits for digital applications operate with pulses of
voltage or current, as shown in the diagram below. A pulse waveform is either completely ON or OFF
because of the sudden changes in amplitude. In-between values have no function. Note that ON and
OFF stage can also be labeled as HIGH and LOW, or 1 and 0 in binary notation. Effectively the digital
pulses correspond to the action of switching circuits that are either on or off.

Voltage or current variations with a continuous set of values form an analog waveform, as shown
below. The 60-Hz power line and audio and video signals are common examples. Note that the
values between 0 and 10 V are marked to indicate that all the in-between values are an essential part
of a waveform.
Actually, all the possible applications in the types of electronic circuits can be divided into two just two
types- digital circuits that recognize pulses when they are HIGH or LOW, and analog circuits that use
all values in the waveform. The applications of digital electronics, including calculators, computers,
data processing and data communications, possibly form the largest branch of electronics. In addition
many other applications, including radio and television, use both analog and digital circuits.
In addition to all the general applications in communications, digital equipment, and electric services,
several fields that could be of specific interest include automotive electronics, industrial electronics,
and medical electronics. Both digital and analog techniques are used.
In automotive electronics, more and more electronic equipment is used in cars for charging the
battery, power assist functions, measuring gages, and monitoring and control of engine performance.

Perhaps the most important application is the electronic ignition. This method provides better timing

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Chapter 1

Introduction to Electronics

of the ignition spark, especially at high speeds. On-board computer monitor and control a wide auto
functions.
Industrial electronics includes control of welding and heating processes, the use of elevator control,
operation of copying machines. Metal detectors and smoke detectors, moisture control, and
computer-controlled machinery. In addition there are many types of remote control-functions, such as
automatic garage door openers and burglar alarms. Closed-circuit television is often used for
surveillance.
Medical electronics combines electronics with biology. Medical research diagnosis, and treatment
all use electronic equipment. Examples are the electron microscope and electrocardiograph machine.
In hospitals, oscilloscopes are commonly used as the display to monitor the heartbeat of patients in
extensive care.

Job titles
Different specialties in electronics are indicated by the following titles for engineers: antenna, audio,
computer, digital, illumination, information theory, magnetic, microwave, motors and generators,
packaging, power distribution, radio, semiconductor, television, and test equipment. Many of these
fields combine physics and chemistry, especially for semiconductors.
The types of jobs in these fields include engineer for research, development, production, sales, or
management, teacher, technician, technical writer, computer programmer, drafter, service worker,

tester and inspector. Technicians and service workers are needed for testing, maintenance and repair
of all the different types of electronic equipments.

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Chapter 1

5

Introduction to Electronics
Score:
Instructor’s signature:
Date:
Remarks:

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Exercise 1. Electronics safety comprehension exam
1. In your own words, enumerate five electronics safety tips that you understand in this lesson.
(2 points each)
a.

b.

c.

d.

e.

2. What field of electronics interests you most? Why? (5 points)

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Resistors

2

CHAPTER

The resistor's function is to reduce the flow of electric current. This
symbol
is used to indicate a resistor in a circuit diagram,
known as a schematic.

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2-1 Types of Resistors

Resistance value is designated in units called the "Ohm." A 1000

Ohm resistor is typically shown as 1K-Ohm ( kilo Ohm ), and 1000 KOhms is written as 1M-Ohm ( mega ohm ).

2-2 Resistor Color Codes
2-3 The Ohmmeter

There are two classes of resistors; fixed resistors and the variable
resistors. They are also classified according to the material from
which they are made. The typical resistor is made of either carbon
film or metal film. There are other types as well, but these are the
most common.

2-4 The Ohmeter
2-5 The Multimeter
2-6 Variable Resistors
2 -7 Rating of Resistors

The resistance value of the resistor is not the only thing to consider
when selecting a resistor for use in a circuit. The "tolerance" and the
electric power ratings of the resistor are also important.

2-8 Resistor Troubles

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The tolerance of a resistor denotes how close it is to the actual rated
résistance value. For example, a ±5% tolerance would indicate a
resistor that is within ±5% of the specified resistance value.
The power rating indicates how much power the resistor can safely
tolerate. Just like you wouldn't use a 6 volt flashlight lamp to replace
a burned out light in your house, you wouldn't use a 1/8 watt resistor

when you should be using a 1/2 watt resistor.
The maximum rated power of the resistor is specified in Watts.
Power is calculated using the square of the current ( I2 ) x the
resistance value ( R ) of the resistor. If the maximum rating of the
resistor is exceeded, it will become extremely hot, and even burn.
Resistors in electronic circuits are typically rated 1/8W, 1/4W, and
1/2W. 1/8W is almost always used in signal circuit applications.
When powering a light emitting diode, comparatively large current
flows through the resistor, so you need to consider the power rating
of the resistor you choose.

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Resistors

Section 2.1 Types of Resistors
A fixed resistor is one in which the value of its resistance cannot change.

Carbon film resistors
This is the most general purpose, cheap resistor. Usually the tolerance of the resistance value is
±5%.

Power
ratings
of
1/8W,
1/4W
and
1/2W
are
frequently
used.
Carbon film resistors have a disadvantage; they tend to be electrically noisy. Metal film resistors are
recommended for use in analog circuits. However, I have never experienced any problems with this
noise.
The physical size of the different resistors are as follows.

Rough size
Rating power Thickness Length
(W)
(mm)
(mm)
From the top of the photograph
1/8W
1/4W
1/2W

1/8

2

3

1/4

2

6

1/2

3

9

This resistor is called a Single-In-Line(SIL) resistor network. It is made
with many resistors of the same value, all in one package. One side of
each resistor is connected with one side of all the other resistors inside.
One example of its use would be to control the current in a circuit
powering many light emitting diodes (LEDs).
In the photograph on the left, 8 resistors are housed in the package. Each of the leads on the
package is one resistor. The ninth lead on the left side is the common lead. The face value of the
resistance is printed. ( It depends on the supplier. )
Some resistor networks have a "4S" printed on the top of the resistor network. The 4S indicates that
the package contains 4 independent resistors that are not wired together inside. The housing has
eight leads instead of nine. The internal wiring of these typical resistor networks has been illustrated
below. The size (black part) of the resistor network which I have is as follows: For the type with 9
leads, the thickness is 1.8 mm, the height 5mm, and the width 23 mm. For the types with 8
component leads, the thickness is 1.8 mm, the height 5 mm, and the width 20 mm.

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Resistors

Metal film resistors
Metal film resistors are used when a higher tolerance (more accurate value) is needed. They are
much more accurate in value than carbon film resistors. They have about ±0.05% tolerance. They
have about ±0.05% tolerance. I don't use any high tolerance resistors in my circuits. Resistors that
are about ±1% are more than sufficient. Ni-Cr (Nichrome) seems to be used for the material of
resistor. The metal film resistor is used for bridge circuits, filter circuits, and low-noise analog signal
circuits.

Rough size
Rating power Thickness Length
(W)
(mm)
(mm)
From the top of the photograph
1/8W (tolerance ±1%)
1/4W (tolerance ±1%)
1W (tolerance ±5%)
2W (tolerance ±5%)

1/8

2

3

1/4

2

6

1

3.5

12

2

5

15

CDS Elements
Some components can change resistance value by changes in the amount of light hitting them. One
type is the Cadmium Sulfide Photocell. (Cd) The more light that hits it, the smaller its resistance value
becomes.
There are many types of these devices. They vary according to light sensitivity, size, resistance value
etc.
Pictured at the left is a typical CDS photocell. Its diameter is 8 mm, 4 mm high,
with a cylinder form. When bright light is hitting it, the value is about 200 ohms,
and when in the dark, the resistance value is about 2M ohms.
This device is using for the head lamp illumination confirmation device of the car.

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Resistors

Other Resistors
There is another type of resistor other than the carbon-film type and the metal film resistors. It is the
wirewound resistor.
A wirewound resistor is made of metal resistance wire, and because of this, they can be
manufactured to precise values. Also, high-wattage resistors can be made by using a thick wire
material. Wirewound resistors cannot be used for high-frequency circuits. Coils are used in high
frequency circuits. Since a wirewound resistor is a wire wrapped around an insulator, it is also a coil,
in a manner of speaking. Using one could change the behavior of the circuit. Still another type of
resistor is the Ceramic resistor. These are wirewound resistors in a ceramic case, strengthened with
a special cement. They have very high power ratings, from 1 or 2 watts to dozens of watts. These
resistors can become extremely hot when used for high power applications, and this must be taken
into account when designing the circuit. These devices can easily get hot enough to burn you if you
touch one.
The photograph on the left is of wirewound resistors.
The upper one is 10W and is the length of 45 mm, 13
mm thickness.
The lower one is 50W and is the length of 75 mm, 29
mm thickness.
The upper one is has metal fittings attached. These
devices are insulated with a ceramic coating.

The photograph on the left is a ceramic (or cement) resistor of 5W and
is the height of 9 mm, 9 mm depth, 22 mm width.

Thermistor ( Thermally sensitive resistor )
The resistance value of the thermistor changes according to temperature.
This part is used as a temperature sensor.There are mainly three types of thermistor.
NTC(Negative Temperature Coefficient Thermistor)
: With this type, the resistance value decreases continuously as the temperature rises.
PTC(Positive Temperature Coefficient Thermistor)
: With this type, the resistance value increases suddenly when the temperature rises above a specific
point.
CTR(Critical Temperature Resister Thermistor)
: With this type, the resistance value decreases suddenly when the temperature rises above a
specific point.
The NTC type is used for the temperature control.

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Resistors

The relation between the temperature and the resistance value of the NTC type can be calculated
using the following formula.

R

T
R0
T0
B

: The resistance value at the temperature T
: The temperature [K]
: The resistance value at the reference temperature T0
: The reference temperature [K]
: The coefficient

As the reference temperature, typically, 25°C is used.
The unit with the temperature is the absolute temperature(Value of which 0 was -273°C) in K(Kelvin).
25°C are the 298 Kelvins.

Section 2.2 Resistor color code
Because carbon resistors are small physically, they are color-coded to mark their value in ohms. The
basis of this system is the use of colors for numerical values as listed in the table below. In
memorizing the colors note that the darkest colors, black and brown, are for the lowest numbers, zero
and one, whereas white is for nine. The color coding is standardized by the Electronic Industries
Association (EIA). These colors are also used for small capacitors.

Example 1
(Brown=1),(Black=0),(Orange=3)
3
10 x 10 = 10k ohm
Tolerance(Gold) = ±5%

Example 2
(Yellow=4),(Violet=7),(Black=0),(Red=2)

2
470 x 10 = 47k ohm
Tolerance(Brown) = ±1%

Color

Value

Multiplier

Tolerance
(%)

Black

0

0

-

Brown

1

1

±1

Red

2

2

±2

Orange

3

3

±0.05

Yellow

4

4

-

Green

5

5

±0.5

Blue

6

6

±0.25

Violet

7

7

±0.1

Gray

8

8

-

White

9

9

-

Gold

-

-1

±5

Silver

-

-2

±10

None

-

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Chapter 2

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Resistors

As illustrated in the diagram above, silver in the fourth band indicates a tolerance of 10 %, gold
indicates 5%. If there is no color band for tolerance, it is 20%. The inexact value of carbon
resistor is a disadvantage of their economical construction. They usually cost only a few cents, or less
in larger quantities. In most circuits, though, a small difference in resistance can be tolerated.
It should be noted that some resistors have five stripes, instead of four. In this case, the first three
stripes give three digits, followed by the decimal multiplier in the fourth stripe and the tolerance in the
fifth stripe. These resistors have more precise values, with tolerances of 0.1 to 2 percent.
Resistance Color Stripes. The use of bands or stripes is the most common system for color-coding
carbon resistors as shown in the diagram above right. Color stripes are printed at one end of the
insulating body, which is usually tan. Reading from left to right, the first band close to the edge gives
the first digit in numerical value of R. The next band marks the second digit. The third band is the
decimal multiplier, which gives the number of zeroes after the two digits.
Resistors under 10Ω
Ω. For these values the third stripe is either gold or silver, indicating a fractional
decimal multiplier. When the third digit is gold, multiply the first two digits by 0.1. Example, if the first
two digits are 25 then, 25 X 0.1 = 2.5 Ω. Silver means a mult4iplier of 0.01 . If the first two digits is still
25 then, 25 X 0.01 = .25 Ω.
It is important to realize that the gold and silver colors are used as decimal multipliers only in the third
stripe. However, gold and silver are used most often in the fourth stripe to indicate how accurate the
R value is.
Resistor Tolerance. The amount by which the actual R can be different from the color-coded value is
the tolerance, usually given in percent. For instance, a 2000Ω resistor with 10 percent tolerance
can have resistance 10 percent above or below the coded value. This R, therefore, is between 1800Ω
to 2200Ω. The calculation are as follows:

10 percent of 2000 is .1 X 2000 = 200
For + 10 percent, the value is
2000 + 200 = 2200Ω
For – 10 percent, the value is
2000 – 200 = 1800Ω

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Resistors

Score:
Instructor’s signature:
Date:
Remarks:

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Exercise 2. Resistor Color Codes
I.

Fill up the table below for the expected value of the resistors in ohms and in kilo-ohms
given its color codes below. (2 points per number)
Value in Ohms

Value in K-ohms

1. Grey, Blue, Red, Silver
2. Yellow, Green, Gold, Gold
3. Violet, Brown, Black, Silver, Gold
4. Brown, Black, Red, Gold
5. Blue, Yellow, Orange, Silver
6. Brown, Black, Silver, Silver
7. Red, Red, Red, Gold
8. Green, Orange, Brown, Silver
9. Brown, Violet, Yellow, Gold
10. Blue, Black, Red, Orange, Gold
II.

Compute for the tolerance value of each resistor given its color codes.(2 points per number)

1. Red, Brown, Orange, Gold
a. Upper Limit
b. Lower Limit
2. Orange, Violet, Brown, Silver
a. Upper Limit
b. Lower Limit
3. Grey, White, Violet, Gold, Silver
a. Upper Limit
b. Lower Limit
4. Blue, Green, Silver, Gold
a. Upper Limit
b. Lower Limit
5. Brown, Black, Gold, Silver
a. Upper Limit
b. Lower Limit

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Resistors

Section 2.3 The Ohmmeter
The two instruments most commonly used to check the continuity (a complete circuit), or to measure
the resistance of a circuit or circuit element, are the OHMMETER and the MEGGER (megohm
meter). The ohmmeter is widely used to measure resistance and check the continuity of electrical
circuits and devices. Its range usually extends to only a few megohms. The megger is widely used
for measuring insulation resistance, such as between a wire and the outer surface of the insulation,
and insulation resistance of cables and insulators. The range of a megger may extend to more than
1,000 megohms.
The ohmmeter consists of a dc ammeter, with a few added features. The added features are:
A dc source of potential (usually a 3-volt battery)
One or more resistors (one of which is variable) A simple ohmmeter circuit is shown in figure 2-1.
The ohmmeter's pointer deflection is controlled by the amount of battery current passing through the
moving coil. Before measuring the resistance of an unknown resistor or electrical circuit, the test
leads of the ohmmeter are first shorted together, as shown in figure 1-31.
With the leads shorted, the meter is calibrated for proper operation on the selected range. While the
leads are shorted, meter current is maximum and the pointer deflects a maximum amount,
somewhere near the zero position on the ohms scale. Because of this current through the meter with
the leads shorted, it is necessary to remove the test leads when you are finished using the ohmmeter.
If the leads were left connected, they could come in contact with each other and discharge the
ohmmeter battery. When the variable resistor (rheostat) is adjusted properly, with the leads shorted,

the pointer of the meter will come to rest exactly on the zero position. This indicates

Zero Resistance
Between the test leads, which, in fact, are shorted together.
The zero reading of a series-type ohmmeter is on the righthand side of the scale, where as the zero reading for an
ammeter or a voltmeter is generally to the left-hand side of
the scale. (There is another type of ohmmeter which is
discussed a little later on in this chapter.) When the test
leads of an ohmmeter are separated, the pointer of the
meter will return to the left side of the scale.
The interruption of current and the spring tension act on the
movable coil assembly, moving the pointer to the left side
(∞) of the scale.
Figure 1-31. - A simple ohmmeter circuit.

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Resistors

Using the Ohmmeter
After the ohmmeter is adjusted for zero reading, it is ready to be connected in a circuit to measure
resistance. A typical circuit and ohmmeter arrangement is shown in figure 2-2
Figure 2-2. - Measuring circuit resistance with an ohmmeter.

The power switch of the circuit to be measured should always

be in the OFF position. This prevents the source voltage of
the circuit from being applied across the meter, which could
cause damage to the meter movement.
The test leads of the ohmmeter are connected in series with
the circuit to be measured (fig. 1-32). This causes the current
produced by the 3-volt battery of the meter to flow through the
circuit being tested. Assume that the meter test leads are
connected at points a and b of figure 1-32. The amount of
current that flows through the meter coil will depend on the
total resistance of resistors R1 and R2, and the resistance of
the meter. Since the meter has been preadjusted (zeroed),
the amount of coil movement now depends solely on the
resistance of R1and R2. The inclusion of R1 and R2 raises the
total series resistance, decreasing the current, and thus
decreasing the pointer deflection. The pointer will now come to rest at a scale figure indicating the
combined resistance of R1 and R2.
If R1 or R2, or both, were replaced with a resistor(s) having a larger value, the current flow in the
moving coil of the meter would be decreased further. The deflection would also be further decreased,
and the scale indication would read a still higher circuit resistance.
Movement of the moving coil is proportional to the amount of current flow.

Ohmmeter Ranges
The amount of circuit resistance to be measured may
vary over a wide range. In some cases it may be only a
few ohms, and in others it may be as great as 1,000,000
ohms (1 megohm). To enable the meter to indicate any
value being measured, with the least error, scale
multiplication features are used in most ohmmeters. For
example, a typical meter will have four test lead jacksCOMMON, R X 1, R X 10, and R X 100. The jack
marked COMMON is connected internally through the

battery to one side of the moving coil of the ohmmeter.
The jacks marked R X 1, R X 10, and R X 100 are
connected to three different size resistors located within
the ohmmeter. This is shown in figure 2-3.
Figure 1-33. - An ohmmeter with multiplication jacks.

Some ohmmeters are equipped with a selector switch
for selecting the multiplication scale desired, so only two
test lead jacks are necessary.

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Resistors

Other meters have a separate jack for each range, as shown in figure 1-33. The range to be used in
measuring any particular unknown resistance (Rx in figure 1-33) depends on the approximate value of
the unknown resistance. For instance, assume the ohmmeter in figure 1-33 is calibrated in divisions
from 0 to 1,000. If Rx is greater than 1,000 ohms, and the R x 1 range is being used, the ohmmeter
cannot measure it. This occurs because the combined series resistance of resistor R X 1 and Rx is
too great to allow sufficient battery current to flow to deflect the pointer away from infinity (∞).
(Infinity is a quantity larger than the largest quantity you can measure.) The test lead would have to
be plugged into the next range, R X 10. With this done, assume the pointer deflects to indicate 375
ohms. This would indicate that Rx has 375 ohms X 10, or 3,750 ohms resistance.
The change of range caused the deflection because resistor R X 10 has about 1/10 the resistance of
resistor R X 1. Thus, selecting the smaller series resistance permitted a battery current of sufficient

amount to cause a useful pointer deflection. If the R X 100 range were used to measure the same
3,750-ohm resistor, the pointer would deflect still further, to the 37.5-ohm position. This increased
deflection would occur because resistor R X 100 has about 1/10 the resistance of resistor R X 10.
The foregoing circuit arrangement allows the same amount of current to flow through the meter's
moving coil whether the meter measures 10,000 ohms on the R X 10 scale, or 100,000 ohms on the
R X 100 scale.
It always takes the same amount of current to deflect the pointer to a certain position on the scale
(midscale position for example), regardless of the multiplication factor being used. Since the multiplier
resistors are of different values, it is necessary to ALWAYS "zero" adjust the meter for each
multiplication fact or selected.
You should select the multiplication factor (range) that will result in the pointer coming to rest as near
as possible to the midpoint of the scale. This enables you to read the resistance more accurately,
because the scale readings are more easily interpreted at or near midpoint.

Ohmmeter Safety Precautions
The following safety precautions and operating procedures for ohmmeters are the MINIMUM
necessary to prevent injury and damage.
Be certain the circuit is deenergized and discharged before connecting an ohmmeter.
Do not apply power to a circuit while measuring resistance.
When you are finished using an ohmmeter, switch it to the OFF position if one is provided
and remove the leads from the meter.
Always adjust the ohmmeter for 0 (or ∞ in shunt ohmmeter) after you change ranges
before making the resistance measurement.

Section 2.4 The Multimeter
A MULTIMETER is the most common measuring device used in the Navy. The name multimeter
comes from MULTIple METER, and that is exactly what a multimeter is. It is a dc ammeter, a dc
voltmeter, an ac voltmeter, and an ohmmeter, all in one package. Figure 1-37 is a picture of a typical
multimeter.

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Resistors

Figure 1-37. - A typical multimeter.

The multimeter shown in figure 1-37 may
look complicated, but it is very easy to use.
You
have
already
learned
about
ammeters, voltmeters, and ohmmeters; the
multimeter is simply a combination of
these meters.
Most multimeters use a d'Arsonval meter
movement and have a built-in rectifier for
ac measurement. The lower portion of the
meter shown in figure 1-37 contains the
function switches and jacks (for the meter
leads).
The use of the jacks will be discussed first.
The COMMON or -jack is used in all
functions is plugged into the COMMON

jack. The +jack is used for the second
meter lead for any of the functions printed
in large letters beside the FUNCTION
SWITCH (the large switch in the center). The other jacks have specific functions printed above or
below them and are self-explanatory (the output jack is used with the dB scale, which will not be
explained in this chapter). To use one of the special function jacks, except +10 amps, one lead is
plugged into the COMMON jack, and the FUNCTION SWITCH is positioned to point to the special
function (small letters). For example, to measure a very small current (20 microamperes), one meter
lead would be plugged into the COMMON jack, the other meter lead would be plugged into the 50A
AMPS jack, and the FUNCTION SWITCH would be placed in the 50V/IA AMPS position. To measure
currents above 500 milliamperes, the +10A and -10A jacks would be used on the meter with one
exception.
One meter lead and the FUNCTION SWITCH would be placed in the 10MA/AMPS position.

Multimeter Controls
As described above, the FUNCTION SWITCH is used to select the function desired; the -DC, +DC,
AC switch selects dc or ac (the rectifier), and changes the polarity of the dc functions. To measure
resistance, this switch should be in the +DC position.
The ZERO OHMS control is a potentiometer for adjusting the 0 reading on ohmmeter functions.
Notice that this is a series ohmmeter. The RESET is a circuit breaker used to protect the meter
movement (circuit breakers will be discussed in chapter 2 of this module). Not all multimeters have
this protection but most have some sort of protection, such as a fuse. When the multimeter is not in
use, it should have the leads disconnected and be switched to the highest voltage scale and AC.
These switch positions are the ones most likely to prevent damage if the next person using the meter
plugs in the meter leads and connects the meter leads to a circuit without checking the function
switch and the dc/ac selector.

Multimeter Scales
The numbers above the uppermost scale in figure 1-38 are used for resistance measurement. If the
multimeter was set to the R x 1 function, the meter reading would be approximately 12.7 ohms.

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Figure 1-38. - A multimeter scale and reading.

The numbers below the uppermost scale
are used with the uppermost scale for dc
voltage and direct current, and the same
numbers are used with the scale just
below the numbers for ac voltage and
alternating current. Notice the difference
in the dc and ac scales. This is because
the ac scale must indicate effective ac
voltage and current. The third scale from
the top and the numbers just below the
scale are used for the 2.5-volt ac function
only.
The lowest scale (labeled DB) will not be
discussed. The manufacturer's technical manual will explain the use of this scale.
The table in figure 1-38 shows how the given needle position should be interpreted with various
functions selected.
As you can see, a multimeter is a very versatile measuring device and is much easier to use than
several separate meters.

Parallax Error
Most multimeters (and some other meters) have a mirror built into the scale. Figure 1-39 shows the
arrangement of the scale and mirror.
Figure 1-39. - A multimeter scale with mirror.

The purpose of the mirror on the scale of a meter is to aid in reducing PARALLAX ERROR. Figure 140 will help you understand the idea of parallax.
Figure 1-40(A) shows a section of barbed wire fence as you would see it from one side of the fence.
Figure 1-40(B) shows the fence as it would appear if you were to look down the fine of fence posts
and were directly in line with the posts. You see only one post because the other posts, being in line,

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are hidden behind the post you can see. Figure 1-40(C) shows the way the fence would appear if you
moved to the right of the line of posts. Now the fence posts appear to the right of the post closest to
you. Figure 1-40(D) shows the line of fence posts as you would see them if you moved to the left of
the front post. This apparent change in position of the fence posts is called PARALLAX.
Parallax can be a problem when you are reading a meter. Since the pointer is slightly above the scale
(to allow the pointer to move freely), you must look straight at the pointer to have a correct meter
reading. In other words, you must be in line with the pointer and the scale. Figure 1-41 shows the
effect of parallax error.
Figure 1-41. - A parallax error in a meter reading.
(A) shows a meter viewed correctly.

The meter reading is 5 units. Figure 1-41(B) shows the same meter as it would appear if you were to
look at it from the right. The correct reading (5) appears to the right of the pointer because of parallax.
The mirror on the scale of a meter, shown in figure 1-39, helps get
rid of parallax error. If there is any parallax, you will be able to see
the image of the pointer in the mirror. If you are looking at the
meter correctly (no parallax error) you will not be able to see the
image of the pointer in the mirror because the image will be
directly behind the pointer. Figure 1-42 shows how a mirror added
to the meter in figure 1-41 shows parallax error. Figure 1-42(A) is
a meter with an indication of 5 units. There is no parallax error in
this reading and no image of the pointer is seen in the mirror.
Figure 1-42(B) shows the same meter as viewed from the right.
The parallax error is shown and the image of the pointer is shown
in the mirror.

Figure 1-42. - A parallax error on a meter with a mirrored scale.

Multimeter Safety Precautions
As with other meters, the incorrect use of a multimeter could cause injury or damage. The following
safety precautions are the MINIMUM for using a multimeter.
Deenergize and discharge the circuit completely before connecting or disconnecting a
multimeter.
Never apply power to the circuit while measuring resistance with a multimeter.
Connect the multimeter in series with the circuit for current measurements, and in parallel for
voltage measurements.
Be certain the multimeter is switched to ac before attempting to measure ac circuits.
Observe proper dc polarity when measuring dc.
When you are finished with a multimeter, switch it to the OFF position, if available. If there is
no OFF position, switch the multimeter to the highest ac voltage position.

Always start with the highest voltage or current range.
Select a final range that allows a reading near the middle of the scale.
Adjust the "0 ohms" reading after changing resistance ranges and before making a resistance
measurement.
Be certain to read ac measurements on the ac scale of a multimeter.
Observe the general safety precautions for electrical and electronic devices.

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Score:
Instructor’s signature:
Date:
Remarks:

_______

Laboratory Experiment 1 Using the Ohmmeter
3. Before connecting the resistors as shown in the diagram below, measure first the values of
each resistors and write down their values in the table below. Then connect the resistors as
follows.

4.

Complete the table below.

Resistor
Number
R1

Color- Code
Value

Expected Value

Measured
Value

R2
R3
R4
R5
R6
R7
R2 & R3

n.a.

Nodes A - B

n.a.

Nodes C - D

n.a.

Nodes A - D

n.a.

From arrow arrow

n.a.

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Variable Resistors
Variable resistors can be wire-wound or the carbon type. Inside the
metal case, the control has a circular disk that is carbon composition
resistance element. It can be a thin coating pressed o a paper or a
molded carbon disk. Joined to the two ends are the external solderinglug terminals 1 and 3. The middle terminal is connected to the variable
arm that contacts the resistor element by a metal spring wiper. As the
shaft of the control is turned, the variable arm moves the wiper to
make contact at different points in the resistor element. The same idea
applies to the slide control, except that the resistor element is straight
instead of circular.
When the contact moves closer to the end, the R decreases between

this terminal and the variable arm. Between the two ends, however,
the R is not variable but always has the maximum resistance of the
control.
Carbon controls are available with a total R from 1000 Ω to 5 MΩ,
approximately. Their power rating is usually ½ to 2 W.

Rheostats and Potentiometers
These are variable resistances, either carbon or wire-wound, used to vary the amount of current or
voltage in a circuit. The controls can be used in either DC or AC applications.
A rheostat is a variable R with two terminals connected in series with a load. The purpose is to vary
the amount of current.
A potentiometer, generally called a pot for short, has three terminals. The fixed maximum R across
the two ends is connected across a voltage source. The variable arm is used to vary the voltage
division between the center terminal and the ends. This function of a potentiometer is compared with
a rheostat in the table below.
Rheostat
Two terminals
In series with load and V
source
Varies the I

Potentiometer
Three terminals
Ends
are
connected
across V source
Taps off part of V

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There are two general ways in which variable resistors are used. One is the variable resistor which
value is easily changed, like the volume adjustment of Radio. The other is semi-fixed resistor that is
not meant to be adjusted by anyone but a technician. It is used to adjust the operating condition of the
circuit by the technician. Semi-fixed resistors are used to compensate for the inaccuracies of the
resistors, and to fine-tune a circuit. The rotation angle of the variable resistor is usually about 300
degrees. Some variable resistors must be turned many times to use the whole range of resistance
they offer. This allows for very precise adjustments of their value. These are called "Potentiometers"
or "Trimmer Potentiometers."
In the photograph to the left, the variable
resistor typically used for volume controls
can be seen on the far right. Its value is
very easy to adjust.
The four resistors at the center of the
photograph are the semi-fixed type. These
ones are mounted on the printed circuit
board.
The two resistors on the left are the
trimmer potentiometers.

This symbol
is used to indicate a variable resistor
in a circuit diagram.

There are three ways in which a variable resistor's
value can change according to the rotation angle of
its axis.
When type "A" rotates clockwise, at first, the
resistance value changes slowly and then in the
second half of its axis, it changes very quickly.
The "A" type variable resistor is typically used for the
volume control of a radio, for example. It is well
suited to adjust a low sound subtly. It suits the
characteristics of the ear. The ear hears low sound
changes well, but isn't as sensitive to small changes
in loud sounds. A larger change is needed as the
volume is increased. These "A" type variable
resistors are sometimes called "audio taper"
potentiometers.

As for type "B", the rotation of the axis and the change of the resistance value are directly related.
The rate of change is the same, or linear, throughout the sweep of the axis. This type suits a
resistance value adjustment in a circuit, a balance circuit and so on. They are sometimes called
"linear taper" potentiometers. Type "C" changes exactly the opposite way to type "A". In the early
stages of the rotation of the axis, the resistance value changes rapidly, and in the second half, the
change occurs more slowly. This type isn't too much used. It is a special use.
As for the variable resistor, most are type "A" or type "B".

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Section 2.6 Rating of Resistors
In addition to having the required ohms value, a resistor should have a wattage rating high enough to
dissipate the power produced by the current flowing through the resistance, without becoming too hot.
Carbon resistors in normal operation are quite warm, up to a maximum temperature of 85°C, which is
close to 100°C boiling point of water. Carbon resistors should not be so hot, however that they
“sweat” beads of liquid on the insulating case. Wire-wound resistors operate at very high
temperatures, a typical value being 300°C for the maximum temperature. If a resistor becomes too
hot because of excessive power dissipation, it can change appreciably in resistance value or burn
open.
The power rating is a physical property that depends on the resistor construction. Note the following:

1. A larger physical size indicates a higher power rating.
2. Higher-wattage resistors can operate at higher temperatures.
3. Wire-wound resistors are physically larger with higher wattage ratings than carbon resistors.

Section 2.7 Resistor Troubles
The most common trouble in resistors is an open circuit. When the open resistor is a series
component, there is no current in the entire path.
Noisy controls. In applications such as volume and tone control, carbon controls are preferred
because the smoother change in resistance results in less noise when the variable arm is rotated.
With use, however, the resistance element becomes worn by the wiper contact, making the control
noisy. When a volume or tone control makes a scratchy noise as the shaft is rotated, it indicates a
worn out resistance element.
Checking resistors with ohmmeter. Resistance measurements are made with an ohmmeter. The
ohmmeter has its own voltage source so that it is always used without any external power applied to
the resistance being measured. Separate the resistance from the circuit by disconnecting one lead of
the resistor. Then connect the ohmmeter lead across the resistance to be measured

An open resistor reads indefinitely high ohms. For some reason, an infinite ohm is often confused
with zero ohms. Remember, though, that an infinite ohm means an open circuit. The current is zero,
but the resistance is infinitely high. Furthermore it is practically impossible for a resistor to become
short-circuited in itself. The resistor may be short-circuited by some other part of the circuit. However,
he construction of resistors such that the trouble they develop is an open circuit with infinitely high
ohms.
The ohmmeter must have an ohms scale capable of reading the resistance value, or the resistor
cannot be checked. In checking a 10 MΩ resistor, for instance, if the highest R the ohmmeter can
read is 1 MΩ, it will indicate infinite resistance, even if the resistors’ normal value is 10 MΩ. An ohms
scale of 100 MΩ or more should be used for checking such resistances.
To check resistors of less than 10 Ω, a low ohms scale of about 100 Ω or less is necessary. Center
scale should be 6 Ω or less. Otherwise, the ohmmeter can read a normally low resistance value as
zero ohms.

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When checking resistance in a circuit, it is important to be sure there are no parallel paths across the
resistor being measured. Otherwise, the measured resistance can be much lower than the actual
resistor value.

Section 2.8 Resistor Connections
The total resistance depends on the series or parallel connections. However, the combination has a
power rating equal to the sum of the individual values. Weather resistors are in series or parallel. The

reason is that the total physical size increases with each added resistor. Equal resistors are generally
used in order to have equal distribution of I, V and P.
In general, series resistors add for a higher RT. With parallel resistors, REQ is reduced.

Series Combinations of Resistors
Two elements are said to be in series whenever the same current physically flows through both of the
elements. The critical point is that the same current flows through both resistors when two are in
series. The particular configuration does not matter. The only thing that matters is that exactly the
same current flows through both resistors. Current flows into one element, through the element, out of
the element into the other element,
through the second element and
out of the second element. No part
of the current that flows through
one resistor "escapes" and none is
added. This figure shows several
different ways that two resistors in
series might appear as part of a
larger circuit diagram.

You might wonder just how often you actually find resistors in series. The answer is that you find
resistors in series all the time.
An example of series resistors is in house wiring. The leads from
the service entrance enter a distribution box, and then wires are
strung throughout the house. The current flows out of the
distribution box, through one of the wires, then perhaps through a
light bulb, back through the other wire. We might model that
situation with the circuit diagram shown below.

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In many electronic circuits series resistors are used to get a different voltage across one of the
resistors. We'll look at those circuits, called voltage dividers, in a short while. Here's the circuit
diagram for a voltage divider.
Besides resistors in series, we can also have other elements in
series - capacitors, inductors, diodes. These elements can be in
series with other elements. For example, the simplest form of
filter, for filtering low frequency noise out of a signal, can be built
just by putting a resistor in series with a capacitor, and taking the
output as the capacitor voltage.
As we go along you'll have lots of opportunity to use and to
expand what you learn about series combinations as you study
resistors in series.

Let's look at the model again. We see that the wires are actually small resistors (small value of
resistance, not necessarily physically small) in series with the light bulb, which is also a resistor. We
have three resistors in series although
two of the resistors are small. We know
that the resistors are in series because
all of the current that flows out of the
distribution box through the first wire
also flows through the light bulb and
back through the second wire, thus
meeting our condition for a series

connection. Trace that out in the circuit
diagram and the pictorial representation
above.
Let us consider the simplest case of a series resistor connection, the case of just two resistors in
series. We can perform a thought experiment on these two resistors. Here is the circuit diagram for
the situation we're interested in.
Imagine that they are embedded in an opaque piece of plastic, so
that we only have access to the two nodes at the ends of the
series connection, and the middle node is inaccessible. If we
measured the resistance of the combination, what would we find?
To answer that question we need to define voltage and current variables for the resistors. If we take
advantage of the fact that the current through them is the same (Apply KCL at the interior node if you
are unconvinced!) then we have the situation below.

Note that we have defined a voltage across each
resistor (Va and Vb) and current that flows through
both resistors (Is) and a voltage variable, Vs, for the
voltage that appears across the series combination.

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Let's list what we know:
The current through the two resistors is the same.

The voltage across the series combination is given by:
Vs= Va + Vb
The voltages across the two resistors are given by Ohm's Law:
Va = Is Ra
We can combine all of these relations, and when we do that we find the following.
Vs= Va + Vb
Vs= Is Ra + Is Rb
Vs= Is (Ra + Rb)
Vs= Is Rseries
Here, we take Rseries to be the series equivalent of the two resistors in series, and the expression for
Rseries is:
Rseries = Ra + Rb
What do we mean by series equivalent? Here are some points to observe.
If current and voltage are proportional, then the device is a resistor.
We have shown that Vs= Is X Rseries, so that voltage is proportional to current, and the constant
of proportionality is a resistance.
We will call that the equivalent series resistance.
There is also a mental picture to use when considering equivalent series resistance. Imagine that you
have two globs of black plastic. Each of the globs of black plasic has two wires coming out. Inside
these two black plastic globs you have the following.
In the first glob you have two resistors in series. Only the leads of the series combination are
available for measurement externally. You have no way to penetrate the box and measure things
at the interior node.
In the second box you have a single resistor that is equal to the series equivalent. Only the leads
of this resistor are available for measurement externally.
Then, if you measured the resistance using the two available leads in the two different cases you
would not be able to tell which black plastic glob had the single resistor and which one had the series
combination.
Here are two resistors. At the top are two 2000W resistors. At the bottom is single 4000W resistors.
(Note, these are not exactly standard sizes so it took a lot of hunting to find a supply store that sold

them!). You can click the green button to grow blobs around them.

After you have grown the blobs around the resistors there is no electrical measurement you can make
that will allow you to tell which one has two resistors and which one has one resistor. They are
electrically indistinguishable! (Or, in other words, they are equivalent!)

Building skills for success