Recall that Unit 1 presented a table of
many electrical quantities, along with their units and abbreviations.
The three quantities that technicians measure most often are voltage,
current, and resistance. Another fundamental quantity that you must understand
(even though you won’t have to measure it very often) is charge. In this
unit you’ll develop a better understanding of these four quantities.
We’ll also look in more detail at resistor color codes and at different
types of resistors. Finally, we’ll also look at a mathematical topic
that is not discussed in the book: significant
Unit 2 Review
This unit will build on material that you studied in Unit
2. So let’s
begin by taking this self-test to review what you learned in that unit.
When discussing circuits, we often draw diagrams representing those
These diagrams, which are called schematic diagrams, do not
show the circuit’s components as they actually look. Instead, the diagrams
contain standard symbols that represent electric components.
Here are some examples of these symbols.
The schematic symbol for a resistor:
The schematic symbol for a capacitor:
The schematic symbol for an inductor:
As you’ve seen in the lab, resistors, capacitors, and inductors have two
metal leads (or "legs," as
some people call them). Therefore, the schematic symbols for these
components have two terminals.
(A terminal is a connection point where the symbol can be attached
to other symbols.) In the schematic symbols shown
above, the left-hand end point of each symbol is one terminal, and
the right-hand end point is another terminal.
Components in Series
When we wish to show that components are connected to each other,
we draw their schematic symbols with lines connecting the terminals
For example, from Unit 2 you know that the photograph below shows two
resistors connected in series on a breadboard.
Here is a schematic diagram showing two
resistors connected in series. In particular, notice that
one terminal of resistor R1 is connected to one terminal of resistor
R2, but the other terminals of R1 and R2 are not connected
Similarly, below is a schematic diagram of three resistors
connected in series,
corresponding to the situation shown in this photograph:
Components in Parallel
You also know from Unit 2 that the photograph below shows two resistors
connected in parallel on a breadboard.
To indicate a parallel connection in a schematic diagram, we would
draw the resistor symbols with both pairs of terminals connected to
each other, as shown here:
For three resistors in parallel, as shown in this photo,
draw something like this:
(A black circle simply indicates the intersection point of several lines.)
Atoms and Electrons
All matter is composed of tiny atoms. Each atom has a centralnucleus and
one or more electrons that travel in orbits around the nucleus.
The electron is a fundamental component of matter and is considered
to have the smallest possible unit of negativecharge.
When an electron breaks away from its “parent ” atom, it is called
a free electron.
Most metals have many free electrons. That’s what
makes them good conductors of electricity.
The best conductors are silver, copper, and gold, in that order.
Since copper is much less expensive than silver, copper is the most
widely used conductive material.
In a material whose electrons are tightly held to their parent atoms,
there are relatively few free electrons.
Such a material is a poor conductor of electricity and is called
Some examples of insulators are plastics, ceramics, rubber, paper,
wood, and most liquids and gases.
A special class of materials called semiconductors have
fewer free electrons than conductors, but more free electrons than
These materials have unique electrical properties that make them
extremely useful. Diodes, transistors, and integrated circuits are
made out of semiconductor material.
The most common semiconductor materials are silicon and germanium.
Electrical charge is a fundamental property
of electrons and protons.
Charge comes in two types, which we call positive and negative.
A proton carries the smallest possible positive charge, while an electron
carries the smallest possible negative charge.
The unit of charge is the coulomb (C).
One coulomb of negative charge is the total charge carried by 6.242 × 1018 electrons.
The symbol Q is used to represent a quantity of charge. For
example, to say that the charge in an area is 100 microcoulombs,
you would write Q = 100 μC.
Voltage (Electromotive Force)
Electric circuits depend on the motion of electrons.
To make electrons move, we must exert a force on them.
A fancy name for this force is electromotive force (or emf).
The more common name is voltage.
The symbolV is used to represent
Voltage is measured in volts (abbreviated V).
Example: To say that a voltage has a value of 15 volts, you
would write V = 15 V.
A device that provides the force needed to move electrons is called
Examples of voltage sources include batteries, solar cells, generators,
and dc power supplies:
Batteries (such as flashlight batteries
or car batteries) convert chemical energy into electrical energy.
When they are fresh and fully charged, flashlight batteries produce a
fixed voltage of approximately 1.5 V. This is true whether they are
the large D-cells (pictured below), or the smaller C-cells, AA-cells, or AAA-cells.
The main difference between the different sizes is how long they
will last before they need to be replaced or recharged.
If you’ve ever replaced the battery in a home smoke detector, you’ll recognize the batteries in the picture shown below. These provide a fixed voltage of approximately 9 V.
The following picture shows one of these batteries with its cover removed. It actually contains six smaller 1.5 V batteries, connected in such a way that their voltages add.
Most car batteries produce a fixed voltage of approximately 12 V.
Some batteries must be replaced when they become discharged, while other
batteries can be recharged and used again. The technical term for
non-rechargeable batteries is "primary batteries," while rechargeable
batteries are called "secondary batteries."
Solar cells (also called photovoltaic cells)
convert light energy into electrical energy. You’ve probably seen solar-powered
calculators that use solar cells instead of batteries.
Generators convert mechanical energy into electrical energy. The utility
company uses huge generators to create the electricity that is sent
to your home.
DC power supplies convert electrical energy from one form (ac electricity)
to another form (dc electricity). Recall from Unit 1 that the trainer
that we use in our labs has a built-in DC power supply that looks like
Actually, the trainer contains four different DC power supplies, all
of which are shown in the photo above.
It contains a fixed DC power supply that provides a constant voltage
of +5 V. To use this power supply, you would connect one wire to the
red terminal labeled "+5V" and one wire to the black terminal
It contains a fixed DC power supply that provides a constant voltage
of −5 V. To use this power supply, you would connect one wire
to the red terminal labeled "−5V" and one wire to the black
terminal labeled "GND."
It contains a variable DC power supply whose output you can adjust between
and +15 V. To use this power supply,
you would connect one wire to the red terminal labeled "0~+15V" and
one wire to the black terminal labeled "GND," and then adjust
the left-hand knob (labeled +V) to get the exact voltage that
It contains a variable DC power supply whose output you can adjust between
and −15 V. To use this power supply, you would connect one wire
to the red terminal labeled "0~−15V" and one wire to the
black terminal labeled "GND," and then adjust the right-hand
knob (labeled −V)
to get the exact voltage that you want.
Electrical current exists in a circuit or material when there is
a net transfer of charge through the circuit or material, from one
place to another.
For example, in a flashlight, when the switch is in the ON position,
electrons flow from the battery through the switch and light bulb,
and back again into the battery. This flow of electrons is what makes
the bulb light up. Depending on the strength
of the battery and the type of bulb, we may have many electrons flowing
(a large current), or just a few electrons flowing (a small current).
When the flashlight’s switch is in
the OFF position, no electrons can flow, so we have no current.
The symbol I is used to represent current.
Current is measured in amperes, or amps (abbreviated A).
For instance, to say that the current in a circuit is 5 amperes,
you would write I = 5 A.
Relating Current to Charge and Time
Mathematically, current is defined as therate at
which charge is transferred. In other words, it’s the amount of charge
that moves past a point in a unit of time:
I = Q ÷ t (Equation
where Q is the number of coulombs of charge that pass
a point in t seconds.
For example, if 20 coulombs of charge flow through a wire in 5 seconds,
then the current through the wire is 4 amperes.
If you find it easier to remember equations as words instead of
symbols, you can remember the equation above as
Current equals charge divided by time.
Using a little algebra, we can rearrange that equation to
solve it for charge. Multiplying both sides of the equation
by t gives us
Q = I × t
In words, this says that
Charge equals current multiplied by time.
Finally, we can rearrange that equation
once again to solve it for time. Dividing both sides of
the previous equation by I gives us
t = Q ÷ I
In words, this says that
Time equals charge divided by
Resistance is opposition to the flow of electrons. This may
sound like a bad thing, but in fact every circuit must contain some
resistance to operate correctly.
The symbol R is used to represent resistance.
Resistance is measured in ohms (abbreviated Ω).
The symbol Ω is a letter called "omega" from the
Example: To say that a component has a resistance of 250 ohms, you
would write R = 250 Ω.
A perfect conductor would have zero resistance and a perfect
insulator would have infinite resistance.
Conductance is thereciprocal of resistance. In other
words, it’s equal to 1 divided by resistance.
The symbol for conductance is G. So we can
write a simple equation that relates resistance and conductance:
G = 1 ÷ R
We can rearrange that equation to solve for the resistance R if
we know the conductance G:
R = 1 ÷ G
Since resistance and conductance are the reciprocal of each other,
when one gets larger, the other one gets smaller. For instance, a big
resistance has a small conductance, and a small resistance has a big
The unit of conductance is the the siemens, abbreviated S.
Example: A resistor with a resistance of 2.2 kΩ has a
conductance of approximately 455 µS.
Note: The siemens used to be called the mho (which is “ohm” spelled
backwards). You may still hear some old-timers using the term “mho” instead
As you learned in Unit 1, a resistor is
a component manufactured to have a specific amount of resistance.
Resistors have several common uses. Their most common use is limiting
current. Other uses include dividing voltage (you’ll learn about this
in a later course) and generating heat.
In Unit 2 you learned the color code used to identify the values
of resistors. For instance, you learned that a resistor labeled with
the color bands yellow-violet-red-gold is a 4.7 kΩ resistor with
a 5% tolerance.
The coding system that you learned is called the four-band
color code. This coding system is used for almost all of the
resistors in our labs. However, resistors
may instead be labeled with a five-band color code or with numeric
of color codes.
The resistors that we’ve dealt with so far, such as the one shown
below, are called fixed resistors. This means that their resistance
is set at a certain value and cannot easily be changed.
In some cases we want instead to use a variable
resistor, whose resistance can be changed, either by hand
The two most common kinds of variable resistors are called potentiometers and rheostats. These have knobs or some other way
for you to change the resistance by hand.
Two other kinds of variable resistors are thermistors and photoconductive
cells. A thermistor’s resistance changes automatically as its
temperature changes. A photoconductive cell’s resistance changes automatically
as the light intensity around it changes.
Apotentiometer is a type of variable resistor that
is widely used in a variety of electronic circuit applications. For
instance, the volume control on a car stereo may be a potentiometer.
As you turn the volume control,
you’re actually adjusting a variable resistor. This adjusts the amount
of current flowing to your stereo’s speakers, which in turn makes
the stereo louder or softer.
Here is the potentiometer’s schematic
symbol, which shows a resistor symbol with an arrow pointing to the
middle of the resistor.
As the symbol shows, a potentiometer is a three-terminal device.
The middle terminal (represented by the arrow) is called the wiper
terminal. Think of it as being able to move from end to end across
the resistor. You manually adjust the position of a potentiometer’s
wiper, either by turning a knob with your fingers or by turning a screw
head with a screwdriver.
The resistance between the two end terminals stays constant, but
the resistance between the wiper and either end terminal will change
as you adjust the potentiometer.
For example, suppose you have a 1 kΩ potentiometer. Then
the resistance between the two end terminals is always 1 kΩ,
no matter how you adjust the potentiometer. But the resistance between
the wiper and the end terminals will change. If the wiper is positioned
all the way at the left end of its range, then the resistance between
the wiper and the left end terminal will be 0 Ω;
and the resistance between the wiper and the right end terminal will
also be 1 kΩ.
If you now adjust the potentiometer by slowly moving the wiper to the
right, what will happen? The resistance between the wiper and the left
end terminal will increase, while at the same time the resistance
between the wiper and the right end terminal will decrease.
The trainer that you use in Sinclair’s labs has two built-in potentiometers, shown below. Terminals 1, 2, and 3 connect to a 1 kΩ potentiometer, which is adjusted by turning the left-hand knob. Terminals 4, 5, and 6 connect to a 100 kΩ potentiometer, which is adjusted by turning the right-hand knob.
A rheostat is an variable resistor that has only two
terminals. Its schematic symbol shows a resistor symbol with an arrow
drawn through it.
In this symbol, the two ends of the resistor symbol represent the
rheostat’s two end terminals. The end of the arrow does not represent
a third terminal, as it does in the case of the potentiometer.
Rather, the arrow is simply showing that this is a variable resistor
instead of a fixed resistor.
As with a potentiometer, you manually adjust a rheostat either by
turning a knob with your fingers or by turning a screw head with a
For example, suppose you have a 1 kΩ rheostat. Then
the resistance between the two end terminals varies between 0 Ω and
1 kΩ as you adjust the rheostat. If the knob or screw is
turned all the way to one end of its range, then the resistance
between the two rheostat terminals will be 0 Ω. If you now
adjust the rheostat by slowly turning the knob or screw, what will
happen? The resistance between the two terminals will gradually increase
up to 1 kΩ.
You can make a potentiometer behave like a rheostat
by connecting the potentiometer’s wiper to either of its end terminals.
(Remember, a potentiometer has three terminals, while a rheostat has
only two terminals. By connecting two of the potentiometer’s terminals
to each other, in effect we reduce the number of terminals from three
to two.) The diagram below shows a potentiometer configured as a rheostat.
The left-hand end serves as one of the rheostat’s terminals, and
the dot on the right-hand end serves as its other terminal.
Recall from Unit 1 that a digital multimeter (or DMM) is an instrument
that is used to measure voltage, current, or resistance. As a technician,
you’ll probably use a DMM more often than any other piece of
Sinclair’s labs are equipped with several types of DMM’s, including
the Fluke model 8050 shown below. In this week’s lab you’ll use this
multimeter to measure resistance, and in next week’s lab you’ll use
it to measure voltage and current.
Multimeter Challenge Game
You’ll need to become an expert at setting the controls on a digital
start learning this skill, take some time right now to play Multimeter
Challenge. In particular, work through the game’s "Study" section,
which is a tutorial containing several pages of notes to help you
identify and use the multimeter’s controls. This will be a good
preparation for using a real multimeter
to make measurements.
The number of significant digits in a number is the number
of digits used to express it, not counting any leading zeros. (Leading
zeros are zeros that appear to the left of the first non-zero digit.)
Example: 23.9 has three significant digits.
Example: 0.9640 has four significant digits. The leading zero
is not significant, but the 9, the 6, the 4, and the final 0 are
Example: 0.0602 has three significant digits. The two leading
zeroes are not significant, but the 6, the 0, and the 2 are significant.
How Many Digits Should You Write?
When making calculations in labs, on homework, or on tests, round
your answers to 3 significant digits.
When recording a measurement result from the multimeter, round
to 3 significant digits.
Rules for Rounding
When you round off a number, if the first digit that you’re
dropping is 0 through 4, do not round up the last digit that
Example: 53.247 rounded to three significant digits is 53.2.
We do not round up, since the first digit that we’re dropping is
If the first digit that you’re dropping is 5 through 9,
do round up the last digit that you record.
Example: 53.247 rounded to four significant digits is 53.25.
We do round up, since the first digit that we’re dropping is a
Unit 3 Review
This e-Lesson has covered several important topics, including:
conductors, insulators, and semiconductors
charge, voltage, current, and resistance
resistor coding systems
fixed versus variable resistors
significant digits and rounding.
To finish the e-Lesson, take this self-test to check your understanding
of these topics.
Congratulations! You’ve completed the e-Lesson for this unit.