 # Unit 3. Voltage, Current, & Resistance

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 digits.

##### Schematic Symbols
• When discussing circuits, we often draw diagrams representing those circuits.
• 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 together.
• 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 together. • 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, we would 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 central nucleus 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 negative charge.
##### Conductors
• 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.
##### Insulators
• 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 an insulator.
• Some examples of insulators are plastics, ceramics, rubber, paper, wood, and most liquids and gases.
##### Semiconductors
• A special class of materials called semiconductors have fewer free electrons than conductors, but more free electrons than insulators.
• 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.
• ##### Charge
• 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 symbol V is used to represent a voltage.
• 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.
##### Voltage Sources
• A device that provides the force needed to move electrons is called a voltage source.
• 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 this: • Actually, the trainer contains four different DC power supplies, all of which are shown in the photo above.
1. 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."
2. 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."
3. It contains a variable DC power supply whose output you can adjust between 0 V 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 you want.
4. It contains a variable DC power supply whose output you can adjust between 0 V 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.
• • ##### Current
• 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 the rate 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 2-3)

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 current.

• ##### Resistance
• 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 Greek alphabet.
• 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
• Conductance is the reciprocal 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 conductance.
• 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 of "siemens".
• ##### Resistors
• 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.
##### Resistor Codes
• 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 labels instead of color codes.
##### Variable Resistors
• 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 or automatically.
• 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.
##### Potentiometers
• A potentiometer 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. • • ##### Rheostats
• 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 screwdriver.
• 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. • • ##### Digital Multimeter
• 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 equipment.
• 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 multimeter.
• To 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.

##### Significant Digits
• 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 significant.
• 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 you record.
• 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 a 4.
• 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 7.
• ##### 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.