Resistors
There are many different types of electrical components. Shown below is a photograph of part of a circuit board. On this circuit board are many electrical components including some resistors.
There are resistors, capacitors, diodes and integrated circuits. Using plated copper and solder on the reverse side of the board, these components are interconnected and when a supply voltage is provided, these components can interact. Electrical engineers need to know how to design larger circuits like this and to control those interactions to achieve some purpose.
In this lesson you are going to learn about the simplest sort of electrical component, the resistor. What you learn about resistors is a starting point. That knowledge helps you as you begin to learn about all of the other kinds of electrical/electronic components. Still, although resistors are basic elements, they occur everywhere. On the board below, all of the resistors are marked with a yellow dot.
Goals
Almost every electrical product is constructed from a collection of fundamental electrical components. For example,
V = I R
While it is true that a piece of metal, like a wire for example, is a resistor of sorts, you need to know that today resistors are made with specific values, and they often take a common form. Typically they look like the one shown at the right - only they' be pretty small, maybe a half to three quarters of an inch long for the body.
All you have to do to measure a resistance is to connect your resistor to the ohmmeter as shown at the right, and be sure that the ohmmeter (or DVM or DAU) is set to measure resistance. Don't get uptight about which lead goes on which end of the resistor. It doesn't matter. (The resistor is a "bilateral" element and should be the same either way!)
R = rL/A
There are many different types of electrical components. Shown below is a photograph of part of a circuit board. On this circuit board are many electrical components including some resistors.
In this lesson you are going to learn about the simplest sort of electrical component, the resistor. What you learn about resistors is a starting point. That knowledge helps you as you begin to learn about all of the other kinds of electrical/electronic components. Still, although resistors are basic elements, they occur everywhere. On the board below, all of the resistors are marked with a yellow dot.
Goals
This lesson introduces you to some simple concepts about resistors and resistance. At the end of the lesson, you want to be able to do the following.
Given a common electrical device,
Know when the device is a resistor
Almost every electrical product is constructed from a collection of fundamental electrical components. For example,
- a radio,
- a portable tape player,
- a television,
- a telephone,
- a cellular phone,
- the electronic ignition in a car,
- a computer circuit board
- resistors,
- capacitors,
- inductors,
- transistors,
- microwave generating tubes,
- and many more.
The array of electrical components now available includes a vast and diverse number of components with varying shapes and numbers of leads. Here are some more electrical components you may be familiar with:
- light bulbs,
- computer chips,
- solar cells,
- inductors,
- heating elements on stoves,
- Light Emitting Diode (LED) displays on calculators,
- operational amplifiers,
- thermistors,
- and many others.
One way of categorizing the items on the previous page is that all of the items above produce heat as a by-product of their operation. Here are some more devices that produce heat when a voltage is applied - a stove heating element, a toaster and two light bulbs.
In fact, all of the items on the pictures above are resistors.
There are numerous places where resistors are used. Here are some places where resistors are used.
- Heating Applications:
- Home baseboard heaters
- Toasters
- Clothes Dryers
- Measurement Applications:
- Photoresistors to measure light intensity (Photgraphic light meters in a camera)
- Thermistors to measure temperature
- Strain gages to measure strain (Used in bathroom scales, measurements on bridges)
Resistors are ubiquitous today. They are literally everywhere, not only in electronic equipment but are they are in many of the ordinary devices we rely on like toasters, irons, stoves and light bulbs.
To really understand resistors you need to understand the law they obey - Ohm's Law - which gives a relationship between the current through a resistor and the voltage across the resistor. That's something you may not have considered yet. A resistor is a device that establishes a unique relationship between a current and a voltage.
The Genesis of Electrical Devices and Theories
Work on electrical devices all started with resistors and resistance. The concept of resistance was first enunciated by Georg Simon Ohm who was the first to point out that voltage and current in a wire were related mathematically. That's an important idea. Since Ohm's time many different devices have been discovered and generalizations of Ohms' Law are used to describe those devices.
Ohm found that mathematics could be applied to what was going on in resistors, and the mathematical relation he found was just the start of the application of mathematics to electrical phenomena.
The Application of Mathematics to Electrical Science
You are probably accustomed to the idea that physical phenomena can be described using the language of mathematics. That's an idea that wasn't always accepted, and when Ohm first proposed to describe electrical phenomena using mathematics he was taken to task vehemently. (That happened even though Newton had described mechanical phenomena mathematically two hundred years earlier, and had, in fact, invented calculus in order to do that!)
Ohm didn't even have the concepts of current and voltage to work with. He had to invent the concepts and then show that there was an experimental relationship between voltage and current, and that that relationship could be described mathematically.
It all sounds simple today, especially since we have nice clean concepts of voltage and current as we discussed in the first chapter. In Ohm's time, things were not so clear, and his discoveries really include clarification of the concepts of voltage and current as well as resistance.
Working with very primitive instruments that he designed and constructed himself, Ohm discovered that voltage and current were linearly related in wires. That means that if you measure voltage across a wire and plot that against the current through the wire you get a straight line in the plot.
Working with very imprecise measurements, Ohm was able to determine that voltage and current for any fixed geometrical structure built from conducting material satisfied a relationship:
where
- V is the voltage across the device,
- I is the current flowing through the device,
- R is a constant.
- R depends upon the material from which the device is constructed and the geometry of the material.
There are several different ways that Ohm's Law can be represented.
- Graphically:
- We can draw/sketch/diagram/plot the relationship.
- Mathematically:
- We can represent the relationship mathematically with anequation:
- Vr = Ir R
- Symbolically:
- We can devise a symbol for the resistor and use it in circuit diagrams to stand for any element that satisfies Ohm'sLaw. The standard symbol is shown below along with polarity definitions for the voltage and current.
We will use the symbol R for any resistor, although there will occasionaly be devices (like light bulbs) that are really resistors but which have a special symbol that can be used for them. Still, you can use this symbol for an resistive device.
Ohm's Law - Continued
Electrical engineers communicate with symbols. Circuit diagrams are abstract representations of real circuits and are composed of symbols for the various elements in the circuit. Here is the circuit symbol for a resistor.
The symbol for a resistor should include definitions for the voltage across the resistor and the current through the resistor. The definitions include:
- A symbolic name for the variable ( Vr for the voltage and Ir for the current for the symbol shown above).
- A definition of the polarity (Shown by "+" and "-" for the voltage and an arrow for the current).
Ohm's Law gives us a relationship between the voltage across a piece of conducting material (a resistor) and the current flowing through that resistor. Those two variables are represented algebraically with symbols, Vr for the voltage across the resistor, and Ir for the current flowing through the resistor.
It's important to remember that the voltage across the resistor, and the current through the resistor are related by Ohm's Law: Vr = RIr when the polarities are as shown below.
We need to be very precise when we consider Ohm's law because the polarities are very important.
- Ohm's law holds - that is Vr = RIr - only when the current is defined positive flowing into the terminal that is labelled positive for the voltage.
- We paraphrase that by saying that Ohm's law holds in the usual form whenever the arrow defining positive current flows into the "+" terminal (referring to voltage polarity definition).
Physical Resistors
While it is true that a piece of metal, like a wire for example, is a resistor of sorts, you need to know that today resistors are made with specific values, and they often take a common form. Typically they look like the one shown at the right - only they' be pretty small, maybe a half to three quarters of an inch long for the body.
A resistor is typically formed from some sort of resistive material and put into a cylindrical form. Usually the resistor will have a brownish body with several stripes painted on the resistor body. Those stripes are in a code that will tell you the value of the resistors (in ohms). Here's what's important.
The resistor shown above is 1000 ohms = 10x102
Notice how cleverly we put certain parts of the result in bold text and colored it. The bolded text corresponds to the stripes, and the colors are shown on the bold text. Here is the color code.
| 0 | Black | Black |
| 1 | Brown | Brown |
| 2 | Red | Red |
| 3 | Orange | Orange |
| 4 | Yellow | Yellow |
| 5 | Green | Green |
| 6 | Blue | Blue |
| 7 | Violet | Violet |
| 8 | Gray | Gray |
| 9 | White | White |
Given a resistor, to calculate the value of the resistance you use the three stripes. (If there are four stripes, just use the first three. The last stripe tells you how accurate the resistance value is.) Here is the algorithm.
- The first stripe is the most significant digit, X, in XY x 10Z.
- The second stripe is the next digit, Y, in XY x 10Z.
- The third stripe is the exponent in XY x 10Z.
Here is an example/problem.
In this section you'll learn a little about how to measure resistances. You'll need to have an ohmmeter, a digital multimeter or a data acquisition unit. When you use any of those instruments to measure a resistance, the same thing happens. It's just that a digital multimeter can make voltage and current measurements, while a data acquisition unit can measure frequency and temperatures.
We'll also assume that you're in a lab running these lessons and that you have a lab notebook that you are using. (You should always have a lab notebook for lab work!)
An ohmmeter measures resistance, and gives you a value of the measured resistance in ohms, kilohms or megohms. Many ohmmeters look like the following diagram.
There's an internal source that provides a voltage. That source may be a battery or a small power supply. The source drives a voltage divider - two resistors in series. One of those resistors is internal to the meter, and the other resistor is the resistor being measured. An internal meter measures the voltage across the resistance being measured and converts that voltage into a resistance reading. The resistance being measured is connected to the ohmmeter terminals, and the terminals are often colored black and red.
All you have to do to measure a resistance is to connect your resistor to the ohmmeter as shown at the right, and be sure that the ohmmeter (or DVM or DAU) is set to measure resistance. Don't get uptight about which lead goes on which end of the resistor. It doesn't matter. (The resistor is a "bilateral" element and should be the same either way!)
Here's the way you connect the ohmmeter (or digital voltmeter or data acquisition unit) to the resistor. Here we're using the same resistor as was used in the questions above. The ohmmeter shown here includes all of the circuitry shown above including a power supply or battery and an internal resistance. To measure the resistance it applies a small voltage across the resistance.
At this point, you are ready to start the first laboratory exercise on resistors. Click here to go to that lab problem.
The resistance of a resistor is determined by several physical properties of the resistor. We're going to limit ourselves to resistors that have a constant cross section - like a wire. Here are the properties.
- The geometry of the conductor, including:
- The length, L
- The cross-sectional area, A
- A constant of the material called the resistivity, r.
If you have those quantities, then the resistance is given by:
You may be tempted to conclude that there are no serious "What If?" questions for resistors. Actually, there are many questions about these devices. Note the following characteristics of resistors.
- Resistors have voltage directly proportional to the current. That's true at every instant of time and for every frequency. Is it possible to have a situation in which voltage and current are not proportional?
- In diodes - and many other devices, current and voltage are nonlinearly related. There are many devices in which the relationship is not proportional or linear.
- The voltage across a resistor and the current through the resistor depend upon the values at the same time. Is it possible to have other kinds of relationships?
- In a capacitor, we have i(t) = Cdv(t)/dt.
- In an inductor, we have v(t) = Ldi(t)/dt.
- Capacitors and inductors have voltage and current related to derivatives! That's really a different situation because it means you have to learn how to solve differential equations ot predict behavior of circuits with these components. That's a whole new kettle of fish.
- A resistor is a two-terminal device. Transistors have three terminals. That means that the analysis is much more complicated.
And, if Ohm hadn't discovered his famous law - and lost his job and been blackballed for ten years - you wouldn't be reading this now.
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