Why Do You Need To Know About Resistors?You are at: Elements  Resistors  ResistorsOhm's Law  What You Need To Know About Resistors.Measuring ResistanceWhat If QuestionsProblems
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.
P1. How
many resistors do you see on this board?
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
Given a resistorBe able to use Ohm's Law to compute resistance when voltage and current are given,
Be able to use Ohm's Law to compute voltage when resistance and current are given,
Be able to use Ohm's Law to compute current when voltage and resistance are given.
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:
One way of categorizing the items on the previous page is that all of the items above produce heat as a byproduct 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.
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 TheoriesWork 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 ScienceYou 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:
V = I R
where
P3. You
have an electrical device. You notice that when 5 volts is applied
across the device, that 10 milliamps flows through the device. What
is the resistance of the device?
P4. Next, you apply 10 volts across the device and 50 milliamps flows through the device. What do you conclude?
P5. The
data below are all taken from measurements of the same resistor.
What is the value of the resistance?










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:
It's important to remember that the voltage across the resistor, and the current through the resistor are related by Ohm's Law: V_{r} = RI_{r} 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.
Q11. Which is the correct expression for Ohm's law when polarities are defined as shown below?
Q12. Which is the correct expression for Ohm's law when polarities are defined as shown below?
Q13. Which is the correct expression for Ohm's law when polarities are defined as shown below?
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 = 10x10^{2}
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.
P6. For the resistor at the right answer the following questions. Note, for this problem, if you do not get a grade of 100 you answered incorrectly. Now, what is the first digit on the resistor's set of stripes? Enter your answer in the box below, then click the button to submit your answer.
P7. What is the second digit on the resistor's set of stripes? Enter your answer in the box below, then click the button to submit your answer.
P8. What is the third digit on the resistor's set of stripes  the power of ten stripe? Enter your answer in the box below, then click the button to submit your answer.
P9. And, what is the value of the resistor? Enter your answer in the box below, then click the button to submit your answer.
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.
R = rL/A
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.