Resistor

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.

• 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)

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.

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.

• Graphically:
• We can draw/sketch/diagram/plot the relationship.
• Mathematically:
• We can represent the relationship mathematically with anequation:
• V_r = I_r 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.