### Table of Contents

# Introduction

This is part 2 of the circuit design tutorial. This tutorial will focus on resistance. It will explain what resistance is and how to measure a materials resistance. Furthermore, it will explain how temperature affects the resistance of a material. Also, it will describe how to read the color code of resistors and a brief description of different types of resistors. Finally, it will describe conductance and how it relates to resistance. After reading this tutorial, one should have a good understanding of what is resistance.

# Resistance

As electron flow through a material it encounters opposition. The electron collides with one another and other atoms which converts the energy to heat, thus energy is lost. This is known as resistance. Another way to think about resistance is to think back to water hose example in the previous tutorial. Let’s say some rocks got into the hose and restrict the water flowing from the hose. This is acting like a resistance to the water flow.

# Measuring Resistance

The resistance of a material that has a uniform cross-sectional area is dictated by four factors: Kind of material, length, cross-sectional area and temperature. Resistance is proportional to the kind of material and its length, and inversely proportional to its area. Furthermore, as the temperature of a material increases the resistances of the most material increases. The following equation can be used to measure resistance of a material. We will assume that the temperature of the material is held constant at room temperature (20 C).

R = p (l/A) R = resistance in ohms P = resistivity of the material at 20 C L = length in feet A = cross-sectional area in circular mils (CM)

Circular Mills is not measured in square meters or square inches but whether it is measure by the area of a circle in thousandths of an inch.

The area of a circle is πr2 = πd2/2 1 in. = 1000 mils Using these two equation one can get an equation between square mils and circular mils which is 1 CM = π/4 square mills

For a wire with a diameter of N mils

A = πd2 = πN2/4 sq. mils Substituting the fact that 4/π CM= 1 sq mils, one gets A cm = (Dmils)2

Table of resistivity of some common materials

------------------------------------------------------------------- Materials p @ 20C ------------------------------------------------------------------- Silver 9.9 Copper 10.37 Gold 14.7 Aluminum 17.0 Tungsten 33.0 Nickel 47.0 Iron 74.0 -------------------------------------------------------------------

Example Problem

’ What is the resistance of a thousand feet of length of copper wire that has the diameter of 0.020 in. at the temperature of 20 C? P= = 10.37 0.020 in = 20 mils Acm = (Dmils)2 = (20)2 = 400 R = p(l/A) = (10.37)(1000)/400 = 25.9 Ω

# Temperature Effects

Due to the increase in moment of molecular when temperature increase, most conductors will increase in resistances. This is due to the electrons having an increase chance of bumping into other atoms or electrons. Note, semiconductors have the opposite affects; increase in temperature will result in a decrease in resistance. We will not worry about that at the moment as I will go over that in later tutorial. Since temperature does affect the resistance of material, it is important that one have some method of determining resistance of a material at any temperature. Most material will have a near linear relationship between resistance and temperature over the operating range of the material. The linear relationship does break down at extreme cold or heat but we will only worry about the range of temperature where the material will have a linear relationship between temperature and resistance. Since, at the present we will be working with the linear part of the temperature versus resistance data set, one can use the equation for a line from basic algebra y=mx+b to describe how temperature affects resistance. Basically we need the slope or temperature coefficient to determine resistance at different temperatures. Table of temperature coefficient of some common materials at 20 C is listed below.

--------------------------------------------------------------------- Material Temp. Coefficient ᾳ at 20 C -------------------------------------------------------------------- Silver 0.038 Copper 0.00393 Gold 0.0034 Aluminum 0.00391 Tungsten 0.005 Nickel 0.006 Iron 0.0055 ------------------------------------------------------------------

The equation to determine the resistance value of a resistor at a certain temperature is listed below.

R2 = R1[1 + ᾳ(t2 - t1)] R1 = initial resistance ᾳ = temperature coefficient t1 = initial temperature of the resistor t2 = the second temperature

Example Problem

What is the resistance of aluminum wire at 100 C, if it is 75 Ω at 20 C? R2 = R1[1 + ᾳ(t2 - t1)] = 75[1+0.00391(100-20)] R2 = 75[1+0.0391(80)]= 75[1.3128] R2 = 98.46 Ω

# Types of Resistors

There are many types of resistors but I will only go through a few of them in this tutorial. The two main groups of resistors are fixed and variable. A fix resistor has a fix resistance value whereas a variable resistor can be adjusted to a range of resistance values. The symbols of a fixed resistor are shown below.

**Fixed resistor**

# Color Coding of Resistors

Standard resistor has a color code that defines what its resistance is. They will have four color bands on the resistor and are always read from left to right when determining the resistance. The color of a band will represent a numeric value. The first and second bands will represent the first and second digit of the resistance value respectfully. The third band will be a multiple factor which the first and second digital will multiple against to get is resistance value. The forth band will represent the value of manufacturer tolerance or the range of error the resistance might be off from the actually value. For example, it the first three bands tell a person that the resistance value is 100 Ω and the forth band is silver (which stands for 10%), it would mean that the actually resistance is in the range of plus or minus 10% of the 100 Ω value. Or other words the actually resistance value will be between 90 Ω and 110 Ω. The color coding chart is shown below.

----------------------------------------------------- Color (first 3 bands) Numeric Value ---------------------------------------------------- Black 0 Brown 1 Red 2 Orange 3 Yellow 4 Green 5 Blue 6 Violet 7 Gray 8 White 9 Gold 0.1 *only used in the third band Silver 0.01 *only used in the third band -------------------------------------------------- Color (forth band) Tolerance ------------------------------------------------- Gold 5% Silver 10%

Example Problem

What are the resistance and the tolerance level of a resistor that has the following bands: first band is red, the second band is black, the third band is orange and the last band is Gold. 1st band 2nd band 3rd band 4th band --------------------------------------------------------------------------------------- red black orange gold 2 0 x3 5% R = 20000 Ω with 5% tolerance = 20 kΩ with 5% tolerance

# Conductance

Conductance is how well the material conducts electricity. The conductance of a material is measured by taking the reciprocal of the resistance. Conductance is measured in mhos with the symbol of inverted omega Ʊ. The letter symbol is G. The following is the equation form for conductance.

G = 1/R mhos G = A/(pl) mhos

Example Problems

What is the conductance of a resistor with the following color bands: 1st band is blue, the 2nd band is red, the 3rd band is red and the last band is silver. 1st band 2nd band 3rd band 4th band ------------------------------------------------------------------------------ 6 2 X2 10% R = 6200 Ω = 6.2 KΩ with a 10% tolerance G = 1/R = 1.613 X 10 -4 mhos with a 10% tolerance

# Conclusion

This goal of this tutorial is to give the basic knowledge of resistance and conductance. The first part of the tutor explains resistance and how to measure it. The second part describes how temperature affects the resistance of a material. The next part showed how to read the resistance of a resistor color code. Lastly, the tutor discusses how conductance is related to resistance. The next tutorial will be explaining Ohm’s Law. Resistance is a key concept in understanding circuit design.