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Number Search Volume 3

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Over 150 fun family friendly challenging number search puzzles (with answer sheets). This volume focuses on random number words between 30000 thru 39999. Minimum of 40 number words per puzzle. Each puzzle is on its own page, which not only reduces crowding but also allows for larger word print sizes for easier reading. Answer sheets for each puzzle are provided in the back of the book. Fun for yourself and for the entire family. This makes for a great gift idea as well.

Electrical Resistance : Part 1

In this blog post I would like to explain the overall basics of what Electrical Resistance is and how it is made, as I currently understand it to be.


Most, if not all, metals are composed of atoms of minerals which are very tightly bound together, and those atoms arrange themselves into a crystalline lattice network structure formation very similar to that of normal crystals. This atomic formation structure becomes important when trying to understand why some materials are more conductive than others.

The directed movement of electrons is known as current flow. At the atomic level, electrons do not actually move freely through a conductor's crystalline structure as one might think. Some materials offer little opposition to current flow, while others greatly oppose current flow, but they all offer some amount of opposition. Just as there is no such thing as a perfect insulator, this is no such thing as a perfect conductor. This opposition to current flow is known as Resistance (R), and the unit of measure is the Ohm.

As a way to standardize the measurement of resistance throughout the world, it has been accepted world wide that the standard of measure for one ohm is said to be the resistance provided at zero degrees Celsius by a column of mercury having a cross-sectional area of one square millimeter and a length of 106.3 centimeters. A conductor is said to have one ohm of resistance whenever an applied potential of one volt produces a current flow of one ampere.

The symbol used to represent the ohm is the Greek letter omega (Ω)

Although resistance is an electrical property, it is determined by the physical structure of a material, which is governed by many of the same factors that control current flow.

Factors That Affect Resistance

The magnitude of resistance is determined in part by the quantity of free electrons that are available within the material. Since a decrease in the number of free electrons will decrease the current flow, it can be said that the opposition to current flow (resistance) is greater in a material with fewer free electrons. Therefore, the resistance of a material is determined by the number of free electrons available in a material.

The type of material, physical dimensions, and temperature will also play a role in affecting the resistance of a conductor.

Type Of Material

Depending upon the atomic structure of the atoms used in a material, different materials will have different quantities of free electrons. Therefore, the various conductors (made up of various materials) that are used in electrical applications will have different values of resistance.

For simple metallic substances, the atoms of such crystalline structured elements are so physically close together that the electrons in the outer shell (the Valence Shell) of an atom is often attracted to the nucleus of both its parent atom and its neighboring atoms. As a result, the force of attachment of an outer electron with an individual atom is practically zero. Depending on the metal, at least one electron, sometimes two, and in a few cases three electrons per atom exist in this state. In such a case, a relatively small amount of additional electron energy would easily free the outer electrons from the attraction of the nucleus of its parent atom. At normal room temperature materials of this type have many free electrons, resulting in that material to be considered a good conductor, since good conductors have a low resistance to electron current flow.

However, if the atoms of a material are spaced farther apart, the electrons in the outer shells of an atom will not be equally attached to several atoms as they orbit the nucleus of their parent atom, and therefore those outer electrons will only be attracted by and to the nucleus of that electrons parent atom. Because of this, a greater amount of energy is required to free any of those electrons. Materials of this type are poor conductors and offer a high resistance to electron current flow.

Silver, gold, and aluminum are good conductors. Therefore materials composed of their atoms would have a low (or lower) resistance.

The element known as Copper is the most widely accepted conductor used in electrical applications today, largely in part because Copper is less expensive. Silver has a lower resistance than copper but its higher cost limits usage to circuits where a high conductivity is demanded. Aluminum, which is considerably lighter than copper, is used as a conductor when weight is a major factor.

Effect Of Cross-Sectional Area

The Cross-sectional area of a material greatly affects the magnitude of resistance.

If the cross-sectional area of a conductor is increased, a greater quantity of electrons are available for movement through the conductor. Therefore, a larger current will flow for a given amount of applied voltage. An increase in current indicates that when the cross-sectional area of a conductor is increased, the resistance must have decreased.

If the cross-sectional area of a conductor is decreased, the number of available electrons decreases and, for a given applied voltage, the current through the conductor decreases. A decrease in current flow indicates that when the cross-sectional area of a conductor is decreased, the resistance must have increased.

This observation demonstrates that the resistance of a conductor is inversely proportional to its cross-sectional area.

The diameter of conductors used in electronics is often only a fraction of an inch, therefore, the diameter is expressed in mils (thousandths of an inch). It is also standard practice to assign the unit circular mil to the cross-sectional area of the conductor.

The circular mil is found by squaring the diameter, when the diameter is expressed in mils. For example, if the diameter is 35 mils (0.035 inch), the circular mil area is equal to 35^2, or 1225 circular mils.

Effect Of Conductor Length

The length of a conductor is also a factor which determines the resistance of a conductor.

If the length of a conductor is increased, the amount of energy given up increases. As free electrons move from atom to atom some energy is released and radiated in the form of heat. The longer a conductor is, the more energy is lost to heat. The additional energy loss subtracts from the energy being transferred through the conductor, resulting in a decrease in current flow for a given applied voltage. A decrease in current flow indicates an increase in resistance, since voltage was held constant. Therefore, if the length of a conductor is increased, the resistance increases.

The resistance of a conductor is directly proportional to its length.

Effect Of Temperature

The temperature changes of a material can affect the resistance of that material, and temperature changes can affect different materials in different ways. In some materials an increase in temperature causes an increase in resistance, whereas in other materials an increase in temperature causes a decrease in resistance.

The amount of change of resistance per unit change in temperature is known as the Temperature Coefficient.

For a material whose resistance increases with an increase in temperature, that material is said to have a Positive Temperature Coefficient.

For a material whose resistance decreases with an increase in temperature, that material is said to have a Negative Temperature Coefficient.

Most conductors used in electrical applications today (such as copper) have a positive temperature coefficient. However, carbon, which is becoming more popular, is a substance that has a negative temperature coefficient.

There also exists some other materials, such as the alloys known as constantan and manganin, are considered to have a Zero Temperature Coefficient because their resistance remains relatively constant for changes in temperature.

Continue with Electrical Resistance - Part 2

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