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Lesson 1: Electric Potential Difference

Electric Field and the Movement of Charge

Electric Potential

Electric Potential Difference

 

Lesson 2: Electric Current

What is an Electric Circuit?

Requirements of a Circuit

Electric Current

Power: Putting Charges to Work

Common Misconceptions Regarding Electric Circuits

 

Lesson 3: Electrical Resistance

Journey of a Typical Electron

Resistance

Ohm's Law

Power Revisited

 

Lesson 4: Circuit Connections

Circuit Symbols and Circuit Diagrams

Two Types of Connections

Series Circuits

Parallel Circuits

Combination Circuits

 

Lesson 3: Electrical Resistance

Resistance

An electron traveling through the wires and loads of the external circuit encounters resistance. Resistance is the hindrance to the flow of charge. For an electron, the journey from terminal to terminal is not a direct route. Rather, it is a zigzag path which results from countless collisions with fixed atoms within the conducting material. The electrons encounter resistance - a hindrance to their movement. While the electric potential difference established between the two terminals encourages the movement of charge, it is resistance which discourages it. The rate at which charge flows from terminal to terminal is the result of the combined affect of these two quantities.

 

Variables Affecting Electrical Resistance

The flow of charge through wires is often compared to the flow of water through pipes. The resistance to the flow of charge in an electric circuit is analogous to the frictional affects between water and the pipe surfaces as well as the resistance offered by obstacles which are present in its path. It is this resistance which hinders the water flow and reduces both its flow rate and its drift speed. Like the resistance to water flow, the total amount of resistance to charge flow within a wire of an electric circuit is affected by some clearly identifiable variables.

First, the total length of the wires will affect the amount of resistance. The longer the wire, the more resistance that there will be. There is a direct relationship between the amount of resistance encountered by charge and the length of wire it must traverse. After all, if resistance occurs as the result of collisions between charge carriers and the atoms of the wire, then there is likely to be more collisions in a longer wire. More collisions means more resistance.

Second, the cross-sectional area of the wires will affect the amount of resistance. Wider wires have a greater cross-sectional area. Water will flow through a wider pipe at a higher rate than it will flow through a narrow pipe. This can be attributed to the lower amount of resistance which is present in the wider pipe. In the same manner, the wider the wire, the less resistance that there will be to the flow of electric charge. When all other variables are the same, charge will flow at higher rates through wider wires with greater cross-sectional areas than through thinner wires.

A third variable which is known to affect the resistance to charge flow is the material that a wire is made of. Not all materials are created equal in terms of their conductive ability. Some materials are better conductors than others and offer less resistance to the flow of charge. Silver is one of the best conductors but is never used in wires of household circuits due to its cost. Copper and aluminum are among the least expensive materials with suitable conducting ability to permit their use in wires of household circuits. The conducting ability of a material is often indicated by its resistivity. The resistivity of a material is dependent upon the material's electronic structure and its temperature. For most (but not all) materials, resistivity increases with increasing temperature. The table below lists resistivity values for various materials at temperatures of 20 degrees Celsius.

Material

Resistivity

(ohm•meter)

Silver

1.59 x 10-8

Copper

1.7 x 10-8

Gold

2.4 x 10-8

Aluminum

2.8 x 10-8

Tungsten

5.6 x 10-8

Iron

10 x 10-8

Platinum

11 x 10-8

Lead

22 x 10-8

Nichrome

150 x 10-8

Carbon

3.5 x 105

Polystyrene

107 - 1011

Polyethylene

108 - 109

Glass

1010 - 1014

Hard Rubber

1013

As seen in the table, there is a broad range of resistivity values for various materials. Those materials with lower resistivities offer less resistance to the flow of charge; they are better conductors. The materials shown in the last five rows of the above table have such high resistivity that they would not even be considered to be conductors.

 

 

Mathematical Nature of Resistance

Resistance is a numerical quantity which can be measured and expressed mathematically. The standard metric unit for resistance is the ohm, represented by the Greek letter omega - . An electrical device having a resistance of 5 ohms would be represented as R = 5 . The equation representing the dependency of the resistance (R) of a cylindrically shaped conductor (e.g., a wire) upon the variables which affect it is

where L represents the length of the wire (in meters), A represents the cross-sectional area of the wire (in meters2), and represents the resistivity of the material (in ohm•meter). Consistent with the discussion above, this equation shows that the resistance of a wire is directly proportional to the length of the wire and inversely proportional to the cross-sectional area of the wire. As shown by the equation, knowing the length, cross-sectional area and the material that a wire is made of (and thus, its resistivity) allows one to determine the resistance of the wire.

 

 

Check Your Understanding

 

1. Household circuits are often wired with two different widths of wires: 12-gauge and 14-gauge. The 12-gauge wire has a diameter of 1/12 inch while the 14-gauge wire has a diameter of 1/14 inch. Thus, 12-gauge wire has a wider cross section than 14-gauge wire. A 20-Amp circuit used for wall receptacles should be wired using 12-gauge wire and a 15-Amp circuit used for lighting and fan circuits should be wired using 14-gauge wire. Explain the physics behind such an electrical code.

 

 

 

2. Based on the information stated in the above question, explain the risk involved in using 14-gauge wire in a circuit that will be used to power an 16-ampere power saw.

 

 

 

3. Determine the resistance of a 1-mile length of 12-gauge copper wire. Given: 1 mile = 1609 meters and diameter = 0.2117 cm.

 

 

 

4. Two wires - A and B - with circular cross-sections have identical lengths and are made of the same material. Yet, wire A has four times the resistance of wire B. How many times greater is the diameter of wire B than wire A?

 

 

 

 

Lesson 3: Electrical Resistance

 

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