Figure 1: Equipment for Electricity balance copper wire glass rod heater wire multimeter ohmmeter power supply resistors ruler wire cutters 
Electricity
After the exploration of a mechanicalmechanical energy conversion in the last lesson and covering energy conversion in some form in each of the last three lessons, the general idea of energy conversion should be familiar to you. For much of what we do with energy in our homes, we start with electricity and convert it to other forms of energy.
In this lesson we will begin our discussion of electricity itself. In the simplest microscope model of conduction in a metal, each atom in the crystal lattice gives up one or more of its outer electrons. These electrons are then free to move through the crystal lattice, colliding with stationary positive ions. If there is no electric field, the electrons move in straight lines between collisions, the direction of their velocities is random, and on average they never get anywhere. But if an electric field is present, the paths curve slightly because of the acceleration caused by electric field forces (see the description in the handout).
Objectives [At the end of this lesson students will be able to...]
Startup questions
Electricity and Ohm's Law
You have almost certainly encountered ohm's law at some point in your life. Do you recall what it says? It is one equation that relates three terms, and can be written in three equivalent ways:
V=IR or I=V/R or R=V/I
Can we use a normal resistor to verify ohm’s law? We will certainly try. We will pass current through a resistor and measure all three terms.
Voltage across the resistor =
Current through the resistor =
Resistance value =
What happens to the resistor when I pass current through it?
Now we will discuss the factors that contribute to the resistance of a long wire. These are the diameter, length and the material that make up the wire. The diameter and length are extrinsic properties because they can be changed, while the material that makes up the wire itself has intrinsic properties.
There are four terms used in describing how these factors contribute to the resistance of a wire. They are electrical conductivity, electrical resistivity, electrical conductance and electrical resistance.
r (resistivity, unit of W·m) (This is independent of shape, intrinsic property)
s (conductivity, unit of 1/W·m) (this is independent of shape also, intrinsic)
R (resistance, unit of W) = V/I = r (L/A) (depends on shape, extrinsic)
C (conductance, unit of mho) = 1/R (depends on shape, extrinsic)
Among the description of these relationships above was a geometric connection between resistivity and resistance:
R = r (L/A)
This is an important point. It reveals the direct relationship between resistivity and resistance, so that for two "wires" of equal dimensions, the difference in resistance will be determined completely by the intrinsic resistivities of the materials making up the two wires. This will be illustrated later with two different materials, copper and glass.
Let's look at the resistance found in wires that deliver electricity to our homes. Copper is usually used for wiring in houses. Using the following chart, compare the resistance (R) and conductance (1/R) of copper with steel, aluminum, glass, and wood. Glass has a very high resistance and therefore is used as an insulator.
Resistivities at Room Temperature
Metal 
r (W·m) 
Substance 
r (W·m)  
Silver 
1.47×10^{8} 
Pure Carbon 
3.5×10^{5} 

Copper 
1.72×10^{8} 
Amber 
5×10^{14} 

Gold 
2.44×10^{8} 
Glass 
10^{10}  10^{14} 

Aluminum 
2.63×10^{8} 
Lucite 
>10^{13} 

Steel 
20×10^{8} 
Mica 
10^{11}  10^{15} 

Lead 
22×10^{8} 
Quartz 
75×10^{16} 

Mercury 
95×10^{8} 
Sulfur 
10^{15} 

Teflon 
>10^{13} 

Wood 
10^{8}  10^{11} 
We will illustrate the concept of resistivity and resistance through the use of wires of different composition and size. We will use copper and glass to illustrate the effect of resistivity, and measure the resistivity of two different materials in class.
Material 1:
Length =
Cross sectional area =
Electrical current =
Voltage drop =
Resistance =
Resistivity =
Material 2:
Length =
Cross sectional area =
Electrical current =
Voltage drop =
Resistance =
Resistivity =
Any change in physical condition may give a body a new resistance different from its previous value. Impurities, change in temperature, changes in hardness, and mechanical strains affect this. The relationship between resistance and temperature is shown in the following formula:
R = R_{o}(1 + aT)
where R_{o} = resistance at 0°C
R = resistance at T°C
a = constant for the material
T = temperature in °C
Is there a temperature dependence for resistivity? In an ideal crystal lattice with no atoms out of place, a correct quantummechanical analysis would let the free electrons move through the lattice with no collisions at all. But the atoms vibrate about their equilibrium positions. As temperature increases the amplitude of these vibrations increase, and collisions become more frequent. Therefore resistivity of a metal increases with temperature.
Assessment questions