Chapter 18

Electric Currents

Objectives: The students will be able to:

• Describe what resistivity depends on.

• Solve problems relating to resistivity.

Electrical ResistanceWhen electric current flows through a metal wire there exists a hindrance to the flow, known as electrical resistance.

This is because as the electrons move through they will collide with the atoms of the conductor.

The SI unit of resistance is the ohm (Ω), after Georg Simon Ohm (1787-1854), a German physicist, who discovered Ohm’s law.

A resistor is a material that provides a specified resistance in an electric circuit.

18.4 Resistivity

The resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area:

(18-3)

The constant ρ, the resistivity, is characteristic of the material.

Resistance,R and Resistivity,ρ

The resistance of a conductor is directly proportional to the length since the current needs to pass through all the atoms in the length.

The resistance is inversely proportional to the cross-sectional area since there is more room for the current to pass through.

The above observations can be combined and the resistance, R of the conductor is written as follows,

.A

LR

Resistance

• Depends on type of material, size and shape, temperature.

R=ρ L

A

L: length of the wire

A: cross-sectional area

ρ: resistivity (inherent to material)

18.4 Resistivity

Example:

• What happens to the resistance when the length is doubled and the area is quadrupled?

• Answer: It changes by 1/2

Factors Affecting Factors Affecting ResistanceResistance

1. The 1. The length Llength L of the material. Longer of the material. Longer materials have greater resistance.materials have greater resistance.

1 1

LL

2 2

2L2L

2. The cross-sectional 2. The cross-sectional area Aarea A of the of the material. Larger areas offer material. Larger areas offer LESSLESS resistance.resistance.

2 2 AA

1 1

22AA

Factors Affecting R (Cont.)Factors Affecting R (Cont.)3. The 3. The temperature Ttemperature T of the material. of the material.

The higher temperatures usually The higher temperatures usually result in result in higherhigher resistances. resistances.

4. The kind of 4. The kind of materialmaterial. Iron has more . Iron has more electrical resistance than a electrical resistance than a geometrically similar copper geometrically similar copper conductor.conductor.

RRoo

R > RR > Roo

RRii > R > RccCopperCopper IronIron

ExampleExample What What lengthlength LL of of copper wire is required to copper wire is required to produce a produce a 4 m4 m resistor? resistor? Assume the diameter of the Assume the diameter of the wire is wire is 1 mm 1 mm and that the and that the resistivity resistivity of copper is of copper is 1.72 x 1.72 x 1010-8 -8 ..mm ..

ExampleExample What What lengthlength LL of copper wire is of copper wire is required to produce a required to produce a 4 m4 m resistor? resistor? Assume the diameter of the wire is Assume the diameter of the wire is 1 1 mm mm and that the resistivity and that the resistivity of copper is of copper is 1.72 x 101.72 x 10-8 -8 ..mm ..

2 2(0.001 m)

4 4

DA

AA = 7.85 x 10 = 7.85 x 10-7-7 m m22

LR

AL

RA

-7 2

-8

(0.004 )(7.85 x 10 m )

1.72 x 10 m

RAL

L = 0.183 mRequired length is:Required length is:

Period 1 stopped here.

18.4 Resistivity

For any given material, the resistivity increases with temperature:

(18-4)

Semiconductors are complex materials, and may have resistivities that decrease with temperature.

Multiply the above equation by L/A; so using Equation 18-3 you can get the next equation onnext slide.

Temperature coefficient is α

Solve this equation to get….

Temperature CoefficientTemperature CoefficientFor most materials, the resistance For most materials, the resistance RR changes in proportion to the initial changes in proportion to the initial resistance resistance Ro and to the change in and to the change in temperature temperature tt..

0R R t 0R R t Change in Change in resistance:resistance:

The The temperature coefficient of temperature coefficient of resistance, resistance, is the change in resistance is the change in resistance per unit resistance per unit degree per unit resistance per unit degree change of temperature.change of temperature.

00

1; Units:

C

R

R t

00

1; Units:

C

R

R t

ExampleExample The resistance of a copper wire The resistance of a copper wire is is 4.00 m4.00 m at at 202000CC. What will be its . What will be its resistance if heated to resistance if heated to 808000CC? Assume ? Assume that that = 0.004 /C= 0.004 /Coo..

ExampleExample The resistance of a copper The resistance of a copper wire is wire is 4.00 m4.00 m at at 202000CC. What will be its . What will be its resistance if heated to resistance if heated to 808000CC? Assume ? Assume that that = 0.004 /C= 0.004 /Coo..

0 00 ; (0.004 / C )(4 m )(60 C )R R t R

RRoo = 4.00 m = 4.00 mt = 80t = 80ooC – 20C – 20ooC = 60 C = 60

CCoo

R = 1.03 mR = 1.03 m R = RR = Roo + + RR

R = R = 4.00 m4.00 m + 1.03 mm

R = 5.03 mR = 5.03 m

HomeworkHomework

Chapter 18 Problems#12, 13, 21

Note: for Cu use 3 x 10-5

Closure:Closure:

Kahoot 18-4Kahoot 18-4