Transcript 18-4_Resistivity - mrhsluniewskiscience

Chapter 18
Electric Currents
Objectives: The students will be able to:
• Describe what resistivity depends on.
• Solve problems relating to resistivity.
Electrical Resistance
When 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,
L
R .
A
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 Resistance
1. The length L of the material. Longer
materials have greater resistance.
L
2L
1W
2W
2. The cross-sectional area A of the material.
Larger areas offer LESS resistance.
2A
A
2W
1W
Factors Affecting R (Cont.)
3. The temperature T of the material. The
higher temperatures usually result in
higher resistances.
R > Ro
Ro
4. The kind of material. Iron has more
electrical resistance than a geometrically
similar copper conductor.
Copper
Iron
Ri > R c
Example What length L of copper
wire is required to produce a 4 mW
resistor? Assume the diameter of
the wire is 1 mm and that the
resistivity  of copper is 1.72 x 10-8
W.m .
Example What length L of copper wire is
required to produce a 4 mW resistor? Assume
the diameter of the wire is 1 mm and that the
resistivity  of copper is 1.72 x 10-8 W.m .
A
D
2
4
L
R
A

 (0.001 m)
2
4
A = 7.85 x 10-7 m2
RA (0.004 W)(7.85 x 10-7 m2 )
L

-8

1.72 x 10 W m
Required length is:
Period 1 stopped here.
L = 0.183 m
18.4 Resistivity
For any given material, the resistivity
increases with temperature:
(18-4)
Temperature coefficient is α
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 on
next slide.
Solve this equation to get….
Temperature Coefficient
For most materials, the resistance R changes
in proportion to the initial resistance Ro and
to the change in temperature Dt.
Change in
resistance:
DR   R0 Dt
The temperature coefficient of resistance,  is
the change in resistance per unit resistance
per unit degree change of temperature.
DR

;
R0 Dt
1
Units: 0
C
Example The resistance of a copper wire is
4.00 mW at 200C. What will be its resistance if
heated to 800C? Assume that  = 0.004 /Co.
Example The resistance of a copper wire is
4.00 mW at 200C. What will be its resistance if
heated to 800C? Assume that  = 0.004 /Co.
Ro = 4.00 mW; Dt = 80oC – 20oC = 60 Co
DR   R0 Dt; DR  (0.004 / C )(4 mW)(60 C )
0
DR = 1.03 mW
R = Ro + D R
R = 4.00 mW + 1.03 mW
R = 5.03 mW
0
Homework
Chapter 18 Problems
#12, 13, 21
Note: for Cu use 3 x 10-5
Closure:
Kahoot 18-4