The Line of Resistance

1
The Line of Resistance

• APS Teachers Day Workshop
• Los Angeles, CA
• March 22, 2005
• Dr. Larry Woolf
• General Atomics
• Larry.Woolf_at_gat.com
• www.sci-ed-ga.org (click on Presentations to see
  all these slides)

2
Multimeter Operation

• Work with your group
• With leads together, R 0
• With leads not touching, R open

3
Draw a line using the graphite pencil and measure
its resistance

• Is the resistance measurement reproducible? Why
  or why not?
• How could you optimize the line shape and the
  measurement technique to make the measurement
  more reproducible?

4
Design an experiment to determine how the
resistance varies with length

• Discuss possible ways to do this with your group

5
Perform an experiment to determine how the
resistance varies with length

• Discuss your data with your group
• What model supports your data?

6
How does resistance vary with length?

• Write an equation that reflects this variation

7
R L
8
Design an experiment to determine the total
resistance of 2 resistors in series

• Discuss possible ways to do this with your group

9
Perform an experiment to determine the total
resistance of 2 resistors in series

• Discuss your data with your group
• What model supports your data?

10
What is the total resistance of 2 resistors in
series?

• Write an equation that describes this relationship

11
RT R1 R2
12
Predict the resistance - if you double the
length of a resistorand - for 2 equal resistors
in series
13
Single resistor R that doubles L RT ? 2R 2
equal resistors R in series RT ? 2R
14
Design an experiment to determine how the
resistance varies with width

• Discuss possible ways to do this with your group

15
Perform an experiment to determine how the
resistance varies with width

• Discuss your data with your group
• What model supports your data?

16
How does resistance vary with width?

• Write an equation that reflects this variation

17
R 1/Wor1/R W
18
Design an experiment to determine the total
resistance of 2 resistors in parallel

• Discuss possible ways to do this with your group

19
Perform an experiment to determine the total
resistance of 2 resistors in parallel

• Discuss your data with your group
• What model supports your data?

20
What is the total resistance of 2 resistors in
parallel?

• Write an equation that describes this
  relationship
• (Hint Consider 1/R values of each resistor and
  of the resistors in parallel)

21
1/R1 1/R2 1/RT
22
Predict the resistance - if you double the width
of a resistorand - for 2 equal resistors in
parallel
23
Single resistor R that doubles W RT ? R/2 2
equal resistors R in parallel RT ? R/2
24
How does resistance vary with length and width?

• Write an equation that reflects this variation

25
We found that R L and R 1/Wso R L/WHow
does R vary with thickness?Why do you think so?
26

• Generally
• R ?L/(Wt) ?L/A (AWt) ? is called the
  electrical resistivity(t is thickness)

27
Resistivity and resistors-in-series
relationshipR ?L/AIf L L1 L2R ?(L1
L2)/A ?L1/A ?L2/A R1 R2
28
Resistivity and resistors-in-parallel
relationship R ?L/AIf A A1 A2R ?L/
(A1 A2) 1/R (A1 A2)/ ?L1/R A1/ ?L A2/
?L 1/R 1/R1 1/R2
29
Creative Dramas
30
What is the difference between

• Insulator
• Semiconductor
• Conductor

31
Creative drama for microscopic electron behavior
for insulator, semiconductor. and conductor
32
Conductor 1023 free electrons/cm3Semiconductor
1012 1022 free electrons/cm3Insulator
lt1010 free electrons/cm3
33
When a resistors width is doubled, what happens?
34
Creative drama for microscopic electron behavior
for width dependence of resistance
35
When a resistors length is doubled, what happens?
36
Creative drama for microscopic electron behavior
for length dependence of resistance
37
Lets look in more detail at the microscopic
behavior of electrons in a resistor
38
Electrical Resistance

• Resistance to flow of electrons when a voltage is
  applied
• Apply a force (voltage)
• Measure response to force (current)
• Resistance is proportionality between force and
  response
• Flow is due to
• Number of electrons that move past a point
  (plane) per second
• (River current flow analogy water current flow
  depends on width and depth of water, density of
  water, and the speed of the water water flow is
  the number of water molecules that pass a point
  (plane perpendicular to motion) per second. In a
  similar manner, electron current flow depends on
  width and thickness of conductor, density of free
  electrons, and the speed of the electrons
  electron flow is number of electric charges that
  pass a point (plane perpendicular to motion) per
  second.)

39
Known properties of circuits
V
Resistor with resistance R
I
I
L
Measurements confirm constant I in the
resistor. Therefore charges in wire move with
constant velocity. But charges are subject to
FmaqEqV/L, so they should accelerate, not move
with constant velocity! Why?
40
A model consistent with the data

• Charges do not move freely from one end of the
  resistor to the other they have lots of
  collisions, on average every time ?.

Vfinal a ?
Therefore, charges move along the resistor with
constant average drift velocity - vD that is
proportional to the acceleration. (vD a ?, not
½ a ? see references for details)
41
Electrical/Mechanical Analogy
V
L
H
L
Collision barriers
42
Pegboard model of Ohms LawAllows connection
betweenforce and motionandelectrical
properties/Ohms Law
43
Pegboard Model of Electrical Resistance

• Balls conduction electrons
• Pegs scattering centers in a solid
• Height voltage (V)
• Pegboard length resistor length (L)
• Height/pegboard length electric field (EV/L)
• Ideally, fixed density of balls fixed density
  of conduction electrons in solid then current is
  number of balls that pass a line (perpendicular
  to electric field) per unit time and RV/I

44
Pegboard model of RV/I
45
Pegboard with Pegs
46
Close up of pegboard with pegs
47
References for pegboard model

• Electricity and Magnetism, (Berkeley Physics
  Course volume 2), Edward M. Purcell, section 4.4
  A Model for Electrical Conduction
• A mechanical analogy for Ohms Law, M. do Couto
  Tavares et al., Phys. Educ. volume 26, 1991, p.
  195-199.
• http//www.iop.org/EJ/abstract/0031-9120/26/3/012
• On an analogy for Ohms Law, P. M. Castro de
  Oliveira, Phys. Educ. Volume 27, 1992, p. 60-61.
• http//www.iop.org/EJ/abstract/0031-9120/27/2/001
• Feynman Lectures on Physics, volume 1, section
  43, especially section 43-3.
• Pegs Vermont American ¼ inch x 1 ¼ inch wood peg
• Available at Home Depot in the tool section 2
  for pack of 36
• Pegboard 2 feet wide x 4 feet long
• Available at Home Depot in lumber section 6

48
Conclusion

• Simple experiments to examine length and width
  dependence of resistance and series and parallel
  combinations of resistors
• Relationship between equation for resistivity and
  for series and parallel combinations of resistors
• Pictorial (graphite lines) and mathematical
  connection
• Microscopic behavior of electrons as the length
  and width of resistors are changed.
• Creative dramas
• Pegboard model Connection between force and
  motion concepts and Ohms Law
• This workshop is based on The Line of Resistance,
  available from the Institute of Chemical
  Education
• http//ice.chem.wisc/edu/catalog.htm