1 The Line of Resistance APS Teachers Day Workshop Los Angeles, CA March 22, 2005 Dr. Larry Woolf...
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Transcript of 1 The Line of Resistance APS Teachers Day Workshop Los Angeles, CA March 22, 2005 Dr. Larry Woolf...
1
The Line of Resistance
APS Teachers Day WorkshopLos Angeles, CAMarch 22, 2005Dr. Larry WoolfGeneral Atomics
[email protected] (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?
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
12
Predict the resistance - if you double the length of a resistorand - for 2 equal resistors in series
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?
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)
22
Predict the resistance - if you double the width of a resistorand - for 2 equal resistors in parallel
27
Resistivity and resistors-in-series relationshipR = L/A
If L = L1 + L2
R = (L1 + L2)/A = L1/A + L2/A = R1 + R2
28
Resistivity and resistors-in-parallel relationship R = L/A
If A = A1 + A2
R = L/ (A1 + A2) 1/R = (A1 + A2)/ L1/R = A1/ L + A2/ L 1/R = 1/R1 + 1/R2
32
Conductor: ~1023 free electrons/cm3
Semiconductor: ~ 1012 – 1022 free electrons/cm3
Insulator: <1010 free electrons/cm3
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
I I
Resistor with resistance R
L
Measurements confirm constant I in the resistor.
Therefore charges in wire move with constant velocity.
But charges are subject to F=ma=qE=qV/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
HL
Electrical resistance
Voltage V and resistor length L
F = qE = q V/L = ma
a ~ V/L
Electrical/Mechanical Analogy
Mechanical ramp
Height H and ramp length L
Framp = mgsin = mgH/L = ma
a ~ H/L
V
L
Collision barriers
42
Pegboard model of Ohm’s Law
Allows connection between:force and motion
andelectrical properties/Ohm’s 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 (E=V/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 R=V/I
44
Pegboard model of R=V/IChange: Effect:
L (at fixed V) E so a so vD so I so R
W (at fixed V) I so R
V E so a so vD so I
Density of balls(higher carrier density)
I so R (at fixed V)
Density of pegs(more defects)
or size of pegs (higher temperature – larger vibration amplitude of ions)
vD so I so R (at fixed V)
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 Ohm’s 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 Ohm’s 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 Ohm’s Law• This workshop is based on The Line of Resistance,
available from the Institute of Chemical Education– http://ice.chem.wisc/edu/catalog.htm