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The Line of Resistance. APS Teachers Day Workshop Los Angeles, CA March 22, 2005 Dr. Larry Woolf General Atomics Larry.Woolf@gat.com www.sci-ed-ga.org (click on Presentations to see all these slides). Multimeter Operation. Work with your group With leads together, R = 0

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The line of resistance l.jpg

The Line of Resistance

APS Teachers Day Workshop

Los Angeles, CA

March 22, 2005

Dr. Larry Woolf

General Atomics

Larry.Woolf@gat.com

www.sci-ed-ga.org (click on Presentations to see all these slides)


Multimeter operation l.jpg
Multimeter Operation

  • Work with your group

  • With leads together, R = 0

  • With leads not touching, R = open


Draw a line using the graphite pencil and measure its resistance l.jpg
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?


Design an experiment to determine how the resistance varies with length l.jpg
Design an experiment to determine how the resistance varies with length

  • Discuss possible ways to do this with your group


Perform an experiment to determine how the resistance varies with length l.jpg
Perform an experiment to determine how the resistance varies with length

  • Discuss your data with your group

  • What model supports your data?


How does resistance vary with length l.jpg
How does resistance vary with length? varies with length

  • Write an equation that reflects this variation


Slide7 l.jpg
R ~ L varies with length


Design an experiment to determine the total resistance of 2 resistors in series l.jpg
Design an experiment to determine the total resistance of 2 resistors in series

  • Discuss possible ways to do this with your group


Perform an experiment to determine the total resistance of 2 resistors in series l.jpg
Perform an experiment to determine the total resistance of 2 resistors in series

  • Discuss your data with your group

  • What model supports your data?


What is the total resistance of 2 resistors in series l.jpg
What is the total resistance of 2 resistors in series? 2 resistors in series

  • Write an equation that describes this relationship


R t r 1 r 2 l.jpg
R 2 resistors in seriesT = R1 + R2


Predict the resistance if you double the length of a resistor and for 2 equal resistors in series l.jpg
Predict the resistance 2 resistors in series- if you double the length of a resistorand - for 2 equal resistors in series


Single resistor r that doubles l r t 2r 2 equal resistors r in series r t 2r l.jpg
Single resistor R that doubles L: R 2 resistors in seriesT  2R 2 equal resistors R in series: RT 2R


Design an experiment to determine how the resistance varies with width l.jpg
Design an experiment to determine how the resistance varies with width

Discuss possible ways to do this with your group


Perform an experiment to determine how the resistance varies with width l.jpg
Perform an experiment to determine how the resistance varies with width

  • Discuss your data with your group

  • What model supports your data?


How does resistance vary with width l.jpg
How does resistance vary with width? varies with width

  • Write an equation that reflects this variation


R 1 w or 1 r w l.jpg
R ~ 1/W varies with widthor1/R ~ W


Design an experiment to determine the total resistance of 2 resistors in parallel l.jpg
Design an experiment to determine the total resistance of 2 resistors in parallel

  • Discuss possible ways to do this with your group


Perform an experiment to determine the total resistance of 2 resistors in parallel l.jpg
Perform an experiment to determine the total resistance of 2 resistors in parallel

  • Discuss your data with your group

  • What model supports your data?


What is the total resistance of 2 resistors in parallel l.jpg
What is the total resistance of 2 resistors in parallel? 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)


1 r 1 1 r 2 1 r t l.jpg
1/R 2 resistors in parallel1 + 1/R2 = 1/RT


Predict the resistance if you double the width of a resistor and for 2 equal resistors in parallel l.jpg
Predict the resistance 2 resistors in parallel- if you double the width of a resistorand - for 2 equal resistors in parallel


Single resistor r that doubles w r t r 2 2 equal resistors r in parallel r t r 2 l.jpg
Single resistor R that doubles W: R 2 resistors in parallelT  R/2 2 equal resistors R in parallel: RT R/2


How does resistance vary with length and width l.jpg
How does resistance vary with length and width? 2 resistors in parallel

  • Write an equation that reflects this variation


We found that r l and r 1 w so r l w how does r vary with thickness why do you think so l.jpg
We found that R ~ L and R~ 1/W 2 resistors in parallelso R ~ L/WHow does R vary with thickness?Why do you think so?


Slide26 l.jpg

Generally: 2 resistors in parallel

R = L/(Wt) = L/A (A=Wt) is called the electrical resistivity(t is thickness)


Slide27 l.jpg

Resistivity and resistors-in-series relationship 2 resistors in parallelR = L/AIf L = L1 + L2R = (L1 + L2)/A = L1/A + L2/A = R1 + R2


Slide28 l.jpg

Resistivity and resistors-in-parallel relationship 2 resistors in parallelR = L/AIf A = A1 + A2R = L/ (A1 + A2) 1/R = (A1 + A2)/ L1/R = A1/ L + A2/ L 1/R = 1/R1 + 1/R2


Creative dramas l.jpg
Creative Dramas 2 resistors in parallel


What is the difference between l.jpg
What is the difference between: 2 resistors in parallel

  • Insulator

  • Semiconductor

  • Conductor


Creative drama for microscopic electron behavior for insulator semiconductor and conductor l.jpg
Creative drama for microscopic electron behavior for 2 resistors in parallelinsulator, semiconductor. and conductor


Slide32 l.jpg
Conductor: ~10 2 resistors in parallel23 free electrons/cm3Semiconductor: ~ 1012 – 1022 free electrons/cm3Insulator: <1010 free electrons/cm3



Creative drama for microscopic electron behavior for width dependence of resistance l.jpg
Creative drama for microscopic electron behavior for 2 resistors in parallelwidth dependence of resistance



Creative drama for microscopic electron behavior for length dependence of resistance l.jpg
Creative drama for microscopic electron behavior for 2 resistors in parallellength dependence of resistance



Electrical resistance l.jpg
Electrical Resistance electrons in a resistor

  • 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.)


Known properties of circuits l.jpg
Known properties of circuits electrons in a resistor

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 F=ma=qE=qV/L, so they should accelerate, not move with constant velocity!

Why?


A model consistent with the data l.jpg
A model consistent with the data electrons in a resistor

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)


Slide41 l.jpg

Electrical/Mechanical Analogy electrons in a resistor

V

L

L

H

Collision barriers


Slide42 l.jpg
Pegboard model of Ohm’s Law electrons in a resistorAllows connection between:force and motionandelectrical properties/Ohm’s Law


Pegboard model of electrical resistance l.jpg
Pegboard Model of Electrical Resistance electrons in a resistor

  • 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


Pegboard model of r v i l.jpg
Pegboard model of R=V/I electrons in a resistor


Slide45 l.jpg

Pegboard with Pegs electrons in a resistor


Close up of pegboard with pegs l.jpg
Close up of pegboard with pegs electrons in a resistor


References for pegboard model l.jpg
References for pegboard model electrons in a resistor

  • 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


Conclusion l.jpg
Conclusion electrons in a resistor

  • 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