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# The Line of Resistance - PowerPoint PPT Presentation

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

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)

• With leads together, R = 0

• With leads not touching, R = open

• 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?

• Discuss possible ways to do this with your group

Perform an experiment to determine how the resistance varies with length

• What model supports your data?

How does resistance vary with length? varies with length

• Write an equation that reflects this variation

R ~ L varies with length

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

• What model supports your data?

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

• Write an equation that describes this relationship

R 2 resistors in seriesT = R1 + R2

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 2 resistors in seriesT  2R 2 equal resistors R in series: RT 2R

Discuss possible ways to do this with your group

Perform an experiment to determine how the resistance varies with width

• What model supports your data?

How does resistance vary with width? varies with width

• Write an equation that reflects this variation

R ~ 1/W varies with widthor1/R ~ W

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

• What model supports your data?

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 2 resistors in parallel1 + 1/R2 = 1/RT

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 2 resistors in parallelT  R/2 2 equal resistors R in parallel: RT R/2

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 2 resistors in parallelso R ~ L/WHow does R vary with thickness?Why do you think so?

Generally: 2 resistors in parallel

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

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

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 2 resistors in parallel

What is the difference between: 2 resistors in parallel

• Insulator

• Semiconductor

• Conductor

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

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 2 resistors in parallelwidth dependence of resistance

Creative drama for microscopic electron behavior for 2 resistors in parallellength dependence of resistance

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 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 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)

Electrical/Mechanical Analogy electrons in a resistor

V

L

L

H

Collision barriers

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

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 electrons in a resistor

Pegboard with Pegs electrons in a resistor

Close up of pegboard with pegs electrons in a resistor

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 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