breed [atoms] breed [charges] globals [dEnergy current charge-density spacing cooling-rate ] charges-own [ x-vel deltax dxrad dxtan dh new-heading vel new-vel energy ] atoms-own [energy temperature ] to startup setup end to setup ca set dEnergy .1 set spacing 3 set voltage 0 set cooling-rate 5 set charge-density 5 set collision-chance 50 ask patches[ set pcolor 27 if abs pycor = max-pycor [set pcolor blue - 1] if pxcor mod spacing = 0 and pycor mod spacing = 0 and abs pxcor < max-pxcor and abs pycor < max-pycor [sprout 1 [ set breed atoms set color white set size 2 set shape "circle" set Energy .015 set temperature energy * 100 fd 1 ] ] if pxcor mod spacing != 0 and pycor mod spacing != 0 and random 10 < charge-density [sprout 1 [ set breed charges set color blue set shape "dot" set heading random 360 set vel .1 set x-vel vel * sin heading ] ] ] ;;if follow-electron = true ;; [ask one-of charges [ set color blue pd set size 3]] plot-x-axis end to go set voltage precision voltage 1 ask charges [ if ycor > (max-pycor - 1) and (heading <= 90 or heading >= 270) [set heading (180 - heading) ] if ycor < (min-pycor + 1) and (heading > 90 and heading < 270) [set heading (180 - heading) ] if ycor > max-pycor [set ycor (max-pycor - 1)] if ycor < min-pycor [set ycor (min-pycor + 1)] fd vel ] collide apply-field ask atoms [ change-temperature lose-energy ] calculate-current plot-stuff tick end ;;SETUP PROCEDURES ;;GO PROCEDURES to apply-field ask patches with [abs pycor < max-pycor] [ if voltage > 0 [ if pxcor = min-pxcor [set pcolor black] if pxcor = max-pxcor [set pcolor red] ] if voltage < 0 [ if pxcor = min-pxcor [set pcolor red] if pxcor = max-pxcor [set pcolor black] ] if voltage = 0 [ if pxcor = min-pxcor [set pcolor 27] if pxcor = max-pxcor [set pcolor 27] ] ] ask charges [ if vel = 0 [set vel .02] set deltax voltage / 1000 set dxrad deltax * sin heading set dxtan deltax * cos heading set dh (dxtan / vel) * 360 / (2 * pi) set new-vel vel + dxrad set new-heading heading + dh if abs (90 - new-heading) < 1 [set new-heading random 360] if abs (270 - new-heading) < 1 [set new-heading random 360] ] ask charges [ set heading new-heading set vel new-vel ;; if abs pycor-of patch-ahead 0.5 = max-pycor set x-vel vel * sin heading ] end to collide ;;change here to make a constant dEnergy, but a probability of collision that depends on interaction strength ask charges [ if count atoms-here > 0 and collision-chance > random 100 [ if ((vel * vel - dEnergy ) > 0) [ set new-vel sqrt (vel * vel - dEnergy) set [Energy] of one-of atoms-here ([Energy] of one-of atoms-here + dEnergy) ] set vel new-vel set heading random 360 fd .3 ] ] end to calculate-current set current 50 * (sum [ x-vel] of charges) / count charges end to change-temperature ;;atoms procedure set temperature energy * 200 set color (scale-color red temperature 100 1) set color 19.99 - (19.99 - color) / 2 end to lose-energy ;;atoms procedure set energy (energy - (cooling-rate * energy) / 500 ) end to clear-followed-charge ask charges [ if size = 3 [pu set color blue set size 1] ] clear-drawing ask turtles [pu] end ;;PLOTTING PROCEDURES to plot-x-axis set-current-plot "Atom temperature" set-current-plot-pen "x-axis" auto-plot-off plotxy 0 0 plotxy 100000000 0 auto-plot-on end to plot-stuff set-current-plot "Atom temperature" set-current-plot-pen "atom temp" plot (sum [energy * 100] of atoms) / count atoms set-current-plot-pen "current" plot current ;;set-current-plot-pen "voltage" ;; plot voltage end @#$#@#$#@ GRAPHICS-WINDOW 10 172 630 333 30 6 10.0 1 10 1 1 1 0 1 1 1 -30 30 -6 6 0 0 1 ticks CC-WINDOW 5 347 639 442 Command Center 0 BUTTON 17 64 83 97 Reset setup NIL 1 T OBSERVER NIL NIL NIL NIL BUTTON 15 12 86 46 go/stop go T 1 T OBSERVER NIL NIL NIL NIL SLIDER 107 10 212 43 voltage voltage -10 10 0 0.1 1 NIL HORIZONTAL PLOT 239 10 629 161 Atom temperature time no units 0.0 100.0 0.0 10.0 true true PENS "atom temp" 10.0 0 -2674135 true "current" 10.0 0 -16777216 true "voltage" 10.0 0 -10899396 false "x-axis" 1.0 0 -16777216 false BUTTON 13 129 128 162 watch one electron ask one-of charges\n[ pd \nwatch-me] NIL 1 T OBSERVER NIL NIL NIL NIL BUTTON 137 129 224 162 stop watching reset-perspective\nclear-followed-charge NIL 1 T OBSERVER NIL NIL NIL NIL SLIDER 94 66 217 99 collision-chance collision-chance 0 100 50 1 1 NIL HORIZONTAL @#$#@#$#@ WHAT IS IT? ----------- This is a model of electrical resistance in a wire. It is intended to help one visualize how electric current heats a wire when moving electrons collide with atoms. It was developed for 5-8 graders. This model is used by the Concord Consortium in the UDL (Universal Design for Learning) project. To see the model in the context of an activity, go to http://udl.concord.org. Find the Intermediate Electricity Unit (Grades 56) and go to the activity called "Heat a wire". HOW IT WORKS ------------ The wire is composed of electrons (blue dots) and atoms (larger white dots). If voltage is applied, the electrons are accelerated to the left or right, depending on the polarity of the voltage. When an electron is on the same patch as an atom, it "collides", which in this model means that it transfers a portion of its energy to the atom and heads off in a random direction. Each atom can accumulate energy in this way, balanced by a constant cooling rate. The atom becomes redder as its energy or temperature goes up. HOW TO USE IT ------------- The 'voltage' slider can apply voltage in either direction. The 'collision-chance' slider changes the chance that an electron will "collide" with an atom if they are on the same patch. If collision-chance is 0, the electrons go right by the atoms without interacting. The 'watch one electron' button allows one to follow the path of an individual electron. This is a wrap-around model. Electrons that leave one end of the wire show up on the other end, going in the same direction. THINGS TO NOTICE ---------------- The graph plots average behavior of the electrons and atoms. Atom temperature is the average temperature (energy) of the atoms. The units have no meaning. Current is the average x-velocity of the electrons. Note that it can be positive or negative. Note also that if the electrons are all moving randomly, the current will be zero. THINGS TO TRY ------------- Run the model and change the voltage slider. Notice the effect on the motion of the electrons. Also notice the effect on their average behavior in the graph. See if you can find a relationship between the voltage, the current, and the temperature of the atoms. Run the model, apply a set voltage, and change the collision-chance slider. If the value is zero, what happens? This would be equivalent to the wire having no resistance at all. EXTENDING THE MODEL ------------------- The cooling rate of the atoms could be changed into a slider. This would be like a hot wire that you blow on to cool it, which is one way to make a measuring device for wind speed. It has not been confirmed that this model follows Ohm's Law. See if it does. See if the exact rule for collisions has an effect on this relationship. NETLOGO FEATURES ---------------- Note that the x-axis is displayed by plotting x=0. CREDITS AND REFERENCES ---------------------- This model was written by Ed Hazzard at the Concord Consortium (www.concord.org) for the Universal Design for Learning (UDL) Project, in March 2008. @#$#@#$#@ default true 0 Polygon -7500403 true true 150 5 40 250 150 205 260 250 airplane true 0 Polygon -7500403 true true 150 0 135 15 120 60 120 105 15 165 15 195 120 180 135 240 105 270 120 285 150 270 180 285 210 270 165 240 180 180 285 195 285 165 180 105 180 60 165 15 arrow true 0 Polygon -7500403 true true 150 0 0 150 105 150 105 293 195 293 195 150 300 150 box false 0 Polygon -7500403 true true 150 285 285 225 285 75 150 135 Polygon -7500403 true true 150 135 15 75 150 15 285 75 Polygon -7500403 true true 15 75 15 225 150 285 150 135 Line -16777216 false 150 285 150 135 Line -16777216 false 150 135 15 75 Line -16777216 false 150 135 285 75 bug true 0 Circle -7500403 true true 96 182 108 Circle -7500403 true true 110 127 80 Circle -7500403 true true 110 75 80 Line -7500403 true 150 100 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