XRAISE OUTREACH LABORATORY INVESTIGATION

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1 XRAISE OUTREACH LABORATORY INVESTIGATION Title: Original: Revisin: Frmatted: Authrs: Apprpriate Level: Abstract: NY Standards Met: 4 April April 2009 May 2015 by CLASSE Xraise Bicircuits: Signal Lss in Cable Transmissin Mark Baustian, Julie Nucci, and Bruce Jhnsn 9-12 Regents Physics, AP Physics B In this lab students will investigate a basic and imprtant simple electric circuit and shw hw it can be used t mdel nerve cnductin. They will use Ohm's law t predict vltage and current flw in a simple vltage divider. Students will build a mdel electrical cable using a series f vltage dividers and experiment with strategies t reduce current lss and vltage decay alng the cable. Students will use the cable they build t shw hw the same strategies they discvered are used in nature t slve the very imprtant prblem f nerve cnductin and appreciate hw the cable mdel predicts prblems assciated with an imprtant disease, Multiple Sclersis. Physical Setting: Physics 4.1l All materials display a range f cnductivity. At cnstant temperature, cmmn metallic cnductrs bey Ohm s Law*. 4.1 Circuit cmpnents may be cnnected in series* r in parallel.* Schematic diagrams are used t represent circuits and circuit elements. 4.1m The factrs affecting resistance in a cnductr are length, area, temperature, and resistivity.* 5.1d An bject in linear mtin may travel with a cnstant velcity* r with acceleratin*.(nte: Testing f acceleratin will be limited t cases in which acceleratin is cnstant.) Living Envirnment 1.2a Imprtant levels f rganizatin fr structure and functin and whle rganisms. 1.2f Cells have particular structures that perfrm specific jbs. These structures perfrm the actual wrk f the cell. Just as systems are crdinated and wrk tgether, cell parts must als be crdinated and wrk tgether. 1.2g Each cell is cvered by a membrane that perfrms a number f imprtant functins fr the cell. These include: separatin frm its utside envirnment cntrlling which mlecules enter and leave the cell, and recgnitin f chemical signals. The prcesses f diffusin and active transprt are imprtant in the mvement f materials in and ut f cells.

2 Special Ntes: Created by the CNS Institute fr Physics Teachers via the Nanscale Science and Engineering Initiative under NSF Award # EEC , and the NYS Office f Science, Technlgy & Academic Research under NYSTAR Cntract # C Pre-Lab: Signal Lss in Cable Transmissin Multiple sclersis is a nerve cnductin prblem. The bdy is sending ut a signal fr smething t happen and the message just isn't getting t the brain in time r at all. This is similar t the prblem a cmmunicatins engineer might experience with a data signal in a cmputer cable. The data ges in ne end but by the time it gets t the ther end the signal has becme weak and nisy. This prblem was riginally encuntered by the telegraph cmpanies in the middle f the 1800s when they tried t lay cables acrss the English Channel and later acrss the Atlantic Ocean. Hw culd they design a cable that culd carry the signal withut significant lss f data and at a cst that the cmpanies and their custmers culd affrd? Enter Lrd Kelvin. Yu may have heard the name assciated with temperature as in: zer Kelvin, Abslute zer, the cldest pssible temperature. Lrd Kelvin, a Barn whse real name was William Thmsn, is abut as famus as they get in physics. Let's see hw physics slved the prblem f the transceanic telegraph and hw physicians used that knwledge t research multiple sclersis. Yur challenge in this lab is t understand what a disease f the nervus system and the transatlantic cable have in cmmn. The basic electrical unit that will be used t analyze bth these things is the vltage divider, which is a basic electrical circuit used t create a smaller utput vltage frm a larger input vltage. Sectin 1: Using Vltage Dividers T Analyze Signal Lss Vltage dividers are used in electrnics t reduce a fixed surce vltage t an apprpriate level fr a particular task. Fr example, if yu have a 12V battery and a lamp that can nly handle 6V, yu can use a vltage divider t drp the vltage t what is needed. A vltage divider is a simple circuit with 2 r mre resistrs added in series (Figure 1). We will put tgether a series f vltages dividers t mdel a vltage drp like the ne that ccurred n the transatlantic cable. We will then apply similar principles t mdel a bilgical system, specifically neurns in the nervus system. Interesting fact: Turns ut the cable equatins that Lrd Kelvin derived in the 1800 s t explain signal lss in the transatlantic cable were fund, almst a century later, able t describe cnductin in the nervus system! Figure 1. A simple vltage divider. Psitive current (i + ) flws frm the psitive ple f the battery thrugh tw resistrs in series t the negative ple f the battery. Accrding t Ohm's law (V=IR), when current flws thrugh a resistr, a vltage equal t I*R appears acrss the resistr. In

3 Figure 1 this vltage is labeled V R1 fr the vltage that appears acrss R 1 and V R2 fr the vltage drp acrss R 2. The ttal vltage drp acrss bth resistrs is equal t the vltage f the battery. V batt = V R1 + V R2 A vltage drp can ccur, bth in physical and bilgical systems, when the inherent prperties f the system prduce a vltage divisin that is NOT s helpful. These inherent prperties can be caused by the internal resistance f the cnducting material, weak resistance f the insulatin material, resistance in cnnectins r cnductrs, etc. Fr the first part f the lab, yu will be mdeling the transatlantic cable, which fr simplicity; will cnsist f a cpper wire wrapped in a certain insulating material. The cpper wire will have an inherent cre resistance R c and the insulating material will als have an inherent resistance, called leak resistance, R L. Cre resistance f a wire: When current flws thrugh a wire it encunters a resistance that is a functin f the material frm which the wire is made and the wire gemetry. This resistance is called the 'cre' resistance (R cre r R C ). A high cre resistance means that the wire is nt a gd electrical cnductr. A lw cre resistance means that the wire is a gd electrical cnductr. Leak resistance f insulatin: At the same time, sme f the current will nt flw alng the wire, but will leak t grund. The better the wire is insulated, the less current will be leaked. The resistance f the insulatin t this current leakage is called the 'leak' resistance (R leak r R L ). A well insulated wire has a high leak resistance. A prly insulated wire has a lw leak resistance. R C = cre resistance f the Insulatin R L = leak resistance f the Cu metal Figure 2. Crss-sectin f an insulated metal wire. If the signal leaks t grund as it travel dwn the cable, then nly part f the riginal signal will be available at the ther end f the cable t d useful wrk. Figure 3 shws a vltage divider mdel f a wire that is similar t what Lrd Kelvin develped t slve the prblem f transmitting telegraph signals acrss the English Channel. Figure 3. Circuit mdel fr signal lsses alng a cable

4 Yu will test this vltage divider mdel using different cmbinatins f cre and leak resistances. Study the figure and be sure yu can identify the vltage dividers. Nte that the utput f the first divider in the Figure 3 is the input t the secnd ne, and s n. Sectin 2: Experimental Sectin Activity 1: In this activity yu will measure the vltage drp acrss different vltage divider set-ups and cmpare yur utput vltages. Materials: Prject Bard (Disclaimer: This prject bard was designed t shw a Multiplar r Mtr Neurn s that later in this lab we can emphasize the cnnectin between physics and bilgy. Fr mre details abut the bard please refer t the Appendix). Multimeter 9V battery Screwdriver (will help pening the slts t insert the leads f the resistrs) LED Resistrs (set f 5 f the 6 resistrs shwn in Table 1.) Cre resistance, R C, f the Cu wire Leak resistance, R L, f the insulatin Table 1: Resistr Values and Crrespnding Clr Cdes HI MED LO Red (400 Ω) Yellw (7,500Ω) Blue (200Ω) Brwn (2,200Ω) Green (100Ω) Black (1,500 Ω) Prcedure: Get yur prject bard ut. Nte that this is designed t shw a Multiplar r Mtr Neurn and will be discussed later in the lab. Fr mre inf n the bard, refer t Appendix. Measure the actual vltage f yur battery and recrd it in Table 2. On yur prject bard, assemble the circuit shwn in Figure 4, using R c =R L = 1,500 Ω (black). The left hand image is the circuit schematic and the right hand image shws hw yu build this circuit n yur prject bard. The right hand image als shws hw t measure the vltage acrss a resistr. The 9V battery is cnnected t the bard using the duble clip leads. TIP: Use the screwdriver r wden ruler t depress the lever and insert the resistr leads. Figure 4. Vltage divider circuit and prject bard wiring diagram.

5 Measure the vltage acrss R C and R L (V ut ). Recrd these values in Table 2. Nte that V RC and V RL must ttal V batt. Cmplete the data table using the ther 3 cmbinatins f resistrs listed. V batt R c Ω clr 1500 (black) 1500 (black) 100 (green) 100 (green) Table 2. Vltage Divider Data R L Ω clr 1500 (black) 100 (green) 1500 (black) 200 (blue) V RC V RL (V ut ) Questins: Based n yur calculatins: Hw wuld yu pick R C and R L t make V ut clse t V batt? Hw abut V ut much smaller than V batt? Activity 2: In this activity yu will investigate the prblem f transmitting electrical signals ver lng distances. In additin t mdeling the perfrmance f a cable, yu will cnduct an engineering assessment f the cst/benefit analysis fr cable design. Materials: Same as abve Prcedure: Assemble the circuit shwn in Figure 3 by using the resistrs values shwn in the first tw clumns f Table 3. All f the resistrs used fr R C must be f the same value, because the wire is hmgenus alng its length. Similarly, all resistrs used fr R L must be f the same value, because the insulating material is als unifrm alng the length f the cable. Cnnect the battery and measure the vltage acrss the 5 R L r leak resistrs (R L1 t R L5 ). Enter the values in Table 3. After yu have recrded yur data cnnect the LED by tuching its leads t the leads f the leak resistr R L5. Recrd whether r nt the LED lights in Table 3.

6 NOTE: It isn t necessary t actually cnnect the LED t the bard. Yu can just tuch the LED leads t the resistr leads. NOTE: LEDs have plarity. Try the LED n bth leads t make sure yu are reading it crrectly. Repeat the prcedure using the ther values fr R C and R L in Table 3. Data fr the six pssible cnfiguratins is pltted in Figure 5. Nte that the unifrmity f R C and R L create an expnential decrease f vltage ver distance frm the battery that can be described by a space r length cnstant. Using yur data and the data in Figure 5, determine which cmbinatin f cre and leak resistances lead t cables capable f lighting an LED. Summarize this infrmatin in Table 4 by writing ON if a particular cmbinatin f cre and leak resistances can light the LED and writing OFF it is cannt. Test yur predictins fr the cmbinatins nt included in Figure 5. Table 3: Vltage Divider Netwrk Data R C R L V ut1 V ut2 V ut3 V ut4 V ut5 LED (n/ff) LO cre resistance (green) LO cre resistance (green) HI cre resistance (red) MED leak resistance (brwn) LO leak resistance (black) LO leak resistance (black) vltage LHi LMed HiHi LL MedL HiL Legend: Cre-Leak resistance cmbinatin 0 Vbatt V1 V2 V3 V4 V5 psitin Figure 5: Vltage Divider Data fr Different Resistr Cmbinatins. The cre resistance is listed first and the leak resistance is listed secnd.

7 Leak Resistance Table 4: Summary shwing which cables culd light the LED. Cre Resistance High Med Lw Lw Med High Questins: What trends d yu ntice in this table? In the real wrld, engineers rarely have the luxury f building the best pssible system since materials cst mney and custmers desire a wrking and reliable slutin that is ecnmically viable. Fr the cable, the cre resistance mdels the resistance f the wire itself. This fllws the equatin: R = ρl/a Fr a given material (with resistivity ρ) and a given length wire (L), hw d yu make a wire with a lw cre resistance? Hw d yu make a cable with a high leak resistance? Given this infrmatin, which cable cnfiguratins d yu think are the least and mst expensive t prduce and why? Histrical data shws that the cst f the transatlantic cable was apprximately 400/nautical mile in British Punds,. Table 5 has estimates fr the cst f the varius cre and leak resistances/nautical mile f cable. The ttal cst per nautical mile is the sum f the cst f the cre and leak resistances.

8 Table 5: Estimated material cst per nautical mile (in British Punds) as a functin f material quality HIGH MED LOW Cre resistance, R C f the wire Leak resistance, R L f the insulatin Assume that yur vltage divider circuit is a gd mdel fr the design and functin f the transatlantic cable. Based n yur LED mdel and the data in Table 5, determine the cst per nautical mile f each wrking mdel fr the transatlantic cable. Shw yur wrk. If yu were the engineer respnsible fr the prject, which cmbinatin f cre and leak resistances wuld yu decide t cnstruct the cable frm? Why?

9 Sectin 3: Finding Physics in a Bilgy Prblem Activity 3: Physics in Bilgy In the pre-lab yu were intrduced t a serius disease that is caused by a failure f nerves t prperly carry signals thrughut the bdy. Our success as animals depends n the ability f these nerves t cnduct signals efficiently and ften rapidly. Yu have prbably had the experience f a painful stimulus causing yu t quickly, withut even thinking, pull yur hand away. Figure 6 shws the nerves (electric wires) used t transmit signals between yur limbs and central nervus system (CNS) in the withdrawal reflex. The little square in this diagram represents an area f skin n yur hand cntaining sensry neurns that are sensitive t painful stimuli. The part f a neurn that carries the signal ver lng distances is a lng thin prcess called the axn. The sensry signal frm the pain travels alng an axn tward the CNS. In the spinal crd, the signal is transferred t anther neurn (mtr neurn) and travels alng its axn back t the muscles in yur arm causing the withdrawal. The axns in this bilgical circuit are analgus t the wires in an electric circuit. The term nerve is ften used instead f axn. A nerve is cmpsed f a bundle f many axns packaged tgether; much like an electrical cable is cmpsed f a bundle f wires. In this lab we are studying axnal cnductin. Materials: Wden ruler r meter stick calculatr Figure 6. Neural circuit f the withdrawal reflex. Prcedure: Vertically hld a ruler between yur fingers and recrd the psitin f yur fingers n the ruler. This is x 1. Open and clse yur fingers as fast as yu can. Recrd the new psitin f yur fingers. This is x 2. x 2 x 1 = d, the distance the ruler fell. Recrd yur values in the Table 6. Calculate the time it tk fr yur hands t pen and clse using the fllwing equatin. Slve fr t in secnds and recrd this value in Table 6. 1 d a 2 t 2 Where: d is the distance the rule mved (m), a is the acceleratin f gravity (9.8m/sec 2 ) and t is the time it tk t pen and clse yur hand (sec)

10 Estimate x, the ttal distance the signal must travel fr yu t pen and clse yur hand by first measuring the distance frm yur fingers t the center f yur spine at the level f yur shulder blades. What yu are actually measuring are tw signals: 0ne t release the ruler and the ther t squeeze it. Duble yur value fr x t accunt fr this. Input this value int Table 6. Calculate the velcity using the equatin in the table and enter the value in Table 6. This is a rugh estimate because we are ignring the timing f the brain cmmands t get t the spinal crd. Initial ruler Psitin, x 1 (m) Table 6: Calculatin f mtr neurn transmissin speed. Final ruler d = x 2 -x 1 Time, t x = nerve psitin, x 2 (m) (sec) pathway (m) length, (m) v nerve = x/ t (m/sec) Think abut experiences in yur daily life r thse f ther creatures yu knw and make a list f situatins where fast respnse is crucial. Make a separate list f situatins where fast reactins are less imprtant. Fast Nt s fast D yu think that the axns making up the neural circuits required fr prducing the behavirs in these tw lists have the same r different physical prperties? Explain which prperties, specifically, are similar and different, addressing at least R C and R L.

11 Activity 4: Cable Cnductin in Bilgy In Activity 1 and 2 yu mdeled the transatlantic cable as a series f vltage dividers. The reasn yu did that n a prject bard with a picture f a nerve cell is that the same vltage divider mdel applies t signal transmissin in the nervus system. T cnvert frm metal cables t the bilgical system, we just need t redefine the variables: Cre resistance f an axn When a signal travels alng a nerve axn it encunters a resistance that is a functin f nerve gemetry. A high cre resistance means that the nerve is thin (small crss sectinal area) A lw cre resistance means that the nerve is thick (large crss sectinal area). Leak resistance f an axn: the myelin sheath Insulatin f axns is prvided by a layer f myelin. A schematic f a neurn with a myelinated axn is shwn in Figure 9. Myelin is used t insulate nerve axns whenever fast cnductin speed is needed. Nt all axns are myelinated. A well insulated axn with a thick myelin layer has a high leak resistance. An axn with n myelin sheath has a lw leak resistance. The graphs belw (Figures 7 and 8) shw the effects f reducing the cre resistance (Rc) f an axn by increasing its diameter and the effects f decreasing the leak resistance (RL) f a neurn n the vltage spread frm a surce. D these graphs have any similarities t the data in Figure 5? Des it lk like cable transmissin in an axn is similar t that in the transatlantic cable? What des this say abut the unifrmity f R C and R L in animal wires? Axn membranes als have a space cnstant fr passive vltage spread. Figure 7. Graph shwing the effects f reducing the cre resistance (Rc) f an axn by increasing its diameter

12 Figure 8. Graph shwing the effects f decreasing the leak resistance (RL) f a neurn n the vltage spread frm a surce In mst parts f the nervus system distances are t lng fr signal transmissin t be effective by cable prperties alne. Fr example, cnsider the signal transmissin in a mtr neurn axn ging frm the spinal crd dwn t a te muscle in a basketball player (r a giraffe!). Vltage sensitive bster statins in axns create sparks f electricity called Actin Ptentials (APs) which then becme the vltage surce t passively transmit the signal like in a cable dwn the axn t ignite the next AP, and s n and s n. In unmyelinated axns, APs are ignited cntinuusly when the passive vltage spread is large enugh (lng space cnstant) t activate the next bster system as shwn belw. It takes time t generate each AP and the passive vltage spreads very quickly. S if the initial vltage stays strng and spreads further, fewer APs have t be initiated in the same length f axn and s signal transmissin will be faster.

13 In myelinated axns (Figure 9) and belw, the AP is nly ignited at the bare internde (green) regins and the myelinated regins (gray) cnduct the vltage spread passively like a cable t the next AP generatin area. It wuld be mre cnsistent t number these figures t and give them a figure legend, but it s fine fr nw. Figure 9. Schematic representatin f a multiplar neurn with myelinated axn.

14 Hw fast is fast? Questins: In nature, animals rely n fast reactins fr survival. Based n yur understanding f cables and nerves, speculate abut strategies nature culd use t increase the speed f cnductin. Give yur answer in terms f bth R C and R L fr axns. Make sure t explain what these values mean in terms f the axn structure. Nt all axns are myelinated. If myelin makes nerve signal transmissin faster, why wuldn t all axns be myelinated? Cnsider that evlutin als makes a cst/benefit analysis when adjusting electrical parameters that affects the speed f signal transmissin. Many invertebrate animals d have relatively fast signal cnductin that are nt insulated with myelin. Based n yur understanding f cable cnductin, what must be a cmmn physical characteristic f these unmyelinated neurns t enable them t transmit signals s quickly? Hw fast were yur neurns? T get a better sense f this, cnvert yur neurn speed frm m/sec int miles/hur. Shw yur wrk. Fun Fact: The rati f the diameter t the length f the transatlantic cable is similar t that f a lng alpha mtr neurn. Engineering prduced the same slutin as bilgy! Here are sme examples f unmyelinated axns in invertebrates: The squid cntracts its mantle prviding a jet pwered escape mechanism using a signal frm an axn knwn as the squid giant axn. It's s big yu can dissect it withut using a micrscpe. The cckrach has a pair f hairs n its tail end called cerci. Large unmyelinated axns carry infrmatin frm these hairs t its brain abut air currents cming frm behind it. The crayfish uses rapid beats f its tail t dart away fr cver. This mvement is stimulated by large unmyelinated axns.

15 Which f these neurns d yu think wuld have myelinated axns? Explain yur reasning. Table 7. Nerve Type Axn Diameter (μm) Signal Velcity (m/s) Squid Giant Axn Myelinated? Yes r N Explanatin α-mtr neurn (skeletal muscle) Sensry neurn (stimulus respnse) c-fiber pain (nt sudden) Fun Fact: The neurns in yur brain have myelinated axns t assure fast cnductin. If they were nt, t achieve the same transmissin speed, the nerves wuld have t be much larger in diameter. In fact, yur head wuld have t be the size f a beach ball! Multiple Sclersis What happens in yur bdy if yu have Multiple Sclersis? This is an autimmune disease, which means yur bdy attacks itself. In multiple sclersis the cre resistance f yur nerves is nt affected. Accrding t what yu have learned in this lab, describe the type f damage that ccurs t a persn's nervus system as a result f having Multiple Sclersis. Hw might this cause AP signal transmissin t be slwed r fail. Refer t the Figure 10 belw fr a hint. Cnsider hw the space cnstant fr the passive vltage spread dwn the axn might be affected in the internde regin. Figure 10. Science has nt figured ut hw t cure this disease. Hw culd stem cell research lead t a ptential cure fr this disease? The axnal membrane has many in channels thrugh which charged ins like sdium and ptassium flw. If we culd blck sme f these in channels with a drug, hw might this help MS patients? What electrical parameter f the membrane wuld be affected?

16 Appendix Figure 11. The Cable Transmissin Prject Bard Even thugh mst f the wrk dne in lab will cncern cnventinal electric circuits, the prject bard used was designed t emphasize the cnnectin between physics and bilgy. There are 3 main areas n the bard. At the tp and t the right is a diagram f a multiplar neurn. This is the type f neurn called a mtr neurn that is used t carry signals t muscles. When activated, these neurns cause muscles t cntract. On the left side f the bard in the large circle is a detailed diagram f a sectin f the cell bdy and the circuit that describes the actin ptential. The cell bdy is where the neurn makes the decisin as t whether r nt it shuld fire an actin ptential. It will nt be used in this activity. At the bttm and t the right is a detailed diagram f a segment f axn. The axn is the structure that transmits the actin ptential generated in the cell bdy and carries it t the muscle. On the left side f this diagram is a symbl fr a battery. This is where yu will attach yur signal surce, a 9V dry cell battery. On the far right is an LED. The LED will be used as the signal that the circuit yu've cnstructed wrks. Study the diagram and see if yu can find any vltage dividers in the circuit between the battery and the LED. References: 1. Facts abut MS. (n.d.). Retrieved frm - See mre at: 2. h t t p : / / w w w. n l m. n i h. g v / m e d l i n e p l u s / m u l t i p l e s c l e r s i s. h t m l