Determination Determination of ohmic relations between current, current, voltage, and resistance resistance by constant variable approach and classification of ohmic properties of various conductors and wire resistance of wires of various dimensions and material Jessica T Cahoy1, Frederic James V Espiritu!, and Jamie " Tomilloso1 1 Department of Industrial Engineering, Engineering, University University of the Philippines, Philippines, Diliman, Diliman, Quezon Quezon City 2 Department of of Mehanial Engineering, Engineering, University University of the Philippines, Diliman, Diliman, Quezon Quezon City *Corresponding author:
[email protected] [email protected] m
#bstract Voltage, current, and resistance make up the very foundation of ho circuits ork. !hus, a good understanding of such concepts is crucial in the study of electrici electricity. ty. !his e"perimen e"perimentt aimed aimed to e"plore e"plore relations relationships hips #eteen #eteen these these $uantities as ell as the uni$ue properties of each #y means of proper methods of measuring using long ires, #ul#s, ohmmeters, ammeters, ammeters, and voltmeters and analy analysis sis of plots plots involv involving ing the three three $uanti $uantitie ties. s. %ocus %ocus as also also given given to additiona additionall supplemen supplementary tary concepts concepts such as resistiv resistivity ity and &hmic &hmic properti properties. es. 'enera 'enerally lly,, it as proven proven from from resul results ts that that the voltag voltagee is indeed indeed direct directly ly proportional to current and resistance. (lso (lso it as concluded that resistance as indirectly proportional to ire cross)sectional area #ut directly to ire length and resistivity. eyords: ohm, voltage, current, resistance, resistivity
1$ %ntroduction !he e"periment as performed as partial fulfillment of the re$uirements for +hysics -.. Complete instructions and detailed procedures ere already provided #eforehand, leaving the authors ith just the e"ecution of the actual e"periment itself and post e"periment analyses. !hus, it follos that no dedicated research and sourcing ere necessary from the authors prior to the e"perimentation e"perimentation proper. /ith regards to similar orks #y other authors, it is greatly anticipated that this very e"periment has had multiple similar replications -121 and closely related variations 41, not to mention that it itself is more or less also a replication of a previously done ork. 3nlike most investigatory projects and research papers, this particular e"periment had differently oriented oriented o#jectives the most important #eing the e"posure and education of student scientists for #etter comprehension of scientific concepts. !he e"periment did not re$uire the heavy use of operational terms for the most part. !echnical terms that ere utili5ed included voltage, current, resistance, and resistivity. Current is defined to #e the amount of charge passing through a given area at a given time. 6imply put, it is the flo of electrical charge carriers and its unit of measurement is (mperes 7(8. Voltage on the other hand is technically knon as the electric potential difference #eteen to points in a circuit. 9t can #e seen as the strength of the flo of electric charge carriers and has a unit measurem measurement ent of Volts Volts 7V8. esistanc esistancee is knon to #e the property property of certain certain materials materials to oppose or resist resist the amount of charge carriers passing through it in a given time and it has a unit measurement of &hms 7 Ω). esistance is determined #y the inherent resistive properties of conductors hich is knon as resistivity. !he first three concepts can easily #e related and their #asic functions e"plained #y the ater pipe analogy, here the flo of ater corresponds to current, the pressure to voltage, and the girth to the inverse of resistance.
$ ðodology !omplete desription of e"perimental set#up$!inlude diagrams of apparatus$!steps employed$!mathematial and statistial methods used$!P% used$!P%&%'&%P( )*&M D%+ D%+ E$ E$
'$ (esults and discussion !figures and graphs *-.$!lahat ng data ta/les sa appendi" I 0(I-$!disuss e"peted and atual results$!use logial reasoning$!sho ho ov3etives are met$
1
Voltag e 7Volts8
f(x) = 3.13x + 0.08 Data R² = 0.97 Linear (Data) 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
Current 7milli(mperes8
%igure / +lot of voltage versus current for the ire as indicated #y !a#le /-
0.95
Current 7(mperes8 0.45 Data 0.3
f(x) = 1.03x + 0.12 R² = 0.96 Linear (Data) 0.4 0.5 0.6 0.7
0.8
;resistance 7;&hms8
%igure /- +lot of current versus reciprocal of resist ance of the ire as indicated #y !a#le /2
3
Voltage 7Volts8
2 1 Data 1.25
f(x) = 0.66x + 0.24 R² = 0.96 Linear (Data) 1.75 2.25 2.75
3.25
esistance 7&hms8
%igure /2 +lot of voltage versus resistance of the ire as indicated #y !a#le /4
esistance 7&hms8 Data
90
f(x) = 0.01x - 0.08 R² = 1 Linear (Data) 110 130 150 170 190
210
%igure /4 +lot of ire resistance versus ire length as indicated #y !a#le /4
9
Voltage 7Volts8
4 -1 Data -2
f(x) = 0.23x - 0.94 R² = 0.97 Linear (Data) 3
8
13
18
23
28
Current 7milli(mperes8
%igure /> +lot of voltage versus current for the light #ul# as indicated #y !a#le />
2
In measuring its resistane, the ire as onneted to the ohmmeter using onnetors made of opper ire4 Do you thin5 this ontri/uted to the deviation /eteen the resistane omputed from E6uation !2$ and the measured resistane !0a/le +1$7 E"plain4 (lthough it can?t certainly #e said that this is the sole reason for the deviation, the use of copper connectors in measuring reactance may have contri#uted to the said inconsistency due to the significantly loer resistivity constant of copper at -0 degrees centigrade 7."0 )8 than that of the 'erman nickel 72.20"0 )8 , hich as later found out to #e the material composing the conductive ire su#ject to e"perimentation. Comment on the linear fit o/tained for eah of the urves in )igures +1, +2, and +84 (o ell do these urves onform to their respetive /est#fit lines7 +hat does this imply7 9t can #e o#served that the linear fit of each graph very closely estimates their corresponding curves. !his conformation #eteen the curves and #est fit lines suggest that there is little deviation #eteen the measured values and the e"pected linear relation given #y the e$uation VA9. !his implies that form #oth calculations and e"perimentation, it can #e concluded that there is a linear relationship #eteen voltage and current and resistance. 0he slope and the y#interept in )igures +1, +2, and +8 represent ertain 6uantities in the e"periment4 In the folloing ta/le, rite don the values of the slope and y#interept, the 6uantities they represent, the e"peted values of these 6uantities, and the perent deviation4 Inlude all orresponding units4
%igure / //2
!a#le +ercent deviation of plot elements from e"perimentation and calculations Corresponding $uantity B"perimental value B"pected Value Dev slope y)int slope y)int slope y)int slope y)int resistance voltage @ 0( 2.22> 0.0>4 -. 0 .E 0.> emf;voltage .024E 0.E2 . 0 2E.0. current @ ∞Ω current voltage@ 0Ω 0.F>> 0.-44 0.F 0 E.2 0.-4
9n / 7voltage vs. current8, the e$uation of the graph is yA2.22>"G0.0>4. !he slope hich is 2.22> represents the material?s resistance, hile the y)intercept, 0.0>4 represents voltage hen there current is not present. Having an e"pected resistance of -. I, e can get a percent deviation of .E. 2.8
−3.1335 2.8
× 100=11.91
9n /- 7current vs. reciprocal of the resistance8, the e$uation of the graph is yA.024E"G0.E2. !he slope hich is .024E represents the Blectromotive force of the circuit, hile the y)intercept, 0.E2 represents current hen there is infinite resistance. Having an e"pected voltage of . V, e can get a percent deviation of 2E.-. 1.7
−1.0349 1.7
× 100=39.12
9n /2 7voltage vs. resistance8, the e$uation of the graph is yA0.F>>"G0.-44. !he slope hich is 0.F>> represents the current of the circuit, hile the y)intercept, 0.-44 represents voltage hen there is no resistance. Having an e"pected voltage of 0.F(, e can get a percent deviation of E.2. 0.6−0.6558 0.6
× 100 =9.3
Calulate the resistivity 9 from )igure +: and ompute the perent deviation of this value from that o/tained in 0a/le +14 ;ho all alulations /elo4
dy R ρ dyA = = ρ= = ( 0.0143 ) ( 1.9634 × 10−7 )= 2.807 × 10−7 dx l A dx
3
|
−7
¿ 2.749 × 10
|∨
¿
−7
− 2.807 × 10
−7
2.749 × 10
× 100=2.1
%deviation =¿ Desri/e the shape of the voltage versus urrent plot of the light /ul/ !a$ /efore it starts to radiate and !/$ after it has /egun to radiate4 Compare this ith the voltage versus urrent plot of the resistane ire4 Does the light /ul/ o/ey *hm
)$ Conclusions !hat as proven in the e"periment$!highlight the most important ontri/ution of this paper, lol$!reommendations# suggestions on ho to redue error and other /asi onepts$
#c*nowledgements /e ould like to acknoledge the Lational 9nstitute of +hysics for alloing us to utili5e their la#oratories and e$uipment, ithout hich the e"periment ould not have #een possi#le. /e ould also like to recogni5e 6ir Denny
(eferences . %reedman ( M Noung HD 7-0-8. University physis ith modern physis 18 e4d . California:+earson Bducation 9nc. -. =63 +hysics and (stronomy Department 7-028. B"periment -, +hysics ->- -;McntA-
#++ED%!a#le /. =easured and calculated parameters for resistivity and resistance Trial Diameter of wire .m/ Temperature .Celsius/ )4 >"0 -. )4 >"0 -E 2 >"0)4 -.E Jest Bstimate >"0)4 -.E !a#le /.- =easured properties of the ire Cross0sectional area .m / "ength of wire .m/
4
.EF24"0) -
-.
(esistivity .hm meter/
!a#le /.2 Deviation of calculated from measured resistance (esistancecalculated (esitancemeasured 2.224 -.
R=
ρL A
ρ=
Q
AR L
2 deviation
¿ 3.30 × 10− (1 + 0.0004 ( 28.9 −20 ) ) 7
( 1.9634 × 10− )( 2.8 ) 7
ρ =
−7
2
¿ 3.3117 × 10
7'erman nickel8
( 3.3117 × 10− )( 2 )
−7
¿ 2.749 × 10
7
R=
ρ ( T )= ρ 20 ( 1 + α ( T − 20 ℃ ) )
−7 1.9634 × 10
R=3.3734 Ω
5
Voltage 0.> 0.F 0. .0 .4
"ength .cm/ -00 0 F0 40 -0 00
"ength .cm/ -00 0 F0 40 -0 00
Voltage 0 0. 0.0.2 0.4 0.> 0.F 0. 0. 0.E
!a#le /- Voltage versus current through the ire Current +arameters held constant 0. 0.E esistance: -. ohms 0.- 0.2 -. 0.2> 0.>> -.> 0.400 0.> -.0.4>> 0.F> .E 0.>-F Voltage: . volts 0..F 0.F-> 0.E .4 0.4 !a#le /4 Voltage versus resistance across the ire Voltage (esistance +arameters held constant -. -. . -.> . -..F .E Current: 0.F amperes .2 .F . .4 !a#le /> Voltage versus resistance across the light #ul# Current Voltage 0.-E .0 2.2 .> 4.0 -.0 >.> -.> F.-E 2.0 F.E0 2.> .E 4.0 . 4.> .FF >.0 E. *
Current E.F4 .E2 4.0 >.> .>> E.-0 -.F0 -2.00 -4.20
