Year 12 Physics EEI: Factors Affecting Electrical Resistance

8/19/2019 Year 12 Physics EEI: Factors Affecting Electrical Resistance

1/18

Year 12 Physics Extended Experimental Investigation: Draft Mr. Gillespie

he resistance to the !o" of electric c#rrent in a material can $e a%ected

$y geometrical and internal factors. he dimensions of material& s#ch as

the length and diameter& as "ell as resistivity& temperat#re and even

magnetism can a%ect the resistance of materials s#ch as metal "ires. he

aim of this experiment "as to investigate the e%ects that length& cross'

sectional area& resistivity and temperat#re have on metal "ires. he

resistances of di%erent materials "ere meas#red "ith m#ltimeters "hile

varying the fo#r varia$les. It "as fo#nd that there are distinct

relationships for length& cross'sectional area and resistivity(material& $#t

temperat#re "as inconcl#sive& as higher temperat#res "ere necessary

and not possi$le to prod#ce d#e to lac) of professional specialised

e*#ipment.

Phillip +oalheira 12P,.-1 pg. 1

Factors AfectingElectrical

By

Philli

p

Soalh

eira


2/18

Year 12 Physics Extended Experimental Investigation: Draft Mr. Gillespie

Introd#ction

he aim of this experiment "as to investigate the e%ects that length&

cross'sectional area& resistivity material/ and temperat#re have on theresistance of certain materials& in this case& copper& constantan and

nichrome "ires. 0or this experiment& the form#lae $elo" "ere re*#ired.

he follo"ing research *#estions needed to $e devised so that a f#ll

#nderstanding of ho" the chosen factors a%ect resistance& and ho" they

co#ld $e meas#red:

1. ,o" does temperat#re a%ect resistance2. ,o" can the a%ect that temperat#re has on resistance $e

meas#red. ,o" sho#ld the m#ltimeter settings $e interpreted

1. V = IR

2. R= ρ l

A

. ρT = ρi(1+α ∆T )

3. RT = Ri (1+α∆T )

RT 4 resistance at temperat#re

/

Ri 4 initial resistance

ρT 4 resistivity at temperat#re

/ ρi 4 initial resistivity

l 4 length

5 4 cross'sectional areaα

4 temperat#re coe6cient∆T 4 temperat#re di%erence

Phillip +oalheira 12P,.-1 pg. 2


3/18

he follo"ing points are the hypotheses for this experiment:

• he greater the length of a material& the greater its resistance.

• he greater the cross'sectional area of a material& the lesser its

resistance.

• he greater the resistivity of a material& the greater its resistance.

• 5n increase in voltage may ca#se a slight increase in resistance d#e

to the temperat#re increase.

he resistance of a metal is the collisions that the positive ions in its

lattice str#ct#re have against the !o"ing electrons of an electric charge

7ohn 8#tnell& 2--9/. Increasing the length of an o$ect increases the

n#m$er of positive ions and the chance of collisions along the o$ect.

Increasing the cross'sectional area decreases the chance of collisions as it

increases the space for the c#rrent to avoid the positive ions. 5s all metalsdo not have the same lattice str#ct#re& they have di%erent resistivities&

depending on "hat material the o$ect is made from ;ichard


4/18

Method = E*#ipment

• m#ltimeters "ith resistance& voltage and c#rrent settings/& "ith

connecting "ires• Metal "ires> to test for resistance

o 8oppero ?ichrome alloy #s#ally consisting of @-A nic)el and 2-A

chromi#m/o 8onstantan alloy #s#ally consisting of BBA copper and 3BA

nic)el/

• 8rocodile clip connecting "ires

• 1 room temperat#re thermometer

• Po"er pac) -'1BC/& alternating c#rrent

• 1 pair of "ooden tongs• 1 pair of metal tongs

>?ot $raided& solid& single strand& not ins#lated& "idths 1.21mm?ichrome and 8onstantan/ and -.13mm 8opper and 8onstantan/& 1mof each "idth of each type of "ire.

1 he circ#it "as set #p as sho"n in 0ig#re 1 the ohmmeter clips as farapart as the length $eing tested/.

1 he approximate room temperat#re as indicated $y thermometer "asrecorded.

2 he resistance of the "ire "ith the po"er pac) t#rned o% "asrecorded no voltage& no c#rrent/. his "as done times& resettingthe circ#it after each time.

he circ#it "as reset& the c#rrent t#rned on alternating c#rrent only&no direct c#rrent/& and the voltage t#rned #p to B volts.

3 he resistance in the "ire and c#rrent thro#gh the circ#it "ererecorded. his "as done times& resetting the circ#it after each time.

0ig#re


5/18

B Caria$les for voltages of B& 1-& and 1B volts length for 1--& @-& F-&B-& 3- and 2-cm and cross'sectional area of -.13mm and1.121mm for constantan only/. 5ll "ire materials "ere #sed in trialsand all data "as recorded.

+afety and ;is) 5ssessments

5s s#ch small amo#nts of c#rrent& heat and voltage are $eing #sed in this

experiment there is not a great amo#nt of ris). ,o"ever& simple

preca#tions "ere carried o#t to ens#re that there co#ld $e no accidents.

he e*#ipment "as handled "ith care& especially the po"er pac) as it is

*#ite heavy& the experiments "ere done a"ay from "ater so#rces to

avoid cond#ction& and o$ects "ere handled "ith care and "ith metal and

"ooden tongs.

;es#lts

Colta

ge C/

8#rrent m5/

trials& mean and

variation


6/18

- - - ±

-

J @-- J J J -.

1.

-

1.

-

1.

-

±

-.1

B.- -.

-.

-.

2

-.

±

-.1

J J J J J 1.

2

1.

-

1.

-

1.

1

±

-.2

1-.- -.

1

-.

1-.

1

-.

1

±

-

J J J J J -.

-.

-.

-.

±

-

1B.- -.

1

-.

1

-.

1

-.

1

±

-

J J J J J -.

-.

-.

-.

±

-

- - - ±

-

J F-- J J J -.

@-.

@

-.

@

-.

@

±

-

B.- -.

2

-.

-.

2

-.

2

±

-.1

J J J J J -.

9

-.

9

-.

@

-.

9

±

-.1

1-.- -.

1

-.

1

-.

1

-.

1

±

-

J J J J J -.

-.

@

-.

@

-.

@

±

-.1

1B.- -.

1

-.

1

-.1

-.

1

±

-

J J J J J -.

@

-.

@

-.@

-.

@

±

-


7/18

- - - ±

-

J B-- J J J -.

F

-.

F

-.

F

-.

F

±

-

B.- 0.

0

0.

0

0.

0

- ±

-

J J J J J -.

F

-.

F

-.

F

-.

F

±

-

1-.- 0.

0

0.

00.

0

- ±

-

J J J J J -.

F

-.

F-.

F

-.

F

±

-

1B.- 0.

0

0.

0

0.

0

- ±

-

J J J J J -.

F

-.

F

-.

F

-.

F

±

-

- - - ±

-

J 3-- J J J -.

F-.

F

-.

F

-.

F

B.- -.

1

-.

1

-.

1

-.

1

±

-

J J J J J -.

F

-.

F

-.

F

-.

F

±

-

1-.- 0.

0

0.

0

0.

0

- ±

-

J J J J J -.

B

-.

F

-.

F

-.

F

±

-.1

1B.- 0.

0

0.

0

0.0

- ±

-

J J J J J -.

F

-.

F

-.B

-.

F

±

-.1


8/18

- - - ±

-

J 2-- J J J -.

-.

-.

-.

±

-

B.- -.

2

-.

2

-.

2

-.

2

±

-

J J J J J -.

-.

-.

3

-.

±

-.1

1-.- -.

2

-.

2-.

2

-.

2

±

-

J J J J J -.

-.

-.

3

-.

±

-.1

1B.- -.

2

-.

2

-.

2

-.

2

±

-

J J J J J -.

-.

-.

-.

±

-

a$le 1.2 K 8onstantan smaller "idth/

- - - ±

-

8onstantan 1--- -.3B9 -.FBF 3×

1-'@-.

-.

-.

-. ±

-

1B.- -.

1

-.

1

-.

1

-.

1

±

-

J J J J J -.

-.

-.

-.

±

-

- - - ±

-

J @-- J J J -.

@

-.

@

-.

@

-.

@

±

-

1B.- -.

1

-.

1-.

-.

1

±

-

J J J J J -.

@

-.

@-.

-.

@

±

-


9/18

1 @- - - ±

-

J F-- J J J -.

B

-.

F

-.B

-.

B

±

-.1

1B.- -.

1

-.

1

-.

1

-.

1

±

-

J J J J J -.

B

-.

F

-.

F

-.

F

±

-.1

- - - ±

-

J B-- J J J -.

B

-.B

-.

B

-.

B

±

-

1B.- -.

1

-.

1

-.

1

-.

1

±

-

J J J J J -.

B

-.

B

-.

B

-.

B

±

-

- - - ±

-

J 3-- J J J -.B

-.

B

-.

B

-.B ±

-

1B.- -.

1

-.

1

-.

1

-.

1

±

-

J J J J J -.

B

-.

B

-.

B

-.

B

±

-

- - - ±

-

J 2-- J J J -.

-.

-.

-.

±

-

1B.- -.

-

-.

--.

- ±

-

J J J J J -.

-.

-.

-.

±

-


10/18

-

a$le 1. K 8onstantan larger "idth/- - - ±

-

8onstanta

n

1--- -.BF1

-

-.@@9 3 ×

1-'@

-.

F

-.

F-.

F

-.

F

±

-

1B.- -.

-

-.

-

-.

-

- ±

-

J J J J J -.

F

-.

F

-.

F

-.

F

±

-

- - - ±

-

J @-- J J J -.

B-.

B

-.

B

-.

B

±

-

1B.- -.

-

-.

-

-.

-

- ±

-

J J J J J -.

B

-.

B

-.

B

-.

B

±

-

- - - ±

-

J F-- J J J -.

B

-.

B

-.

3

-.

B

±

-.1

1B.- -.

-

-.

-

-.

-

- ±

-

J J J J J -.

B

-.

B

-.

B

-.

B

±

-

- - - ±

-

J B-- J J J -.

3

-.

3

-.

3

-.

3

±

-

1B.- -.

-

-.-

- ±

-

J J J J J -.

3

-.3

-.

3

±

-


11/18

-.

-

-.

3- - - ±

-

J 3-- J J J -.

-.

-.

-.

±

-

1B.- -.

-

-.

-

-.

-

- ±

-

J J J J J -.

-.

-.

-.

±

-

- - - ±

-

J 2-- J J J -.

2-.

2

-.

2

-.

2

±

-

1B.- -.

-

-.

-

-.

-

- ±

-

J J J J J -.

2

-.

2

-.

2

-.

2

±

-

a$le 1.3 ' 8opper- - - ±

-

8opper 1--- -.3B9 -.FBF 1.F@

× 1-'@

-.

2

-.

2

-.

2

-.

2

±

-

1B.- -.

-

-.

-

-.

-

- ±

-

J J J J J -.

2

-.

2

-.

2

-.

2

±

-

- - - ±

-

J @-- J J J -.

1

-.

2

-.

2

-.

2

±

-.1

1B.- -.

--.

- ±

-

J J J J J -.

1-.

-.

1

±

-


12/18

-

-.

-

1

-.

1- - - ±

-

J F-- J J J -.

1

-.1

-.

1

-.

1

±

-

1B.- -.

-

-.

-

-.

-

- ±

-

J J J J J -.

1

-.

1

-.

1

-.

1

±

-

- - - ±

-

J B-- J J J -.1

-.

1

-.

1

-.1

±

-

1B.- -.

-

-.

-

-.-

- ±

-

J J J J J -.

1

-.

1

-.1

-.

1

±

-

- - - ±

-

J 3-- J J J -.

1

-.

1

-.

2

-.

1

±

-.1

1B.- -.

-

-.

-

-.

-

- ±

-

J J J J J -.

1

-.

1

-.

1

-.

1

±

-

- - - ±

-

J 2-- J J J -.

1

-.

1

-.

1

-.

1

±

-

1B.- -.

--.

- ±

-

J J J J J -.

1-.

-.

1

±

-


13/18

-

-.

-

1

-.

1

>Red bold text are mar)ed errors& see Disc#ssion

>>;esistivity val#es for each material o$tained from Giancoli& 1B/ andtemperat#re coe6cients o$tained from ?ave& 2-11/

-.1 -.2 -. -.3 -.B -.F -.9 -.@ -. 1

fx/ 4 -.1Fx L -.-3

; 4 -.93

fx/ 4 -.3x L -.1

; 4 -.2

fx/ 4 -.9Fx L -.13

; 4 -.3

fx/ 4 1.11x L -.1

; 4 -.@

Length vs. Resistance (no crrent!

?ichrome inear ?ichrome/

8onstantan& -.13mm "idth inear 8onstantan& -.13mm "idth/

8onstantan& 1.121mm "idth inear 8onstantan& 1.121mm "idth/

8opper inear 8opper/

Length ("!

Resistance

(#!

Graph 1


14/18

-.1 -.2 -. -.3 -.B -.F -.9 -.@ -.D 1

Length vs. Resistance o$ %ichro"e &ire' co"paring voltages

-C

BC

1-C

1BC

Length ("!

Resistance

(#!

>Error $ars "ere not incl#ded on graphs to avoid conf#sion and cro"ding of data&

it sho#ld $e noted that error is estimated to $e ± -.1 for any val#e on the y

axis of $oth graphs

Disc#ssion

5s indicated $y the graphs& "hich are $ased on the averages of sets of

three trials in a$le 1& most data seems to $e consistent "ith theory. 5sindicated $y 0orm#la 2 and proven in Graph 1& there is a distinct linear

Graph


15/18

relationship $et"een length and resistance& implying direct

proportionality. he relationship $et"een area and resistance can also $e

seen in Graph 1& $#t only in the t"o constantan data lines and points. he

constantan "ire "ith a lo"er cross'sectional area has a higher resistance&

and vice'versa& implying indirect proportionality $et"een the t"o. heresistivities of each material are represented& and almost proportional to&

the gradients of the trendlines in Graph 1. he order of resistivities from

largest to smallest "as the same order for trendline gradients from largest

to smallest. he trendlines are *#ite acc#rate& as displayed $y their linear

regressions a$ove -. 8opper $eing the only exception as there are only

t"o di%erent val#es and an acc#rate trendline is very di6c#lt to prod#ce/.

herefore& the resistance of the materials "ith larger gradients increases

m#ch more than those "ith lesser gradients as length decreases/&

implying that resistivity is also directly proportional to resistance.

he last varia$le& voltage& made very little change at all in resistance& as

sho"n in Graph 2 large points are #sed to ma)e overlapping clear/. his

relates $ac) to research *#estions 1 and 2& a$o#t ho" temperat#re a%ects

resistance and ho" it can $e meas#red. he !o" of c#rrent thro#gh a

material is the !o" of electrons& and these electrons and other particles

s#ch as positive ions vi$rate faster "ith a larger temperat#re. 5 larger

voltage ca#ses more electrons to move thro#gh the material& ca#sing

them to vi$rate faster. 5s the non'!o"ing ions and electrons vi$rate

faster& they ca#se more collisions "ith the !o"ing electrons& s#$tractingfrom their )inetic energy and ca#sing an event#al and grad#al increase in

resistance. ,o"ever& as the c#rrent increases& there are more electrons

passing thro#gh a point per second "ith more vi$rational energy& creating

more heat )no"n as 7o#le heating/& and possi$ly& increasing resistance.

5s all of the metals $eing #sed are cond#ctors and have positive

temperat#re coe6cients& this is the case for all of them Nn)no"n&

8ond#ctors = Ins#lators: emperat#re E%ects& 2-11/.

;esearch and early trials not incl#ded in a$le 1/ needed to $e completed

$efore experimenting co#ld $egin. 0irstly& an experiment had $een fo#nd

on the Nniversity of Massach#setts Ooston "e$site& in the physics section&

tal)ing a$o#t investigating hmQs a" Nn)no"n& Experiment ' hmRs

a"& 2--9/. It did give an idea of a "ay that the e%ect that temperat#re

had on c#rrent and resistance co#ld $e meas#red. he temperat#re&

c#rrent and resistance co#ld $e meas#red $efore and after the heating

too) place. It "as prefera$le to do this and s#$ect the "ires to higher

temperat#res to investigate the e%ect that temperat#re had on

resistance. ,o"ever& #se of s#ch e*#ipment& s#ch as a heating plate& "as

not possi$le d#e to time constraints& high ris)& and lac) of specialiste*#ipment. It "as also #n)no"n "hether changing the distance $et"een


16/18

the t"o m#ltimeter clips "o#ld $e the same as changing the length of the

"ire. Early trials of changing the distance $et"een the clips "ere done to

investigate "hether this "as the case& and the maxim#m and minim#m

resistance val#es indicated that changing the distance does have the

same e%ect as changing the length of the "ire. he maxim#m andminim#m val#es for resistance maxim#m resistance at maxim#m length

and vice'versa/ "ere as follo"s:

8onstantan -..13mm "idth/: -.@ ' -.2

8opper: -.2 ' -.1

?ichrome: 1.- ' -.2

,o"ever& the m#ltimeters #sed in this experiment "ere not acc#rateeno#gh to meas#re signiScant di%erences in c#rrent& and co#ld not

meas#re in more than 1 decimal point 2 signiScant Sg#res/ for milliamps.

5lso& a change in temperat#re re*#ires m#ch larger changes in c#rrent&

and very small amo#nts of c#rrent "ere availa$le to $e #sed in this

experiment& not even exceeding 1.B milliamps. 5s indicated $y research

*#estion & it "as #ns#re of ho" to interpret the m#ltimeter "ith the

vario#s settings. 5s it is not a very advanced scientiSc process& no

information a$o#t this "as fo#nd in any o6cial #niversity physics "e$sites

or text$oo)s& $#t an instr#ctional article "as fo#nd on e,o".com&explaining the di%erences $et"een the m#ltimeter settings +chanaman&

Nn)no"n/.

D#e to the m#ltimeter $eing very imprecise& the error margin cannot $e

estimated to $e very large& approximately ± -.2 milliamps for c#rrent

and ohms for resistance/. here "ere other errors in the trials tho#gh. he

red text in ta$le 1.1 ?ichrome data/ sho"s "here another m#ltimeter "as

#sed to meas#re c#rrent. 5fter some trials& it "as realised that the c#rrent

sho#ld have $een at least -.1m5& so it "as replaced "ith the m#ltimeter$eing #sed $efore& and res#lts "ent $ac) to expectations. 8learly& the

other m#ltimeter "as fa#lty. It sho#ld also $e noted that the data val#es

do not St exactly into the form#lae. his is pro$a$ly d#e to the

interference made $y the m#ltimeters& as the clips are made of metal& and

therefore& may a%ect the resistance and c#rrent readings& ma)ing it nearly

impossi$le to get acc#rate data. Despite this& the e%ects that the

investigated varia$les have on resistance are still *#ite visi$le& even if the

val#es are not exactly correct.


17/18

he room temperat#re "as constant at approximately 2.BH8& ± -.BH8.

5s stated $efore& this di%erence of .BH 8 the room temperat#re min#s

the temperat#re for "hich resistivities are calc#lated& 2-H8/ did not ma)e

a signiScant di%erence in resistance. he calc#lations on the next page

sho" ho" small the di%erence $et"een the initial and Snal resistances

"o#ld $e for the copper "ire of 1m length and 1.121mm "idth& in theory.


18/18

area and resistivity "ere fo#nd& $#t voltage(temperat#re remained inconcl#sive

d#e to lac) of far more advanced e*#ipment. ength and resistivity are indeed

directly proportional to resistance& "hereas cross'sectional area is indirectly

proportional. If this experiment "ere to $e done again& it "o#ld $e prefera$le to

have a m#ch larger maxim#m voltage and temperat#re& $#t this is not possi$le

in a high school physics la$oratory d#e to lac) of e*#ipment and ris).Nnfort#nately& not all the data can $e deemed precise or correct& as the

m#ltimeters #sed "ere not acc#rate eno#gh and did not go to eno#gh signiScant

Sg#res. o get acc#rate data in an experiment s#ch as this& either larger val#es

for voltage& c#rrent& and resistance sho#ld $e #sed& or m#ltimeters that can

acc#rately and precisely meas#re lo" val#es of these.

Oi$liography

Giancoli& D. 1B/. Physics. Prentice ,all.

7ohn 8#tnell& T. 7. 2--9/. Physics. Illinois: 7ohn

Year 12 Physics EEI: Factors Affecting Electrical Resistance

Documents

Transcript of Year 12 Physics EEI: Factors Affecting Electrical Resistance