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Carla%Maye%Garcia%Acepcion%
003544;0001%

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IB%HL%Physics%

!
An!experiment!to!investigate!how!the!length!of!a!copper!wire!
affects!its!resistance!

!
Research!Question:!
!

How% does% altering% the% length% of% a% constantan% wire% by% 0
...
%Ohm’s%law%states%that%
when%the%temperature%is%kept%constant,%the%current%through%a%metallic%conductor%is%
€
proportional%to%the%potential%difference%across%it,%R α V, and%inversely%proportional%
to%the%current,%R α

1

...
%
%
Aim:%
%
The% aim% is% to% determine% how% the% length% of% a% constantan% wire,% a% metal% alloy%
composed%of%60%%copper%and%40%%nickel%(Maheshwari,%2006),%altered%10%times%by%
increments%of%0
...
100m,%0
...
300m,%0
...
500m,%0
...
700m,%
0
...
900m%and%1
...
%
%

%

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IB%HL%Physics%

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Hypothesis:!%
%
As%a%result%of%altering%the%wire’s%length,%resistance%will%be%proportional%to%length, R
α L,% increasing% as% length% increases,% and% decreasing% as% length% decreases
...
% The% longer% the% wire% is,% the% more% atoms% there% will% be% within% it% for% the%
electrons% to% collide% with,% increasing% the% number% of% collisions% and% therefore%
resistance%through%the%wire
...
100m
...
100m,% 0
...
300m,% 0
...
500m,% 0
...
700m,% 0
...
900m% and% 1
...
000±0
...
%The%wire%will%be%kept%straight%using%blu%tac%in%
order% to% ensure% precise% measurement
...
000m% then%
decreased%to%the%next%smaller%value%until%all%lengths%have%been%tried
...
%%
%

Dependent!Variable:!
%
The%dependent%variable%is%the%resistance%of%the%wire
...
% Current% I% at% each% length% will# be% measured% using% an%
I

ammeter%with%an%uncertainty%of%±0
...
%
Potential% difference% V% will% be% measured% using% a% voltmeter% with% an% uncertainty% of%
€
±0
...
0V% display
...
0V% (see% controlled%
variables)
...
1 0
...
0
I '
%
For%example,%if%I#=#0
...
01A%then%resistance%will%be%calculated%as%follows:%
%

# 0
...
01&
ΔR = R%
+
(
$ 3
...
1 0
...
00%
+
(%
$ 3
...
50 '
R = ±0
...
0
%
R=
0
...
00Ω
R=

%

∴ R = 6
...
32Ω %
±
!
Controlled!Variables:!!
%
!

How!variable!will!be!

Possible!affect!on!data!if!

Variable%

controlled!and!

not!controlled%

measured%
%

%

%

%

The%same%sample%of%

Different%materials%of%wire%

%

nichrome%wire%will%be%

may%vary%in%conductivity
...
%There%is%no%

ensures%that%the%wire’s%

specified%uncertainty%

resistivity%( ρ )%is%

associated%with%the%

controlled%and%therefore%

material;%the%

the%resistance%calculated%

Material%of%wire%

manufacturing%of%the%wire% will%accurately%reflect%

%

4%

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will%be%trusted
...
%

%
%
%
%
%
%
%
€
Wire%Gauge%%
(Cross%Sectional%Area)%

%

%

The%same%sample%of%

Cross%sectional%area%is%

4
...
%

experiment
...
%

sectional%area,%R α

1
,%
A

meaning%it%would%directly%
affect%the%calculation
...
%%

%
%
%
%
%
Temperature%

%

%

The%environment%in%which% Higher%temperature%
the%investigation%will%be%

means%more%atomic%

carried%out%will%be%kept%at%

vibrations,%essentially%

room%temperature;%

increasing%the%atoms’%

24±1°C%using%the%air%

kinetic%energy,%resulting%in%

conditioning%system
...
%

will%be%left%between%trials%

Without%controlling%

to%prevent%the%wire%from%

temperature,%Ohm’s%law%

heating%up%(see%below%for%

(R%α%V)%does%not%apply
...
%%
%
%
%
%
Time%

%

%

Since%the%wire%heats%up%as%

Higher%temperature%

the%current%moves%

means%more%atomic%

through%it,%an%interval%of%

vibrations,%essentially%

10s%where%the%battery%is%

increasing%the%atoms’%

turned%off,%measured%out%

kinetic%energy,%resulting%in%

using%a%stopwatch%with%

an%increase%in%collisions%

uncertainty%±0
...
%
left%between%trials%to%
ensure%that%the%wire%does%

temperature,%Ohm’s%law%

not%overheat
...
%

%

%

The%potential%difference%

If%not%controlled,%the%

will%be%controlled%at%3
...
1V
...
%%

!
Materials!List:!
!
•

Variable%voltage%power%supply,%set%at%%6V%x1!

•

Circuit%wires%x6!

•

Voltmeter%±0
...
01A%x1!

%

6%

Carla%Maye%Garcia%Acepcion%
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IB%HL%Physics%

•

Variable%resistor%x1%!

•

4
...
000m%x1!

•

Alligator%clips%x2!

•

Meter%stick%±0
...
001s%x1%%

•

Blu%tac%(optional%but%recommended%in%order%to%keep%wire%straight%and%still)%

!
Diagram(s):!
#
Diagram#1:#Full#labeled#diagram#
#
#

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#
Diagram#2:#Live#set#up#
#

#

!
Method:!
!
Part#A#–#Setting#up#
#
1
...
%Connect%2%wires,%1%positive%and%1%negative%to%the%
appropriate%ports%
2
...
Connect%another%negative%wire%with%an%alligator%clip%to%the%unoccupied%end%of%the%
variable%resistor
...
%
4
...
%%
5
...
%Add%an%alligator%clip%to%the%unoccupied%
end
...
%
%

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6
...
0V
...
Add%the%voltmeter%to%the%circuit%by%connecting%the%negative%wire%to%the%alligator%
clip%coming%from%the%variable%resistor,%and%the%positive%wire%to%the%alligator%clip%
coming%from%the%negative%wire%from%the%ammeter
...
Using%the%meter%stick,%measure%out%1
...
%
9
...
Use%blu%tac%to%secure%both%ends%of%the%copper%wire%to%ensure%it%is%kept%straight%
throughout%the%investigation%%
11
...
000m
...
Attach%the%other%alligator%clip%to%the%other%end%of%the%constantan%wire
...
000m%or%0
...
%%
13
...
0V%
14
...
00s%for%circuit%to%cool,%using%the%stop%
watch,%before%commencing%part%B%
Part#B#–#Data#Collection##
15
...
100m%
16
...
100m%
17
...
After%5s,%record%current%displayed%on%ammeter%in%table%(sample%table%1%shown%
below)
...
%
19
...
00s%to%allow%circuit%to%return%to%room%tempterature%
20
...
%%
21
...
200m,%0
...
400m,%
0
...
600m,%0
...
800m,%0
...
000m)%

%

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Part#C#–#Calculation#
%
22
...
Outliers%will%be%redone%and%if%still%inconsistent,%eliminated%from%the%taking%of%
average
...
Using%Iaverage%values,%calculate%resistance% R =

V
I Average

%and%record%in%table%(sample%

table%shown%below)%
25
...
1V 0
...
0V + I
(
$
Average A '
€
%
Sample#table(s)#for#data#collection:#
%
€
Average!Current,!IAverage,!
Length,(
Current,(I,#±0
...
01A!
L,(
(
(
(
(
(
T +T +T +T +T
±0
...
100!
!
!
!
!
!
!
0
...
300!
!
!
!
!
!
!
0
...
50!
!
!
!
!
!
!
0
...
700!
!
!
!
!
!
!
0
...
900!
!
!
!
!
!
!
1
...
1V 0
...
0V I
)
%
Average A (

!
!
!
!
!
!
!
!
!
!

€

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!
Data!Collection:!
!
Table#1:#Table#to#show#how#the#length#of#a#constantan#wire,#±0
...
01A!
Length,!
L,!
Trial!
±0
...
01A!

T1 + T2 + T3 + T4 + T5
5
2
...
36 + 2
...
36 + 2
...
100%

2
...
36%

2
...
36%

2
...
200%
0
...
400%
0
...
600%
0
...
800%
0
...
000%

1
...
02%
0
...
64%
0
...
48%
0
...
37%
0
...
45%
1
...
80%
0
...
54%
0
...
42%
0
...
33%

1
...
02%
0
...
64%
0
...
48%
0
...
37%
0
...
45%
1
...
80%
0
...
55%
0
...
42%
0
...
33%

1
...
02%
0
...
65%
0
...
48%
0
...
37%
0
...
36%
1
...
02%
0
...
64%
0
...
48%
0
...
37%
0
...
0
R=
2
...
27%
2
...
94%
3
...
69%
5
...
25%
7
...
11%
9
...
1V 0
...
0V + I
)
%
Average A (

%
!
$ 0
...
01A '
)
ΔRΩ = RΩ&
& 3
...
1V 0
...
0V 2
...
05%
±0
...
13%
±0
...
23%
±0
...
34%
±0
...
49%
±0
...
001m&affects&resistance,&Ω&within&a&circuit%
%

Graph&to&show&how&the&length&of&a&constantan&wire,&±0
...
00%

Max:%R%=%(9
...
29Ω%

Resistance&of&Constantan&Wire,&R,&±∆RΩ&

9
...
00%
7
...
60Ωm01)L&+&0
...
00%
5
...
00%
3
...
94Ωm;1)L%+%0
...
00%
1
...
00%
0
...
100%

0
...
300%

0
...
500%

0
...
700%

0
...
900%

1
...
100%

Length,&L,&±0
...
09Ω −1
...
000m − 0
...
68Ωm-1
m=

(0
...
27Ω)
(1
...
09Ω) %

%

€

%
%
Conclusion:*
%

€

Table% 1% and% graph% 1% illustrate% the% results% of% the% experiment
...
%Graph%1%shows%resistance%against%length%or%
R
ρL
where R is resistance, ρ% is% the% wire’s%
= ρ A ,% rearranged% from% the equation, R =
L
A

resistivity,%L%is%the%length%and%A%is%the%cross%sectional%area
...
% Again,% this% is% due% to% the% increased% amount% of% collisions%
between% the% wire’s% atoms% and% electrons% as% more% of% the% wire% is% introduced% to% the%
circuit
...
60Ωm −1 ) L + 0
...
40Ωm −1 ) L + 0
...
94Ωm −1 )L + 0
...
% The% accepted% textbook% resistivity% ρ %for%
constantan%is%5
...
%This%cannot%be%directly%compared%
to% the% results% as% units% are% Ωm;1,% not% Ωm
...

A
L

%

€

All%best%fit%lines%do%not%have%a%y;intercept%of%exactly%0
...
%To%have%the%y;intercept%=%
€
0
...
% Theoretically,% if% R α L then

%

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when L = 0
...
00Ω
...
%
%
%
ρL
R=
A
ρ (0m)
%
0Ω =
A
=0
%

%
R
= ρA
L
0Ω
= ρA %
0m
=0

Using%the%original%equation%used%to%calculate%resistance,% R =
R=

V
:%
I

V
I

0Ω =

3
...
0V
=I
0Ω
=0
%
∴ Solution%is%null%and%theoretically%impossible%to%have%exactly%R=%0
...
000m%if%R%is%entirely%directly%proportional L
...
%
Therefore,%the%point%at%which%R=%0
...
000m%has%been%left%out%of%the%data%
and%calculations
...
35Ω%for%the%best%fit%line,%0
...
44Ω% for% the% minimum% line,% which% averages% out% to% be% about% 0
...
05Ω%
(calculations%shown%below)
...
53− 0
...
12

0
...
29 + 0
...
39
%
%

∴0
...
12Ω %
%

%
Although%R≠%0
...
000Ω,%it%is%still%appropriate%to%say%that%R α L%because%
length% when% increases% by% 0
...
88±0
...
%
%
Average%increase%in%resistance:%
%
0
...
87 + 0
...
94 + 0
...
80 + 0
...
97 + 0
...
88
%
%
∴0
...
09Ω %
%
%

%

%
0
...
80
%
2
= 0
...
%Heating%
leaving%a%period%of%
the%circuit%increases%
60
...
001s%measured%out%
the%wire’s%kinetic%
by%stopwatch%in%between%
energy,%and%therefore%
trials%to%let%the%wire%cool
...
%Thus,%the%
improve%upon%this%
need%to%keep%the%wires’%
uncertainty,%temperature%can%
temperature%as%
be%more%rigorously%
constant%as%possible
...
%%
measured%after%every%
trial,%only%monitored%
by%leaving%a%
10
...
001s%interval%
between%trials
...
% Energy%
calculated%using%the%formulae%

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Carla%Maye%Garcia%Acepcion%
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resistor,%the%voltage%

%

IB%HL%Physics%

would%not%be%kept%

V2

...
0V × 2
...
08W

for%resistance
...
%
I

Systematic% The%potential%difference%was%
controlled%to%be%3
...
1V%
using%a%variable%resistor%and%
measured%using%a%voltmeter%
of%±0
...
%By%using%a%
voltmeter%that%reads%to%a%
more%precise%value,%to%at%
least%±0
...
%Aside%from%

€

this%improvement,%however,%
because%this%variable%was%
kept%constant%across%all%trials,%
this%uncertainty%can%be%
considered%less%significant,%if%
not%negligible
...
01A%can%be%further%

affect%the%total%circuit’s%

improved%again%by%using%an%

total%resistance%

ideal%ammeter%with%a%more%

(without%the%variable%

%

current%with%an%uncertainty%

precise%reading,%for%example,%

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Carla%Maye%Garcia%Acepcion%
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resistor
...
001A
...
%%

*

%

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IB%HL%Physics%

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Bibliography*and*References:*
*
Maheshwari,%P
...
%Electronic'components'and'processes

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