Measuring the Resistivity of a Wire

Measuring the Resistivity of a Wire

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Measuring the Resistivity of a Wire

Aim

The aim of this experiment is to find out how the area of the cross
section of the wire affects the resistance and also to find out the
resistivity of the wire having found the resistance over a certain
length and using a certain cross sectional area. I will also
experiment to see how the length of the wire affects the resistance.

Plan

The first thing that I will do is to set up the apparatus as shown
below.

A,V


Except for the experiment where I alter the length, I will keep the
length of the wire constant throughout the experiments and only change
the diameter of the wire. For each width I will record the p.d. and
current displayed on the voltmeter and ammeter. I will then use these
values to calculate the resistance of the wire at that length using
the formula:

[IMAGE]V = IR or R = V (where V = p.d., I = Current, and R =
Resistance)

I

I will then find the cross sectional area of the wire. To do this I
will find the diameter of the wire using a micrometer. Then I will
find the area of the cross section by using the formula:

Area = πr² (where A = Area of cross section, π = pi, and r = radius)

Once I have this value I will be able to calculate the resistivity of
the wire by substituting the values into this formula:

R=rl or r= RA (where A = Area of cross section, R = Resistance, l =

[IMAGE][IMAGE] A l length, and r= resistivity)

I will repeat this for all of the different diameters that I will test
but will remember to keep the length of the wire the same throughout.

The apparatus that I will use for this experiment are listed below:

· Power supply - This will be 3V of power and will be used to power
the circuit so that I can measure the resistance of the wire.

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Related Searches



· Voltmeter - To measure the p.d. in the circuit to then find out the
resistance. This is accurate to 0.01V.

· Ammeter - To measure the current in the circuit to then find out the
resistance. This is accurate to 0.01A.

· Nichrome wire - This is the material that I will be testing on in
wire form; ultimately I am trying to find its resistivity.

· Ruler - To measure the length of the wire that I am testing. This is
accurate to 1mm.

· Micrometer - to measure the diameter of the wire and then be able to
find the area of the cross-section. This is accurate to 0.01mm.

· Variable resistor - to give me more results for each to give me an
idea of accuracy.

· Switch - so that the power is not constantly running through the
circuit thus causing the wire to heat up.

During this experiment I need to be aware of the safety element of it
and therefore prevent any possible hazards before they can occur. As
there is electricity involved I will ensure that the experiment is set
up away from any water or other aquatic conductors. I will make sure
that the power supply does not exceed 3V so as not to have a dangerous
current flowing through it. I will also wear safety goggles to protect
my eyes as there is a possibility of the wires snapping. There is also
a chance of the wire becoming very hot but to prevent this happening I
will put in a switch so that the power is not constantly on.

I will also use a variable resistor that I will use to get different
values for the voltage and current for each wire. This will allow me
to collect more results and have a sufficient amount to plot the
relevant graphs.

To make sure that this experiment is a fair test I will use the same
length of wire for all of my repetitions so that I can compare the
results fairly. I will also keep the temperature in the room as
constant as possible as I know that the temperature can affect the
resistance in a wire. The power supply will not exceed 3V as this a
large supply may also cause the temperature inside then wire rise thus
affecting the resistance. I will also use a switch so that the power
will not be running when I do not require it to.

Results

I will now display the results that I found. This will be shown in
tables of results for each SWG followed by a graph of voltage verses
Current to determine the resistance of that particular wire. Firstly
however, I will show my results for varying the length of the wire.
This will be shown in a table and then a graph plotting the length
against the resistance.

SWG

Diameter (m)

Length (m)

Area (m²)

Current (A)

Voltage (V)

Resistance (Ω)

Resistivity (Ωm)

1

2

3

1

2

3

1

2

3

1

2

3

30

3.15E-04

0.5

7.79E-08

0.17

0.18

0.18

1.25

1.30

1.29

7.35

7.22

7.17

1.15E-06

1.13E-06

1.12E-06

30

3.15E-04

0.4

7.79E-08

0.18

0.19

0.19

1.13

1.19

1.17

6.28

6.26

6.16

1.22E-06

1.22E-06

1.20E-06

30

3.15E-04

0.3

7.79E-08

0.20

0.20

0.21

0.98

1.01

1.00

4.90

5.05

4.76

1.27E-06

1.31E-06

1.24E-06

30

3.15E-04

0.2

7.79E-08

0.22

0.23

0.24

0.71

0.76

0.77

3.23

3.30

3.21

1.26E-06

1.29E-06

1.25E-06

30

3.15E-04

0.1

7.79E-08

0.26

0.26

0.28

0.37

0.38

0.40

1.42

1.46

1.43

1.11E-06

1.14E-06

1.11E-06

30

3.15E-04

0.0

7.79E-08

0.30

0.31

0.32

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

[IMAGE]


SWG

Diameter (m)

Length (m)

Area (m²)

Current (A)

Voltage (V)

38

1.95E-04

0.5

2.98E-8

0.07

2.33

38

1.96E-04

0.5

2.98E-8

0.07

2.27

38

1.95E-04

0.5

2.98E-8

0.08

2.38

38

1.95E-04

0.5

2.98E-8

0.09

2.85

[IMAGE]

Gradient = Resistance

Highest resistance = 33.59Ω

Average resistance = 31.7Ω

Lowest resistance = 29.68Ω

Accurate to +/- 2.02Ω

Confidence limit = +/- 2.02Ω


SWG

Diameter (m)

Length (m)

Area (m²)

Current (A)

Voltage (V)

26

4.4E-04

0.5

1.52E-07

0.23

0.84

26

4.4E-04

0.5

1.52E-07

0.25

0.89

26

4.4E-04

0.5

1.52E-07

0.27

0.97

26

4.4E-04

0.5

1.52E-07

0.32

1.13

26

4.4E-04

0.5

1.52E-07

0.36

1.30

26

4.4E-04

0.5

1.52E-07

0.44

1.56

26

4.4E-04

0.5

1.52E-07

0.58

2.08

26

4.4E-04

0.5

1.52E-07

0.67

2.41

[IMAGE]

Gradient = Resistance

Highest resistance = 4.14Ω

Average resistance = 3.59Ω

Lowest resistance = 3.03Ω

Accurate to +/- 0.56Ω

Confidence limit = +/- 0.56Ω


SWG

Diameter (m)

Length (m)

Area (m²)

Current (A)

Voltage (V)

18

1.19E-03

0.5

1.11E-06

0.31

0.16

18

1.19E-03

0.5

1.11E-06

0.35

0.18

18

1.19E-03

0.5

1.11E-06

0.46

0.23

18

1.19E-03

0.5

1.11E-06

0.56

0.29

18

1.19E-03

0.5

1.11E-06

0.69

0.35

18

1.19E-03

0.5

1.11E-06

1.01

0.52

18

1.19E-03

0.5

1.11E-06

1.82

0.93

18

1.19E-03

0.5

1.11E-06

2.57

1.32

18

1.19E-03

0.5

1.11E-06

2.48

1.27

Gradient = Resistance

Highest resistance = 0.57Ω

Average resistance = 0.51Ω

Lowest resistance = 0.46Ω

Accurate to +/- 0.56Ω

Confidence limit = +/- 0.56Ω

[IMAGE]

SWG

Diameter (m)

Length (m)

Area (m²)

Current (A)

Voltage (V)

22

9.00E-04

0.5

6.36E-07

0.28

0.41

22

9.00E-04

0.5

6.36E-07

1.37

2.01

22

9.00E-04

0.5

6.36E-07

0.27

0.39

22

9.00E-04

0.5

6.36E-07

0.29

0.42

22

9.00E-04

0.5

6.36E-07

0.34

0.49

22

9.00E-04

0.5

6.36E-07

0.42

0.61

22

9.00E-04

0.5

6.36E-07

0.53

0.77

22

9.00E-04

0.5

6.36E-07

0.73

1.05

22

9.00E-04

0.5

6.36E-07

1.09

1.60

[IMAGE]

Gradient = Resistance

Highest resistance = 1.58Ω

Average resistance = 1.47Ω

Lowest resistance = 1.34Ω

Accurate to +/- 0.13Ω

Confidence limit = +/- 0.13Ω


SWG

Diameter (m)

Length (m)

Area (m²)

Current (A)

Voltage (V)

30

3.15E-04

0.5

7.79E-8

0.19

1.34

30

3.15E-04

0.5

7.79E-8

0.21

1.48

30

3.15E-04

0.5

7.79E-8

0.23

1.62

30

3.15E-04

0.5

7.79E-8

0.25

1.80

30

3.15E-04

0.5

7.79E-8

0.29

2.05

30

3.15E-04

0.5

7.79E-8

0.33

2.33

30

3.15E-04

0.5

7.79E-8

0.37

2.65

30

3.15E-04

0.5

7.79E-8

0.18

1.29

Gradient = Resistance

Highest resistance = 8.02Ω

Average resistance = 7.15Ω

Lowest resistance = 6.19Ω

Accurate to +/- 0.96Ω

Confidence limit = +/- 0.96Ω

[IMAGE]

I will also show the graphs comparing resistance to cross sectional
area as well as resistance verses 1/area.

[IMAGE]

[IMAGE]


Now that I have found the resistance of the wire for each SWG, I will
put all of the data found into a table so work out the resistivity of
the wire.

SWG

Length (m)

Area (m²)

Resistance (Ω)

Resistivity (Ωm)

18

0.5

1.11E-06

0.51

1.13E-06

22

0.5

6.36E-07

1.47

1.87E-06

26

0.5

1.52E-07

3.59

1.09E-06

30

0.5

7.79E-08

7.15

1.11E-06

38

0.5

2.98E-08

31.7

1.89E-06

Analysis of results

I will firstly analyse the first part of my experiment which was to
see how the length of the wire affected the resistance. Looking at the
graph that I have drawn plotting resistance against length, you can
clearly see that the length is proportional to the resistance. As the
length of the wire increases, so does the resistance. The graph shows
that this obeys Ohm's law as it is a linear line and that it passes
through the origin. This is generally what I expected to find for this
part of my experiment. The resistance in the wire should increase with
length as the electrons have a longer distance to travel through the
wire.

The rest of my results of tables and graphs are to determine the
resistance of each wire so that I am able to find the resistivity of
nichrome wire. The graphs I have plotted are Voltage against Current
so that I am able to read off the gradient of each graph as it will be
the resistance. The graphs also show that the voltage is proportional
to the resistance and obeys Ohm's law as they are all linear graphs
and should pass through the origin had the results been more accurate.

Once I found the resistance I was able to then calculate the
Resistivity using the formulas already stated above. Looking at my
final values of resistivity I was pleased to see that 3 of them were
almost identical, (SWG 18, 26 and 30), but was curious as to why the
other two were of similar values but different to the other three.

My other two graphs show the resistance against area and resistance
against 1/area. The first graph showed that as the cross sectional
area of the wire increased so the resistance decreased. This is due to
the fact that as the area increases there is a larger space for the
electrons to pass through and so the resistance of them passing
through would decrease.

Evaluation of experiment

I believe that this experiment went well and am pleased with the
results that I recorded. I managed to use the time given affectively
to collect a great deal of results to perform the calculations to
enough detail to get an accurate reading for the resistivity. Looking
at my results however I seem to have two separate readings of
resistivity. In this experiment there should not be very many factors
that would affect my results. There may however have been some
resistance lost internally in the wires used in the experiment. I
doubt that the internal resistance lost in the wires would account to
the two different readings and so there must be another reason for the
result. This may be due to the wires that I used being slightly
different materials. 3 of them seem to be the same leaving the other 2
to a different material.

Another factor that could have affected my results could have been
faulty equipment such as the voltmeter and ammeter may have not been
very accurate or could have been telling me different values
altogether although I am confident that this was the case due to the
shape of my graphs drawn. This is due to my scientific knowledge that
the Voltage and current are proportional to each other as shown in my
graphs.

If I was to repeat this experiment I would do use the same method as I
did in this one as I believe it to be the most effective way in
determining the resistivity of a wire with the equipment available for
me to use.
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