# Measuring the Resistivity of a Wire

# Measuring the Resistivity of a Wire

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More ↓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 = Ï€rÂ² (where A = Area of cross section, Ï€ = 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:

Â· 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

Â· Voltmeter - To measure the p.d. in the circuit to then find out the

resistance. This is accurate to 0.01V.

Â· Ammeter - To measure the current in the circuit to then find out the

resistance. This is accurate to 0.01A.

Â· Nichrome wire - This is the material that I will be testing on in

wire form; ultimately I am trying to find its resistivity.

Â· Ruler - To measure the length of the wire that I am testing. This is

accurate to 1mm.

Â· 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.

Â· Variable resistor - to give me more results for each to give me an

idea of accuracy.

Â· 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 (mÂ²)

Current (A)

Voltage (V)

Resistance (â„¦)

Resistivity (â„¦m)

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 (mÂ²)

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 = 33.59â„¦

Average resistance = 31.7â„¦

Lowest resistance = 29.68â„¦

Accurate to +/- 2.02â„¦

Confidence limit = +/- 2.02â„¦

SWG

Diameter (m)

Length (m)

Area (mÂ²)

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 = 4.14â„¦

Average resistance = 3.59â„¦

Lowest resistance = 3.03â„¦

Accurate to +/- 0.56â„¦

Confidence limit = +/- 0.56â„¦

SWG

Diameter (m)

Length (m)

Area (mÂ²)

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 = 0.57â„¦

Average resistance = 0.51â„¦

Lowest resistance = 0.46â„¦

Accurate to +/- 0.56â„¦

Confidence limit = +/- 0.56â„¦

[IMAGE]

SWG

Diameter (m)

Length (m)

Area (mÂ²)

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 = 1.58â„¦

Average resistance = 1.47â„¦

Lowest resistance = 1.34â„¦

Accurate to +/- 0.13â„¦

Confidence limit = +/- 0.13â„¦

SWG

Diameter (m)

Length (m)

Area (mÂ²)

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 = 8.02â„¦

Average resistance = 7.15â„¦

Lowest resistance = 6.19â„¦

Accurate to +/- 0.96â„¦

Confidence limit = +/- 0.96â„¦

[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 (mÂ²)

Resistance (â„¦)

Resistivity (â„¦m)

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.