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An in Investigation into the Resistance of a Wire.

Extracts from this document...

Introduction

Shee Wah Wan

An in Investigation into the Resistance of a Wire

Aim: To investigate the factors affecting resistance

There are four main factors which affects the resistance and they are:

  • The material
  • The cross-sectional area (thickness)
  • The length
  • The temperature

But in this investigation I am only going to investigate in the factors length and cross sectional area

Background Information

Electricity cannot be seen but you can see the effect electricity has. It can:

  • Make things hot-as in the heating element of an electric fire
  • Make things magnetic-as in an electromagnet
  • Produce light-as in a light bulb
  • Break down certain compounds and solution-as in electrolysis

In a nutshell, electricity is very good at transferring energy.  To understand this, a simple model of what happens in electrical circuits can help.

         If an electrical circuit is made using a battery and a lamp, the battery can be thought of as pushing electrical charge round the circuit to make a current.   The battery also transfers energy to the electrical charge.  The voltage of the battery is a measure of how much ‘push’ it can provide and how much energy it can transfer to the charge.

        Scientists now know that electric current is really a flow of electrons.  The electrons actually flow around the circuit from negative to positive.  Unfortunately, although early scientists knew that there must be a flow of charge in a circuit, they guessed the direction of the flow incorrectly.  Consequently all diagrams were drawn showing the current flowing from positive to negative.  Surprisingly this way of showing the current has not been changed and so the conventional current that everyone uses gives the direction that positive charges would have flown.

        Electric charge is measured in coulombs (C).  Electric current is measured in amperes.

...read more.

Middle

0.94

0.41

0.42

0.98

0.62

0.63

0.98

20

0.05

0.09

0.56

0.57

(0.6)

0.06

0.10

0.60

0.12

0.21

0.57

0.23

0.41

0.56

0.45

0.78

0.58

10

0.03

0.09

0.33

0.37

(0.4)

0.05

0.13

0.39

0.07

0.19

0.37

0.12

0.32

0.38

0.45

1.19

0.38

So this experiment shows me that E32 has the highest resistance of the three wires.  This is because it has a smaller cross sectional area than the other wires.  The thicker the wire is, the lower the resistance so the thinner the wire is the higher the resistance.  So because E26 has the largest cross-sectional area out of the three this would mean that it has a lower resistance than the other two wires.  In the table it also shows that length is proportional to the resistance because if you double the length you double the resistance.  For example 50cm on the E32 wire has the resistance of 4.41 Ohms and in the length 100cm it has the resistance of 8.56 Ohms.

        This shows me that if I am going to investigate in the relationship between the length and the resistance I will need a larger range of lengths to get a more accurate result.

Main Experiment

Investigating in the factor length

From my preliminary experiment I decided to do the main experiment which just one wire E28 but investigating more lengths than the preliminary one.  I chose E28 because it has the average cross sectional area out of three wires I investigated in.

Prediction

I predict that if I double the length of the wire then the resistance will also double.  I mean that if I double the length of the wire there will be twice as many electrons in the wire to carry the charge.  So twice as many metal ions for the electron to collide into so it will cause two times the resistance than the original length of the wire which will result in a greater resistance.

Diagram

image13.pngimage12.png

image53.pngimage54.pngimage05.pngimage03.png

image17.pngimage56.pngimage17.pngimage55.png

image14.pngimage07.png

                                                                                        A

image55.pngimage58.pngimage58.png

image16.pngimage15.pngimage11.png

image04.pngimage03.pngimage05.pngimage15.pngimage16.pngimage03.png

image06.pngimage07.pngimage06.png

image09.pngimage08.png

image11.pngimage12.pngimage10.pngimage13.png

           = main power                                                          = variable resistor

image07.pngimage14.png

           = ammeter                                                              = wireimage11.png

image07.pngimage06.pngimage15.png

           = voltmeter                                             = crocodile clip                                             image16.png

Apparatus

The apparatus that I will need to do this experiment are:

  • A voltmeter
  • An ammeter
  • 5 wires
  • 2 crocodile clips
  • Power pack
  • Rheostat (variable resistor)
  • Sellotape
  • Ruler

Method

I learnt from my pilot investigation that I need to do extra readings in order to obtain a set of accurate results.  First by setting up the apparatus as shown below in the diagram. With the voltmeter parallel to the wire and the ammeter in series with the wire.

Step 1                 Cut 110cm of the wire E28 (not 100cm because extra wire is

        needed to clip the crocodile clips too).  When doing this use two rulers side by side start from measuring at the 10cm mark all the time.

Step 2                Sellotaped the E28 wire to the ruler at one end with a little wire                         extra from the ruler. This is to hold it still so I could measure

                the length of the wire accurately.

Step 3        Straighten the wire and measured to 100cm exactly and put a piece of sellotape edge exactly on the mm of 100.  So that when the wire taken off the ruler the sellotape would still be attached to it.

Step 4        Clip the crocodiles clips exactly to the edge of the sellotape on the wire. The wire that is not in between the two crocodile clips will get no electricity flowing through it because they are not part of the circuit.  

Step 5         Check that all the wires were connected properly to the other apparatus and then turn on the mains power and recorded the voltage and current for that length of that wire.  Take 5 readings for each length of wire.

Step 6        Then repeat steps 2-5 again but for the following lengths 95cm, 90cm, 85cm, 80cm, 75cm, 70cm, 65cm, 60cm, 55cm, 50cm, 45cm, 40cm, 35cm, 30cm, 25cm, 20cm, 15cm, 10cm (stop at 10cm because the wire would be too short and it would start to heat up and would soon break).  Adjust the length by moving the second crocodile clip, keeping the first crocodile clip in place at the 10cm mark.

Factors

In this experiment there was one variable which was not controlled and that was the length of the wire.  But all the rest stay constant and they were:

  • The thickness of the wire (by using the same wire throughout the experiment).
  • The temperature (this was achieved by not turning the circuit on unless I have to as to keep the temperature of the wire as close to room temperature as possible and waiting for a few minutes before I take my next reading to let the wire cool down).
  • The same voltage was used throughout the experiment.
  • The same apparatus-for example voltmeter, an ammeter, wires, variable resistor, power pack and crocodile clips.
  • The same ruler was used to measure the wire each time.

Safety

In this experiment I made sure before I started that there was no water around my apparatus because it is very dangerous.  I also checked for fault in the circuit before I start as well because that could also be dangerous.  When there was a current running through the circuit and there were exposed wires for example the clips I did not touch them because this could be very dangerous because there is electricity going through them.  I also did not touch the experiment wire because it could be hot due to the current and I could have included a switch in my circuit so that I can break the circuit quickly if I needed to.  I made sure that my bag was underneath the table as well so they are not in the way of other people.

Accuracy with the equipment

In order to reduce errors it is necessary to choose accurate and reliable equipment.  But the only equipment that were available for us to use at the time we the normal ammeter and volt meter which are not as accurate as the multi meters.  Because the normal ammeters and volt meters only give the reading to two decimal places whereas the multi meters can give up to three decimal places which means its more accurate than the normal meters.      

Results

For the wire Eureka 28

Length/cm

Voltage/volts (V)

Current/amps (A)

V/I=R (Ω)   Resistance/ohms

Average Resistance/ohms

100

0.32

0.07

4.57

4.57

(4.6)

0.37

0.08

4.63

0.45

0.10

4.50

0.65

0.14

4.64

1.22

0.27

4.52

95

0.31

0.07

4.43

4.42

(4.4)

0.40

0.09

4.44

0.53

0.12

4.42

0.66

0.15

4.40

1.50

0.34

4.41

90

0.33

0.08

4. 13

4.12

(4.1)

0.41

0.10

4.10

0.62

0.15

4.13

1.07

0.26

4.12

2.02

0.49

4.12

85

0.31

0.08

3.88

3.90

(3.9)

0.35

0.09

3.89

0.47

0.12

3.92

0.63

0.16

3.94

1.21

0.31

3.90

80

0.30

0.08

3.75

3.73

(3.7)

0.37

0.10

3.70

0.52

0.14

3.71

0.89

0.24

3.71

1.19

0.32

3.72

75

0.49

0.14

3.50

3.51

(3.5)

0.53

0.15

3.53

0.63

0.18

3.50

0.81

0.23

3.52

1.16

0.33

3.52

70

0.26

0.08

3.25

3.23

(3.2)

0.29

0.09

3.22

0.42

0.13

3.23

0.58

0.18

3.22

1.38

0.43

3.21

65

0.24

0.08

3.00

3.00

(3.0)

0.27

0.09

3.00

0.42

0.14

3.00

0.57

0.19

3.00

1.11

0.37

3.00

60

0.22

0.08

2.75

2.80

(2.8)

0.31

0.11

2.82

0.45

0.16

2.81

0.79

0.28

2.82

1.68

0.60

2.80

55

0.20

0.08

2.50

2.47

(2.5)

0.27

0.11

2.45

0.39

0.16

2.44

0.62

0.25

2.48

1.01

0.41

2.46

50

0.18

0.08

2.25

2.30

(2.3)

0.28

0.12

2.33

0.39

0.17

2.29

0.69

0.30

2.30

1.61

0.70

2.30

45

0.17

0.08

2.13

2.12

(2.1)

0.21

0.10

2.10

0.32

0.15

2.13

0.55

0.26

2.12

0.99

0.47

2.11

40

0.15

0.08

1.88

1.92

(1.9)

0.23

0.12

1.92

0.31

0.16

1.94

0.35

0.18

1.94

0.97

0.51

1.90

35

0.13

0.08

1.63

1.63

(1.6)

0.18

0.11

1.64

0.31

0.19

1.63

0.36

0.22

1.64

0.90

0.55

1.64

30

0.11

0.08

1.38

1.41

(1.4)

0.17

0.12

1.42

0.26

0.18

1.44

0.56

0.40

1.40

0.84

0.60

1.40

25

0.10

0.08

1.25

1.23

(1.2)

0.15

0.12

1.25

0.18

0.15

1.20

0.32

0.26

1.23

0.82

0.68

1.21

20

0.08

0.09

0.89

0.90

(0.9)

0.09

0.10

0.90

0.19

0.21

0.91

0.36

0.40

0.90

0.72

0.79

0.91

15

0.06

0.09

0.67

0.67

(0.7)

0.08

0.12

0.67

0.12

0.18

0.67

0.22

0.33

0.67

0.62

0.92

0.67

10

0.05

0.09

0.56

0.53

(0.5)

0.07

0.13

0.54

0.10

0.19

0.53

0.16

0.31

0.52

0.59

1.18

0.50

Analysis

It can be seen from the table of results (above) and the graph of the relationship between length and resistance that as the length increases, the higher the resistance is.  However the graph is not a curve so the two qualities (length and resistance) are directly proportional.

        Direct proportion means that doubling the length would double the resistance and you can see it is true.  It can be seen from the table that the length of 50cm gives the resistance of 2.3 Ohms and double the length 100cm gives the resistance of 4.6 Ohms.

        Ohm’s law actually states that the current flowing through the circuit is directly proportional to the applied voltage (if you double one, you double the other).

        Also electrons colliding into metal ions causes’ resistance.  So if the length of the wire is double, the electrons will collide into twice as many ions so there will be twice as much resistance.  This happens because of the electrons that flow through the wire.

        These electrons travel at a steady pace, when they come to different piece of wire, they have to slow down in order to be able to pass (different wire meaning the actual wire being used and the wires connecting the apparatus).  While moving through the wire, the electrons need to squeeze together.

        This is because there is not enough room/space for them to pass evenly through the wire.  The more the electrons have collided into each other then the higher the resistance is.  This is because it will take the electrons longer to pass from one end of the wire to the other end.  This is because the current is slowed down.  The longer the wire, the longer the electrons have to stay squashed together and so the longer they take to pass through the wire and therefore the higher the resistance is.

        The results lie on a straight line, which means there is a positive pattern.  The length that was 0cm had no resistance because there was no wire and therefore the circuit would be broken so there will be resistance.

        As the length of the wire increases the resistance increases because the wire is longer so the electrons will collide into more metal ions and that will lead to a higher resistance.  So as the length keeps increasing the electrons are colliding into more metal ions and so the resistance gets greater and greater.

        The resistance of the wire was worked out by using the formula:

V/I=R

        There were no anomalous results which mean the experiment was overall very accurate as the points lie very close to the best fit line.

        My results supported my prediction that if I double the wire the resistance will double.

Evaluation

The measurements taken in the experiment were simple and straightforward and I could over half an hour obtain a set of results, which showed a definite pattern.

        Most of the result lies on the straight line or very near the straight line and there were no anomalous results.  So this means this set of results is fully reliable and it supports my prediction earlier giving a positive pattern result.  But the reliability of the evidence can still be improved.  From my results I work out the accuracy of my results to see how accurate I was. This was done by taking the range of resistance (how much above or below the average resistance) and dividing that by the average resistance then multiplying it by 100% to get the percentage error. An example is shown below for one length of the E28 wire.

E28 at the length of 100cm.  The average resistance is 4.57 Ohms and the range is 4.57±0.07 Ohms. Too work out the percentage error the following is done:

0.07        ×    100%     =   1.5%image09.png

4.7        

So E28 with the length of 100cm has the percentage error of 1.5%

The rest of the results and their percentage errors are shown in the following table.

Length of Wire

Average Resistance (Ω)

Range of Resistance (Ω)

Percentage error (%)

100

4.57

4.57±0.07

1.5

95

4.42

4.42±0.02

0.5

90

4.12

4.12±0.02

0.5

85

3.90

3.90±0.04

...read more.

Conclusion

0.004        ×    100%     =   1.23%

0.324        

So E22 with the fixed length of 15cm has the percentage error of 1.23%

E22 at the fixed length of 30cm.  The average resistance is 0.611Ohms and the range is 0.611±0.003 Ohms. Too work out the percentage error the following is done:

0.003        ×    100%     =   0.49%

0.611        

So E22 with the fixed length of 30cm has the percentage error of 0.49%

The rest of the results and there percentage error is shown in the following tables.

The following table show the percentage error for all the different types of wire at the fixed length of 15cm.

Type of wire

Average resistance (Ω)

Range of resistance (Ω)

Percentage error (%)

E22

0.324

0.324±0.004

1.23

E26

0.478

0.478±0.006

1.26

E28

0.736

0.736±0.004

0.54

E30

1.027

1.027±0.007

0.68

E32

1.375

1.375±0.006

0.44

E34

1.847

1.847±0.013

0.70

E36

2.822

2.822±0.012

0.43

The following table show the percentage error for all the different types of wire at the fixed length of 30cm.

Type of wire

Average resistance (Ω)

Range of resistance (Ω)

Percentage error (%)

E22

0.611

0.611±0.003

0.49

E26

0.934

0.934±0.005

0.54

E28

1.391

1.391±0.008

0.58

E30

1.941

1.941±0.008

0.41

E32

2.668

2.688±0.006

0.22

E34

3.438

3.438±0.006

0.17

E36

5.292

5.292±0.041

0.77

From the calculations above it can seen that the experiment was overall very accurate.  The percentage error is under 1.26% which is very accurate for this experiment. This means my results are fully reliable.

Resistivity- I then decided to work out the percentage error in the resistivity by taking the range of the resistivity (how much above or below the average resistivity) and dividing that by the average resistivity then multiplying it by 100% to get the percentage error.

5.3 × 10-7 ± 0.7 × 10-7 = 13.2%

So there was a 13.2% error in the resistivity this is because the resistivity is a value calculated from value which already has an error.  So this means the resistivity would have a larger error because it the sum of the length, cross sectional area, voltage, current and resistance altogether.

        I could have extended the investigation more by finding how the material in wire (e.g. copper) and the temperature also affected the resistance of the wire to make my result more reliable.

Bibliography

Understanding Physics for Advanced Level by Jim Breithaupt

Physics for You

Accessible Physics

Physics Applied

...read more.

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