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What affects the resistance of a wire?

Extracts from this document...

Introduction

Planning

Introduction

Resistivity:  It is a characteristic property of each material, and is useful in comparing various materials on the basis of their ability to conduct electric currents. High resistivity designates poor conductors.  Resistivity (image00.png) is proportional to the resistance (R) of a wire, multiplied by its cross-sectional area (A), and divided by its length (l).  image00.png= RA / l.  Since lengths are measured in centimetres in this experiment, resistivity would be expressed in units of ohm-centimetre.

Conductivity is the reciprocal of resistivity, and it, too, characterizes materials on the basis of how well electric current flows in them. Good electrical conductors have high conductivities and low resistivities. Good insulators have high resistivities and low conductivities.

(Britannica CD 2000 Deluxe Edition)

Resistance:  It is the property of an electric circuit that transforms electric energy into heat energy in opposing electric current. Resistance involves collisions of the current particles with the fixed particles that make up the structure of the conductor.  The electromotive force or voltage (V) across a circuit, divided by the current (I) through that circuit, defines the amount of electrical resistance (R).R = V / I. Ohm image01.png is the common unit of electrical resistance, equivalent to one volt per ampere.  The resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area. Resistance also depends on the material of the conductor, as better conductors have less resistance seeing as electricity can flow through them more easily.  The resistance of a circuit element generally increases when temperature also increases. When cooled to extremely low temperatures, some conductors have zero resistance.

(Britannica CD 2000 Deluxe Edition)

What affects the resistance of a wire?

There are four main factors that govern the resistance of a wire:

...read more.

Middle

0.38

1.90

30

0.29

0.29

1.45

20

0.20

0.20

1.00

These results evidently show us that as the length decreases, so does the resistance.  This, therefore, supports my initial prediction.  We can also see that the readings for both sets of results were exactly the same except for when the wire was 100cm.  This was merely a slight random error.  Apart from that we can see that all the readings agreed, and a definite trend can be noticed.  

Fair Test

In order to certify that the resistance is depending totally upon the length of the wire, which is what we are investigating, we have to control all the other variables that would otherwise affect the resistance.  This is so that this experiment remains a fair test.  

Cross-sectional area – this will remain the same throughout the experiment because we will initially cut just one piece of wire 1 metre long, and then employ the various lengths using crocodile clips at the different points on the metre stick.  So since the wire will be the same for the entire investigation, the cross-sectional area of that wire will be the same.    

Material – the wire being used for the experiment will be of constantan material, and this will not change at any time.  This is important because different materials would give different resistances, depending on their conductivity.

Temperature – we intend to keep this constant throughout, as the entire experiment will be carried out under room temperature.  We are doing this because a change in temperature in the surrounding would affect the resistance, as the wire would also change temperature.  So controlling the temperature keeps it a fair test, as the temperature will not alter performance of the resistance.      

Current – since it is the potential difference across the wire that is being measured, we have to make sure the current is kept the same for every reading.  Again this is because if the current is not controlled, an increase would cause the wire to heat up and this would have an affect on the resistance.  So I have chosen 0.2 Amps as the standard current reading across the circuit.  

Accuracy

All round accuracy is very important when carrying out an experiment, so that the results obtained are reliable and then truthfully display the trend that should be seen.  Firstly, to accurately measure the wire, it will be firmly placed onto a metre stick so there are no coils in the wire and it can be measured along the metre stick with considerable precision.  Since the crocodile clip heads are 3mm thick, 2cm of extra wire will be measured so that 0.5 cm can be folded over at each end and the clip can get a firm grasp of the wire.  

Amongst the apparatus, some of the items were included to enhance the accuracy and provide precise readings.  We used a digital Ammeter and a digital Voltmeter.  Both these devices measured to the nearest hundredth.  

I intend to carry out the experiment twice, so that I have two sets of results.  If I then notice an anomaly between any two findings I will repeat that one a third time.  All this is essential in order to attain reliability with the results because firstly, any anomaly can be immediately recognised and stamped out.  Then an average is taken to calculate the final resistance, which maximises accuracy and diminishes any discrepancy with the findings.    

Apparatus

When setting up the apparatus for this experiment we require:

  • 1 Power Pack
  • 1 Digital Ammeter
  • 1 Digital Voltmeter
  • 1 Variable Resistor
  • 1 Metre Stick
  • 1 Metre of Constantan Wire
  • 5 wires
  • 2 crocodile clips

Obtaining Evidence

Below are the results I obtained when investigating the resistance of constantan wire at different lengths between 100cm and 10cm:

CURRENT = 0.20 AMPS

Length of Wire (cm)

Potential Difference 1 (V)

Potential Difference 2 (V)

Average of PD

(V)

Resistance

(image01.png)

100

1.86

1.85

1.855

9.28

95

1.76

1.78

1.770

8.85

90

1.68

1.66

1.670

8.35

85

1.59

1.60

1.595

7.98

80

1.48

1.49

1.485

7.43

75

1.39

1.37

1.380

6.90

70

1.32

1.31

1.315

6.58

65

1.20

1.21

1.205

6.03

60

1.12

1.12

1.120

5.60

55

1.04

1.02

1.030

5.15

50

0.96

0.96

0.960

4.80

45

0.86

0.86

0.860

4.30

40

0.77

0.77

0.770

3.85

35

0.67

0.67

0.670

3.35

30

0.57

0.57

0.570

2.85

25

0.47

0.49

0.480

2.40

20

0.40

0.40

0.400

2.00

15

0.31

0.30

0.305

1.53

10

0.21

0.22

0.215

1.08

...read more.

Conclusion

Based on the theory, I predicted that the line on my graph would go through the origin.  However, it does not intercept the origin, which means that there has been a minor systematic error somewhere during the experiment.  A likely error could be linked with the connections of the wire to the circuit.  Since the crocodile clips are not very precise and the connection to the wire is therefore loose, there may have been air in between the connections which would have increased the overall resistance, because the reading would have included the resistance of the clips.  Since this inaccuracy would have affected the entire set of results, this may have pushed my entire graph up so that it doesn’t go through the origin.  One way of resolving this problem is to solder the clip onto the wire, to prevent air between the connections.  Another method id by using something with a smaller surface are so the point in contact with the wire is more exact.  This would improve accuracy and not let other minor factors affect the resistance measured.            

Overall, by looking at the way I carried out the experiment and the results I obtained, I think the investigation was successful and displays a true pattern of how the length of a wire affects its resistance.  However, as I have identified, there are many other ways that I could have carried out in order to improve the reliability and obtain more accurate results.    

...read more.

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