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how the length of a wire affects the resistance of a wire

General Background: Ohm's law states that: "The current through a metallic conductor is directly proportional to its voltage provided that temperature is kept constant".

Resistance (R) = V/I

The amount of current flowing through a circuit can be controlled by changing the resistance of the circuit. This can be done with a resistor which is a component designed to have a specific resistance. Accurate resistors can be made from metal wires. The longer the length of the wires, the greater its resistance.

Hypothesis: Based on the scientific knowledge that 'the longer the length of the wires, the greater its resistance.' I predict that as the length of the copper wire increases its resistance will also increase, so if the length is doubled then the resistance will also be doubled. Proving that the length of the wire is directly proportional to the resistance. The graph I expect to form will be:

Variables:

Independent-

* The length of the wire

Dependent:

* The resistance of the wire.

Controlled:

* The same material of wire for the investigation

* Wire with the same cross-sectional area.

* Temperature

* Same batteries with the same voltage.

Apparatus and Materials:

* Two 1.5V Batteries

* Two Crocodile clips.

* Connecting Wires.

* Voltmeter.

* Ammeter.

* Slightly longer than 1 metre wooden plank.

* A constantan wire which has a length of at least 1.15m and a diameter of 0.11mm.

* Two screws.

* Two nails.

* A micrometer.

Diagram:

Contantan wire

Voltmeter

Ammeter

Method:

1. Using a micrometer measure the cross-sectional area of the constantan wire. It should be 0.11mm. The wire taken is constantan rather than copper as copper has very low resistance. A medium constantan wire is used at ones with small cross-sectional area have a very high resistance and they might burn at times and the thicker wires would not give suitable readings and the range of ammeters could not be too high.

2. Put the ruler in the centre of the wooden plank and nail it into the plank by two nails. After the ruler has been anchored on the plank of wood, screw two screws into the wooden plank at either ends of the ruler, the screws will also be touching the ruler. Tie the constantan wire around the screws more than once, to ensure that the wire is taut and has no kinks to give better accuracy in the results. Connect the Voltmeter around the wire in parallel to the circuit and the ammeter in series to the circuit.

3. Start off by putting the crocodile clips on 10cm of the wire.

4. Read and record the readings of the ammeter and voltmeter for that particular length.

5. Allow the wire to cool for 30 seconds between each two readings. As the length of the wire is changed through changing the crocodile clips, Firstly ensure that the temperature stays the same throughout the experiment by allowing the wire to cool and not keeping the crocodile clips on the wire for too long. The room temperature will also be kept the same by conducting the experiment in the same room and by making sure the wire is not near any window where it could be in direct contact with the sunlight or wind.

6. Repeat the same experiment again, but this time move the crocodile clips 10cm (0.1m) up the wire. A micrometer is used to measure the diameter of the wire.

7. Repeat the same steps from 3-6 moving 10 cm up in every trial till 90 cm.

8. Repeat the entire experiment twice to obtain average results.

Data Collection

Length of Wire

(cm)

Voltage (V)

Current (A)

Resistance (Ω)

- rounded up to 2 d.p

R=V/I

Average R

V1

V2

A1

A2

R1

R2

10.0

1.65

1.63

0.35

0.35

4.72

4.66

4.69

20.0

2.05

2.08

0.22

0.23

9.32

9.04

9.18

30.0

2.20

2.18

0.15

0.16

13.75

13.63

13.69

40.0

2.30

2.32

0.14

0.14

16.43

16.57

16.5

50.0

2.45

2.43

0.11

0.10

22.27

24.30

23.29

60.0

2.50

2.50

0.09

0.09

27.78

27.78

27.78

70.0

2.55

2.54

0.08

0.08

31.88

31.75

31.82

80.0

2.59

2.60

0.07

0.06

37.00

43.33

40.17

90.0

2.75

2.72

0.06

0.05

45.83

54.40

50.12

= 9.5×10-9m2

Length of Wire (cm)

Average R (Ω)

10.0

4.69

20.0

9.18

30.0

13.69

40.0

16.5

50.0

23.29

60.0

27.78

70.0

31.82

80.0

40.17

90.0

50.12

Conclusion / Evaluation

To sum up this experiment, as the length of a wire doubles, the resistance also doubles (supposing that all the other conditions remain constant in this case). In other words, the resistance is directly proportional to the length of a wire because that resistance is caused by electrons bumping against ions. If the length of a wire doubles, the electrons will bump into the ions twice as much and hence, the resistance will double.

In addition to that, when the cross-sectional area of a wire increases, the resistance decreases (supposing that all the other conditions remain constant in this case). That is to say resistance is inversely proportional to cross-sectional area. Thicker wire offers less resistance to current than thinner wire does. This is because current consists of electrons that flow through a wire and jump from atom to atom. A conductor with a larger area (cross-sectional area) allows more electrons to flow. When cross-sectional area increases there is a greater number of pathways that electrons can move down, past the positive ions of the metal. Thus, if the area of a wire is doubled, the resistance will be halved.

It might be better to have more trials, such as three trials for each length / cross-sectional area in order to get more accurate data. There has been some inaccuracy in measuring the Voltage, Current and Length as the ruler used is not exact and voltmeters and ammeters were not always turned on. Apart from these uncertainties in measurements, it would be better to have an experiment with other types of wire materials or cross-sectional areas.

For the experiment, we first tried to measure every 0.11 meter of a wire, but after a few trials, we decided to do the experiment again due to uncertainty. After that, we measured every 0.05 meter of length between 0.4 meter and 0.1 meter. We were trying to measure the resistance of a wire when the length was 0.05 meter but we couldn't precisely measure it because it melted. It seems that Copper has a low resistivity. We should change the material next time to obtain more accurate data. Also, for 18 swg [standard wire gauge], we could not measure the resistance of the wire when the length was under 0.2 meter due to low resistivity of Copper. It would be better to use another material with greater resistivity such as Aluminum or Gold for this experiment.

Conclusion & Evaluation

From the graph created through the results, we can see that the result does in fact support the theory that as you increase the thickness of the wire the resistivity will decrease. As dictated by the graph, there is a proportional relation between the points, however the line of best fit is not as optimal as it does not pass through all the points. This was probably caused by some faulty measurement. However I cannot remove this point and plot the line again, since I need the point to gain a faint idea on what the co-relation is and I have five points only which is the bare minimum.

The graph is not that reasonable because as you can see in the graph, only 2-3 points are proportional to each other, however because of the first and last point the graph has shifted upwards leaving us with an unreasonable line of best fit. I believe there are several errors while I proceeded with my experiment; this is because the equipment used in the experiment such as the voltmeter and ammeters have small errors. The readings from these two equipments were used to calculate the resistance. An error for the area is inevitable as it is extremely hard to measure the thickness of the wire and could have affected the total area when using the equation.

The results from this experiment could have been more accurate if a wider range of wire thicknesses had been used, there could have been more points created on the graph which would reduced the error of the line of best fit, also if more points were used then any errors and anomalies could have been removed/ignored. It would also be beneficial if there was another way of measuring the thickness and area of the wire as the margin of error is huge for humans like us. Also in the experiment the wires that are used to connect up the circuit could have been cleaned before the experiment as oxidation of the wire may have caused unnoticeable errors which could have affected the resistance of the wire.

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