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# An Investigation into Factors Affecting Resistance of a Wire

The possible variables I could use to find out factors affecting resistance are material wire is made of, length of wire, temperature and cross sectional area of wire. I will use cross sectional area of wire and length of wire because I think it will be hard to draw conclusions from the material of wire. I am not doing temperature because it would be hard to get results from and I think they wouldn’t be as accurate.

I will set up a circuit to find out how length and cross sectional area affect resistance.

I will need the following components in my circuit to gather all of the necessary results:

* Component holder- So I can change the wire that I am testing.

* Voltmeter- Measuring potential difference across the wire, it will have to be across the wire and not just anywhere in the circuit so it is measuring the P.D across the wire I am testing only.

* Ammeter – measuring current of the circuit, with his and the voltmeter I will be able to work put resistance (R=V/I).

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As a safety consideration I will keep the Current under 0.5 amps, so the wire doesn’t get too hot.

* Rheostat- So I can vary the voltage in the circuit to take two readings for each wire at different voltages, I will work out an average of the two to reduce the margin of error.

* Switch- A safety consideration, so the wire doesn’t overheat and burn if the circuit is left on for too long.

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I have decided to test length of wire at, 10cm, 30cm, 50cm, 70cm, 90cm, 110cm, 130cm, 150cm and 170cm keeping a constant cross sectional area of 0.028mm2. I will test cross sectional area at the Cross sectional areas of wire: 0.028 mm2, 0.045 mm2, 0.057 mm2, 0.113 mm2, 0.166 mm2 and 0.246 mm2, keeping a constant length of 50cm. My preliminary work reviled that these were the best constants, and variables to use as they gave a wide rang of results. For the length of wire I have decided to keep the wire at a constant width of 0.19MM, and for Cross sectional area a constant length of 50CM to ensure a fair test and to make my results accurate. For both the wire will be made of constantan, for the same reason.

Method: To gather my results I did the following procedure, using the circuit on the next page.

1) Place 10CM of, constantan wire with a cross sectional area of 0.028 mm2 in specimen holders.

2) Press switch to let current flow.

3) Record Potential difference of wire and current of the circuit

4) Work out resistance, (V/I)

5) Repeat for all chosen lengths

6) Once done repeat for cross sectional area, keeping the length at 50cm.

7) For both cross sectional area and length of wire I will repeat steps 1 to 5 twice to decrease the margin of error.

Prediction:

For length I think that the longer the wire, the greater the resistance, I think this is because there is more material for the electrons to collide with when the wire is long, than when it is short. For cross sectional area I predict that the greater the cross sectional area, the less resistance, this is because there is more space for electrons to fit through the wire when it is very thick, and so there will be less collisions between the electrons and the wire, than when it has a small cross sectional area. Below are sketch graphs for the results I expect to get:

Length of Wire:

I will expect to get a straight line that goes through the origin; this will show me that Resistance and Length of wire are in direct proportion to each other. This is because if you double the length of the wire you will double resistance, because the electrons just have twice as much material to pass through.

Resistance

Length of Wire

Cross Sectional Area of Wire:

For this I would expect an inverse line, as the cross sectional area increases the resistance decreases.

Resistance

Cross Sectional Area of Wire

Tables: Below are tables to show my results taken during the practical.

1st Repeat

1st Repeat

1st Repeat

2ndRepeat

2nd Repeat

2nd Repeat

2nd Repeat

Cross Sectional Are of Wire (MM2)

Length of Wire (CM)

Voltage (volts)

Current (amps)

Resistance (ohms)

Voltage (volts)

Current (amps)

Resistance (ohms)

Average Resistance (ohms)

0.028

10

0.98

0.59

1.66

0.54

0.26

2.08

1.87

0.028

30

1.13

0.2

5.65

1.9

0.35

5.43

5.54

0.028

50

2.87

0.33

8.70

1.59

0.17

9.35

9.02

0.028

70

2.89

0.23

12.57

1.91

0.16

11.94

12.25

0.028

90

2.18

0.14

15.57

2.99

0.18

16.61

16.09

0.028

110

3.17

0.16

19.81

2.42

0.12

20.17

19.99

0.028

130

2.58

0.11

23.45

3.42

0.14

24.43

23.94

0.028

150

3.44

0.13

26.46

2.75

0.1

27.50

26.98

0.028

170

2.74

0.09

30.44

3.09

0.1

30.90

30.67

1st Repeat

1st Repeat

1st Repeat

2nd Repeat

2nd Repeat

2nd Repeat

Length of wire (CM)

Cross Sectional Area of Wire (MM2)

Voltage (volts)

Current (Amps)

Resistance

(Ohms)

Voltage (volts)

Current (Amps)

Resistance(Ohms)

Average Resistance (Ohms)

50

0.028

1.98

0.09

22.00

2.34

0.12

19.50

20.75

50

0.045

1.62

0.27

6.00

1.03

0.17

6.06

6.03

50

0.057

0.8

0.19

4.21

1.74

0.41

4.24

4.23

50

0.113

0.6

0.26

2.31

1.34

0.54

2.48

2.39

50

0.166

0.71

0.46

1.54

0.87

0.44

1.98

1.76

50

0.246

0.35

0.29

1.21

0.7

0.57

1.23

1.22

A Table to Show Results Taken When Testing Length against Resistance

A Table to Show Results Taken When Testing Cross Sectional area of a Wire against Resistance

Graphs:

On the previous pages are graphs I have drawn up from my results. The 1st graph shows a straight line passing through the origin, this means that the two factors are in direct proportion (Resistance and Length of Wire). For cross sectional area, I noticed that the line was inversely proportional, to test my theory, I did a graph with 1/Resitance plotted against cross sectional area. It came out as a straight line; this proves they are inversely proportional.

Conclusions:

When electrons travel around a circuit they make collisions with the conductor that they are traveling in, it is the energy given off in these collisions that is resistance. I can take this theory and apply it to my results.

Length of Wire:

I found, as in my prediction that the as the length of wire increases, so does the resistance. I also found that length of the wire and the resistance is in direct proportion with one and other. (If you double one the other will double also). This is because if the current passes through an amount of wire, the electrons will make a certain amount of collisions with the material, and resistance will be cause. If the current passes through double the amount of wire, there will be double the material, so double the collisions with electrons will be made, and double the resistance will be created. Read also does length of wire affect current essay

Cross Sectional Area of Wire:

For cross sectional area of wire, as I predicted, the greater the cross sectional area, the less resistance, this is because there is more space for electrons to fit through the wire when it is very thick, and so there will be less collisions between the electrons and the wire, than when it has a small cross sectional area. From doing a 1/Resistance graph, I found out that it was inversely proportional.

Evaluation:

Overall my investigation went well, I got the results required, I am quite sure that the results are reliable enough to support my conclusion as I took the average of 2 repeats, this reduces the margin of error, as does drawing lines of best fit. However if I were to do the experiment again then I would make several changes, to make my results more accurate.

1) When testing the cross sectional area of wire I would use all the wires available, as I did, but I would double them up to give my self better results. This would make my graph more reliable as I would have more points on it, which looking at it is something that looking at it I think I need.

2) I would attach the wire that I was testing into the circuit fully stretched, this is because sometimes when I was testing the length the wire coiled round and connected with itself, I made sure this didn’t happen, but it took up a lot of time.

3) I would do 3 repeats instead of 2; this would increase the accuracy of my results.

4) On my 1/Resistance graph, it appeared I had a few anomalies, doing more repeats would possibly prevent this from happening the second time round.