How does the length of wire affect resistance?

* Length, resistance increases as length increases

* Cross sectional area, resistance decreases as cross section increases

Fair Test

To make this into a fair test the temperature of the wire, the material the wire is made of and therefore the resistivity and the cross sectional area of the wire have to remain constant. To control the temperature of the wire I have to use a small current and keep the current turned on for as little time as possible.

Prediction

I predict that as the wire length increases, the resistance will increase proportionally.

Resistance (R) is directly proportional to length (l)

Resistance is inversely proportional to cross sectional area (A)

Resistivity (P)

R = Pl

A

To make this a fair test P and A have to remain constant. To achieve this I shall make sure that I always use wire made of constantan with the same cross sectional area.

Because P and A are constant, R and l are proportional so when the length doubles the resistance in the wire should double too. Therefore a straight line graph will be produced.

Apparatus 1

constantan wire

leads

multimeter

metre rule

crocodile clips

Apparatus 2

constantan wire

leads

2 multimeters

metre rule

crocodile clips

power supply

Diagram 1

Diagram 2

Method 1

Set up apparatus 1 as in diagram 1 and clip the crocodile clips together to find the resistance in the leads. Attach one of the crocodile clips to the end of the wire. Put the other crocodile clip on the wire at a length of 10cm. Use a multimeter to measure the resistance in the length of wire and subtract the resistance of the leads. Repeat this with lengths increasing 10cm each time. Repeat the whole experiment twice more to check that your results are reliable.

Method 2

Set up apparatus 2 as in diagram 2. Attach one crocodile clip to the end of the wire and the other clip on the wire at a length of 10cm. Measure the voltage and current with the multimeters set as a voltmeter and ammeter. Use the formula R=V to find the resistance. Repeat this with

I

lengths increasing by 10cm each time. Repeat the experiment to ensure reliability.

Preliminary work

Before I start this experiment I have to choose what cross sectional area to use. I have two thicknesses of wire, 0.19mm and 0.56mm. I want to use the wire that has the highest resistance as the results will be easier to record. This should be the thin wire as the thinner the wire is the higher the resistance because less electrons can get through in the same amount of time. I shall test this to make sure that I am correct.

Cross sectional area of wire

Resistance at 10cm

Resistance at 20cm

0.19

6.3

9.0

0.56

2.6

3.3

My preliminary work shows that I should use the thinner wire as there is the greatest resistance change and therefore less error in my measurements.

Results 1

Length of wire (cm)

Resistance (ohms)

1

2

3

Average

Rounded for graph

0

.3

.3

.2

.2666666667

.3

20

2.6

2.4

2.4

2.533333333

2.5

30

3.7

3.6

3.6

3.6666666667

3.7

40

4.8

4.8

4.8

4.83

4.8

50

6.2

6.1

5.9

6.066666667

6.1

60

7.5

7.3

7.2

7.3

7.3

70

8.5

8.5

8.4

8.467

8.5

80

0.0

9.6

9.5

9.7

9.7

90

0.9

0.9

0.8

0.866666667

0.9

00

2.0

2.2

2.0

2.0666666667

2.1

Results 2

Length of wire (cm)

Voltage (V)

(Volts)

Current (I)

(Amps)

Resistance (R)

(?m)

1

2

1

2

1

2

Average

Rounded for graph

0

0.56

0.54

0.3

0.3

.86

.8

.83

.8

20

.05

.06

0.3

0.3

3.5

3.53

3.515

3.5

30

.58

.58

0.3

0.3

5.26

5.26

5.26

5.3

40

2.14

2.08

0.3

0.3

7.13

6.93

7.03

7.0

50

2.64

2.64

0.3

0.3

8.8

8.8

8.8

8.8

60

3.13

3.11

0.3

0.3

0.4

0.36

0.38

0.4

70

3.63

3.60

0.3

0.3

2.1

2

2.05

2.1

80

4.13

4.16

0.3

0.3

3.76

3.86

3.81

3.8

90

4.63

4.73

0.3

0.3

5.43

5.76

5.595

5.6

00

5.21

5.22

0.3

0.3

7.36

7.4

7.38

7.4

Results 3

This set of results is obtained by using the formula R = Pl

A

to calculate what the resistance should be.

P = 4.9 x 10-7

A = 2.8 x 10-8

Length of wire (cm)

Calculated resistance (?m)

Rounded for graph (?m)

0

.73

.7

20

3.45

3.5

30

5.18

5.2

40

6.91

6.9

50

8.64

8.6

60

0.37

0.4

70

2.07

2.1

80

3.82

3.8

90

5.55

5.6

00

7.28

7.3

Analysis

From my results I conclude that as the length of the wire increases so does the resistance. We can see this on my graph, which shows the increase in resistance. My graph proves that the results are directly proportional because it is a straight line and it goes through point 0, you can see from the graph that as the height doubles the resistance almost exactly doubles too.

The resistance increases as the length increases because of the positive nuclei in the wire. The positive nuclei attract the negative electrons and deflect them from travelling in a straight line. This means the electrons travel a much larger distance to go the same length through the wire and take longer. The vibration of the positive nuclei in the wire also increases the resistance. When the nuclei move around they causes more frequent deflections. This makes the journey of the electrons slower.

My prediction was correct. As the length of the wire increased, so did the resistance. I was also correct when I predicted that the results would be proportional and therefore produce a straight-line graph.

Evaluation

The results obtained are fairly accurate as you can see by the fact that when one doubles the other doubles with only a small degree of inaccuracy. This slight deviation even occurred in results 3 where I calculated the answer using the formula R = Pl . This fact shows that the increase is

A

not completely exact and therefore results 1 and 2 are not as inaccurate as they may seem. I have no anomalous results, which shows that my measurements were probably accurate.

I think that the methods used in this experiment where extremely suitable for this experiment, as they were accurate and reliable. The experiment would have been more accurate if results 1 had been measured to two or three decimal places. Using computer technology to measure the thickness and length of the wire would have also made a difference to the accuracy although I think that this experiment was very accurate in measurements.

The evidence I have collected is sufficient to support my conclusion as I have investigated the theory in three different ways and they have all followed the same trend of being proportional with very little difference between the results of each experiment. Each experiment has ten different measurements which allow me to plot a fairly accurate graph and I have repeated each measurement three times (except results 3 where this was not appropriate) to calculate an average for the graph which makes the experiment more accurate.

If I had more time I could make my experiment more accurate by accounting for the effects of temperature on results 2. To do this I could either:

* Set up diagram 2 with 100cm of wire and measure the temperature of the wire. I would keep the current switched on and at regular temperature intervals I would measure the resistance to find out how much it increases so that I could find out whether that would have affected my results significantly.

* Or I could use the formula R = H to calculate the

I2

resistance with different temperatures and a set current.

(H = heat)