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# The aim of this investigation is to find out if the length of an electrical resistor (graphite putty) affects its resistance.

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Introduction

Physics Coursework: Electrical Resistance

Aim:

The aim of this investigation is to find out if the length of an electrical resistor (graphite putty) affects its resistance.

Prediction:

An electrical current is the movement of electrons through a substance. Resistance occurs when the electrons travelling through the substance collide with the atoms of the substance. This collision slows down the flow of electrons causing resistance. Resistance is the measurement of how hard it is for electrons to move through a substance. The resistance of a substance is measured in Ohms (Ω), which can be shown in the formula:

Voltage

Resistance = ---------------          (Equation 1)

Current

All substances have a resistance, the more resistance a substance has the less current gets through. The resistance of a substance can be altered by factors which include:

• Temperature

Heat energy gives the atoms of the resistor more energy causing them to vibrate. This results in more collisions between the passing electrons and the atoms of the resistor. Therefore, resistance of a resistor is increased if the temperature is increased.

• Cross-sectional area

The larger the cross-sectional area is, the less likely the electrons will collide with the atoms of the substance they are flowing through. Therefore, resistance of a resistor is decreased if the cross-sectional area is increased.

• Length

The electrons have to travel a longer distance if the length of the resistor is increased. More collisions will occur between the electrons and the atoms of the substance. Therefore, an increase in length results in an increase in resistance.

I predict that a longer resistor will give higher resistance.

Middle

3.5

0.88

3

0.04

0.0004

3

3.5

1.17

2

0.04

0.0004

2

3.5

1.75

1

0.04

0.0004

1

3.5

3.50

Method:

## As stated in the plan, except that we did not have time to repeat Method 2 three times.

Safety:

The following are the steps we took to make the investigation safe:

• We used a low voltage to reduce risk of electrocution.
• We did not touch any exposed wires when the power was on.
• We were careful when we cut a segment from the graphite putty.
• We cut the graphite putty on a cutting tile.

Fair Test:

The following are the steps we took to ensure that the investigation was fair:

• We used the same graphite putty for every experiment.
• The width and height of the graphite putty remained constant (width = 2cm, height = 2cm), only the length changed.
• We used the same voltage in every experiment.
• We cleaned the surface of the copper plates to remove any impurities or oxides that may alter our results.
• We covered the whole of the cross sectional area of the graphite putty with the copper plates.
• We performed the experiment in an air-conditioned environment; therefore the temperature was constant.
• We allowed the graphite putty to cool down after each experiment, to prevent an increase in resistance after the current passed through it.

Results and Analysis:

Table 2 in the next page summarizes the results of Method 1 where currents passing through the resistor were measured. For each length, we have included the three individual readings, the calculated average of the three readings, the predicted result as derived in Table 1, and the percent deviation comparing our experimental result to the prediction.

With a quick glance, we notice that the first two experimental results are inconsistent to the rest of the other results. While the rest of the currents we recorded increase as the length of the graphite putty decrease, the current recorded for the length of 14cm was slightly lower than that for the length of 15cm.

Graph 2 illustrates the effect of the length of resistor on the current passing through it. The black line shows the average current obtained from our measurements against the length of the resistor while the red line represents the predicted relationship between the current and the length of the resistor. Both graphs produce upward curves showing an exponential increase in current as the length of the graphite putty decreases. This is because current is inversely proportional to the length of the resistor.

#### Table 2: Results of Method 1

Length of resistor (cm)

Current (A)

% deviation

Average

##### Predicted

15

0.23

0.23

0.22

0.23

0.23

-3

14

0.22

0.22

0.22

0.22

0.25

-12

13

0.24

0.23

0.23

0.23

0.27

-13

12

0.29

0.27

0.26

0.27

0.29

-6

11

0.30

0.30

0.30

0.30

0.32

-6

10

0.36

0.36

0.35

0.36

0.35

2

9

0.39

0.39

0.39

0.39

0.39

0

8

0.44

0.43

0.43

0.43

0.44

-1

7

0.55

0.55

0.55

0.55

0.50

10

6

0.64

0.63

0.62

0.63

0.58

8

5

0.70

0.75

0.73

0.73

0.70

4

4

0.90

0.89

0.88

0.89

0.88

2

3

1.10

1.07

1.16

1.11

1.17

-5

2

1.40

1.39

1.48

1.42

1.75

-19

1

1.98

2.01

1.98

1.99

3.50

-43

Conclusion

Another reason of error in a longer resistor could be that heat energy produced is higher since the resistor is longer and electrons flowing through it collide with more atoms. This heat energy causes the atoms to vibrate more vigorous thus increase the resistivity of the graphite putty and give rise to errors. If I were to repeat this experiment again, I would monitor the temperature of the graphite putty because a change in temperature would change the resistivity of the substance. I would monitor the temperature with a thermometer and only perform the experiment when the graphite putty is at a certain temperature so that the resistivity is the same.

To improve the experiment, I would use acid to clean the surface of the copper plates because this would remove all impurities and oxides from the surface of the copper plates. Using sandpaper to clean the surface of the copper may not have removed all of the impurities. These impurities and oxides may have increased the resistance slightly.

Conclusion:

The results I obtained are accurate enough for me to make the conclusion that the length of a resistor does affect the resistance of the resistor. An increase in length of the resistor results in an increase in resistance because there are more atoms for the electrons to collide with. This supports my original prediction that the resistance will increase if the length of the resistor increases. Furthermore, resistance of a resistor is directly proportional to its length. Doubling the length doubles the resistance because there are twice as many atoms; so there are twice as many collisions. Halving the length would halve the number of atoms in the resistor resulting in half the number of collisions; therefore resistance is halved.

By Tsun-Kidd Wong, 11JI

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