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How Does the Length of a Wire Affect its Resistance?

Extracts from this document...

Introduction

How Does the Length of a Wire Affect its Resistance?

Physics Coursework

How Does the Length of a Wire Affect its Resistance?

PLANNING:

Aim:

        The aim of this experiment is to investigate the relationship between a length of wire and the resistance it gives.

Background Information / Introduction:

        To understand the effects of resistance, we must first take a look at what exactly resistance is affecting. When resistance is changed, both the current and the voltage across will be affected. Current is defined as the rate of flow of electrons and the symbol is I. When electrons flow through a conductor, an electric current is present. The amount of electrical charge that passes any point in a circuit is measured in Coulombs. Coulombs is the measurement for Charge (Q). Therefore the equation for Current, when t = time:

I (A) = Q (C) /t (s)

        Current is measured in amperes (A), which is Coulombs (C) per second (s). An ammeter is used to find the current that will be the same at all points in a series circuit.  The equation for amperes is:

A = C / s

Voltage (V) is defined as the amount of energy (E) per coulomb (C)of charge (Q). The equation for voltage is:

V = E / Q

        Voltage is measured in Volts (V) and the equation for this is:

V = J / C

        The voltage across, or potential difference, is the difference in voltage between two points in a circuit. A voltmeter is attached across a component at two points, to find the amount of voltage across it.

        Resistance in a circuit can be likened to a group of children passing through a corridor. If the corridor is long and narrow, it will be more difficult for them to pass through.

...read more.

Middle

        With the switch turned on, I placed the metal pointer at exactly 10 cm on the ruler and held it there to record the results. This step was repeated in exactly the same way, every 10 cm. I did this until I reached 100 cm. In the end, 10 readings were found.

3rd – Repeat

After the initial readings were taken, the process was repeated two more times.


Results:

Chart Showing how Resistance of a Metal Wire Changes with its Length

Length (cm)

1st I (A)

2nd I (A)

3rd I (A)

1st V (V)

2nd V (V)

3rd V (V)

1st R (Ω)

2nd R (Ω)

3rd R (Ω)

Avg V (V)

Avg I (A)

Avg R (Ω)

10

0.3

0.3

0.3

1.01

1.18

1.04

3.37

3.93

3.47

1.08

0.30

3.59

20

0.18

0.17

0.18

1.21

1.2

1.21

6.72

7.06

6.72

1.21

0.18

6.83

30

0.13

0.13

0.14

1.23

1.23

1.25

9.46

9.46

8.93

1.24

0.13

9.28

40

0.11

0.11

0.1

1.3

1.3

1.3

11.82

11.82

13.00

1.30

0.11

12.21

50

0.09

0.1

0.09

1.38

1.38

1.38

15.33

13.80

15.33

1.38

0.09

14.82

60

0.08

0.08

0.08

1.39

1.39

1.39

17.38

17.38

17.38

1.39

0.08

17.38

70

0.07

0.07

0.07

1.39

1.39

1.39

19.86

19.86

19.86

1.39

0.07

19.86

80

0.06

0.06

0.07

1.39

1.4

1.39

23.17

23.33

19.86

1.39

0.06

22.12

90

0.06

0.05

0.05

1.39

1.4

1.4

23.17

28.00

28.00

1.40

0.05

26.39

100

0.04

0.05

0.05

1.41

1.41

1.4

35.25

28.20

28.00

1.41

0.05

30.48

...read more.

Conclusion

100% over the lengths which were half. However, I saw an average increase in resistance of 88.66%, which is 11.34% less than I had predicted. For the lengths which tripled, such as 10 cm to 30 cm and 30 cm to 90 cm, I would have liked to have seen the resistance increase by approximately 200%. However, I recorded an average increase of 171.44%, which is 28.56% less than I had previously predicted. There was, however, still a close correlation in the doubling of lengths and its affect on resistance which would still suggest that my hypothesis has some accuracy.

        The experiment clearly proved most of my predictions to be correct. If I were to perform the experiment again, I would have allowed a minimum of 40 seconds between each time that I took a reading. This would have allowed the wire to cool down fully, which would have reduced the affect that temperature has on resistance.

        The reason for why the voltage across the wire changes as the length is due to the electromagnetic force of the cell being divided across the internal resistor of the cell and the material. The applied potential difference across the wire pushes the electrons through the wire. The size of the current depends upon the resistance of the wire. At constant temperature, the resistance of the wire is directly proportional to the potential difference across it and Ohms law can be used to calculate the resistance of the length of wire.

        I would have liked to have observed the affects that other variables have on the resistance.        If I had used thicker gauge wire, I could have observed the affects that diameter of a wire has on resistance. Heating up or cooling down the wire would have allowed me to test the affect that temperature has on resistance.

        I feel that I have gained a sound understanding of how the length of a wire affects its resistance.

...read more.

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