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Investigating the length/resistance relationship for a conductor

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Introduction

BENITO SEGARAJASINGHE

11NI

Physics Coursework

Investigating the length/resistance relationship for a conductor

Investigating the length/resistance relationship for a conductor

This investigation will be to determine the relationship between the length of a conductor and its resistance.

        The aim is to test a number of different lengths of nichrome wire to measure the resistance of each length. To ensure a safe procedure, a low voltage battery of 12 volts will be used, and the samples to be tested will be located on an insulating mat to prevent any shorts occurring. In addition a 2 Amp fuse will be placed in the circuit as a protective measure. For a fair test, all other parameters that can affect the resistance will be kept constant. These are the sample material, the diameter of the wire, and the temperature of the wire. To keep the temperature of the wire constant, it will be necessary to keep the current flowing in it constant. This is because the power dissipated in the conductor is I2R, so an increase of current by a factor of 2 will increase the power dissipated by a factor of 4, which can seriously affect the resistance.

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Middle

image06.png

If the metal is attached to a power supply then the electrons flow through the metal but collide with atoms. Resistance is shown below in the diagram below:

The resistance of a metal can be regarded as arising from the interaction, which occurs between the crystal lattice of the metal and the ‘free’ electrons as they drift through it under an applied potential difference. This interaction is due mainly to collisions between defects in the crystal lattice (e.g. impurity atoms and dislocations) also play a part, especially at very low temperatures.

Resistance is measured in Ohms (Ω) Georg Ohm discovered that the current flowing through a metal wire is proportional to the potential difference across it (providing the temperature remains constant).

Therefore:   Resistance, R (Ω) = Potential difference across the wire (V) image07.png

                I= V ÷ R

                V= I x R

                R= V ÷ I

TABLE 1image08.png

RESULTS: Table 1 shows the data recorded and the resulting values for resistance for each length. These were those separate samples of the conductor tested for each length, and the average voltage was used to determine the resistance volume.

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Conclusion

olspan="1" rowspan="1">

0.16

70.00

0.09

25.96

0.19

80.00

0.09

28.78

0.21

90.00

0.09

32.24

0.23

100.00

0.09

35.92

0.26

From the table above we see that there is a relationship between the resistance and the current. We see that from the results table that the power (in Watts) is equivalent to the current (in amps) squared multiplied by the resistance of the wire. From the graph showing Power Vs Length, we can work out the heat transferred in one centimetre of nichrome wire.

Power ÷ Length =Thermal energy transferred (J)

Length (cm)

Current (Amps)

Power (Watts)

10.00

0.09

0.02

20.00

0.09

0.05

30.00

0.09

0.08

40.00

0.09

0.10

50.00

0.09

0.14

60.00

0.09

0.16

70.00

0.09

0.19

80.00

0.09

0.21

90.00

0.09

0.23

100.00

0.09

0.26

Thermal energy transferred (J)        

0.002351667

0.002479167

0.002691667

0.00255

0.00272

0.002606667

0.002679524

0.002599583

0.002587778

0.002595333

From these results we can work out the coulombs of charge in each separate length of nichrome. This result will then allow us to calculate how many electrons had passed through the wire, which further allows us to calculate the time taken for the experiment to take place.

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