Resistance of a Wire

Resistance of a Wire

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Resistance of a Wire

Task

To investigate how the resistance of a wire is affected by the length
of the wire.



Theory
======

What is resistance?

Electricity is conducted through a conductor, in this case wire, by
means of free electrons. The number of free electrons depends on the
material and more free electrons means a better conductor, i.e. it has
less resistance. For example, gold has more free electrons than iron
and, as a result, it is a better conductor. The free electrons are
given energy and as a result move and collide with neighbouring free
electrons. This happens across the length of the wire and thus
electricity is conducted. Resistance is the result of energy loss as
heat. It involves collisions between the free electrons and the fixed
particles of the metal, other free electrons and impurities. These
collisions convert some of the energy that the free electrons are
carrying into heat.

How is it measured?

The resistance of a length of wire is calculated by measuring the
current present in the circuit (in series) and the voltage across the
wire (in parallel). These measurements are then applied to this
formula:

V = I ´ R where V = Voltage, I = Current and R = Resistance

This can be rearranged to:

R = V

I


Ohm's Law

It is also relevant to know of Ohm's Law, which states that the
current through a metallic conductor (e.g. wire) at a constant
temperature is proportional to the potential difference (voltage).
Therefore V ¸ I is constant. This means that the resistance of a
metallic conductor is constant providing that the temperature also
remains constant. Furthermore, the resistance of a metal increases as
its temperature increases. This is because at higher temperatures, the
particles of the conductor are moving around more quickly, thus
increasing the likelihood of collisions with the free electrons.



Variables
=========

Input:

* Length of wire.

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Related Searches

*

* Material of wire.

* Width of wire.

* Starting temperature of wire.

Output:

and thus the resistance of the wire. †

* Voltage across wire.

* Current in circuit.

* Temperature of wire.

The variable marked with a * will be varied, the other input variables
will be kept constant. The output variable marked with a † will be
measured.



Predictions
===========

* The longer the wire, the higher the resistance. This is because
the longer the wire, the more times the free electrons will
collide with other free electrons, the particles making up the
metal, and any impurities in the metal. Therefore, more energy is
going to be lost in these collisions (as heat).

* Furthermore, doubling the length of the wire will result in double
the resistance. This is because by doubling the length of the wire
one is also doubling the collisions that will occur, thus doubling
the amount of energy lost in these collisions.



Method
======

The following circuit was constructed to perform the investigation:


wire


The two dots ( ) represent the crocodile clips that were placed at the
ends of the required length of wire.

1. One metre length of 0.4mm diameter "constantan" (a metal alloy)
wire is fixed to a metre rule.

2. The first crocodile clip is clipped to the wire at the 0cm position
on the metre rule.

3. The second crocodile clip is clipped to the relevant position
depending on the required length of wire.

4. The power supply is turned on. The voltage and current are then
read off the ammeter and voltmeter, and recorded.

5. The power supply is then turned off and the second crocodile clip
is moved to the next position.

The above steps are completed for each length and then the entire
investigation is repeated for accuracy.



Rough Trials
============

In order to decide upon the voltage and lengths of wire to use in the
final experiment, the following rough trials were carried out:

At 3V:

Length (cm)

Voltage (V)

Current (A)

Resistance (W) (to 2 d.p.)

10

0.41

0.90

0.46

20

0.51

0.57

0.89

30

0.56

0.42

1.33

40

0.60

0.32

1.88

50

0.63

0.26

2.42

60

0.64

0.23

2.78

70

0.65

0.20

3.25

80

0.66

0.18

3.67

90

0.67

0.16

4.19

100

0.68

0.15

4.53


At 5V:
------

Length (cm)

Voltage (V)

Current (A)

Resistance (W) (to 2 d.p.)

10

Could not be carried out as the wire simply melted.

20

2.12

2.07

1.02

30

2.25

1.56

1.44

40

2.34

1.24

1.88

50

2.41

1.02

2.36

60

2.45

0.88

2.78

70

2.49

0.77

3.23

80

2.52

0.68

3.71

90

2.54

0.62

4.10

100

2.56

0.55

4.65

After performing these rough trials, it was decided that 3V would be
used in the proper experiment, as it provided results from 10cm up to
100cm and the higher voltage provided no additional ease of
measurement.

Furthermore, it was also decided to allow the wire to cool between
experiments as considerable heat was noticed at lower lengths and, as
mentioned above, an increase in temperature results in an increase in
resistance. By allowing the wire to cool between experiments a fair
test could be assured.



Safety
======

In order to perform a safe experiment, a low voltage of 3V was chosen
so that overheating was minimilised. Furthermore, lengths lower than
10cm were not tried, which also helped to avoid overheating.



Results
=======

Wire 1, Set 1:

Length (cm)

Voltage (V)

Current (A)

Resistance (W) (to 2 d.p.)

10

0.66

1.22

0.54

20

0.84

0.89

0.94

30

0.97

0.70

1.39

40

1.06

0.57

1.86

50

1.16

0.50

2.32

60

1.22

0.44

2.77

70

1.25

0.38

3.29

80

1.27

0.35

3.63

90

1.31

0.29

4.52

100

1.33

0.29

4.59

Wire 1, Set 2:

Length (cm)

Voltage (V)

Current (A)

Resistance (W) (to 2 d.p.)

10

0.51

1.02

0.50

20

0.79

0.79

0.97

30

0.91

0.65

1.40

40

1.02

0.55

1.85

50

1.08

0.48

2.25

60

1.15

0.42

2.74

70

1.19

0.37

3.22

80

1.22

0.33

3.70

90

1.26

0.30

4.20

100

1.27

0.28

4.54

Having completed two sets of results for one wire, it was noticed that
these was a large black mark towards one end of the wire, where it
appeared that it had been melted to some degree at some point. It was
therefore decided to conduct experiments on an additional piece of
wire that was checked for integrity prior to investigation:

Wire 2, Set 1:

Length (cm)

Voltage (V)

Current (A)

Resistance (W) (to 2 d.p.)

10

0.95

1.06

0.90

20

1.19

0.67

1.78

30

1.28

0.48

2.67

40

1.35

0.37

3.65

50

1.38

0.32

4.31

60

1.42

0.27

5.26

70

1.45

0.24

6.04

80

1.46

0.21

6.95

90

1.48

0.19

7.79

100

1.50

0.17

8.82

Wire 2, Set 2:

Length (cm)

Voltage (V)

Current (A)

Resistance (W) (to 2 d.p.)

10

0.92

1.05

0.88

20

1.16

0.66

1.76

30

1.28

0.47

2.72

40

1.34

0.39

3.44

50

1.38

0.32

4.31

60

1.42

0.27

5.26

70

1.45

0.23

6.30

80

1.47

0.21

7.00

90

1.47

0.17

8.65

100

1.48

0.16

9.25

Averages for each wire were then calculated to give these results,
which were then graphed:

Length (cm)

Resistance (W) (to 2 d.p.)

Wire 1

Wire 2

10

0.52

0.89

20

0.96

1.77

30

1.40

2.70

40

1.86

3.55

50

2.29

4.31

60

2.76

5.26

70

3.26

6.17

80

3.67

6.98

90

4.36

8.22

100

4.57

9.04



Conclusions
===========

Having performed the investigation, the following conclusions were
drawn:

* As predicted, an increase in length resulted in an increased
resistance. This can be clearly said for both wires tested.

* Both wires show a strong trend of a straight line, i.e. the length
of the wire is shown to be directly proportional to the resistance
- double the length and the resistance doubles.

* The overall resistance of the two wires seems to differ
considerably. Due to the strong correlation of the results, the
explanation of this is unlikely to be the method used to obtain
the results. The more likely explanation would be that the first
wire was actually of a larger diameter than the second one.
Obviously this is a rather important oversight and this will be
discussed more in the Evaluation section. The reason why this is
the likely explanation is because resistance is known to be
inversely proportional to the cross-sectional area, i.e. if you
increase the cross-sectional area (by increasing the diameter)
then you decrease the resistance. This is because a wider wire
means less likelihood of the free electrons having collisions and
losing energy.

It is important to realise, however, that despite the fact that it
would appear that the resistance of wire 2 is double that of wire 1,
that does not mean that the diameter is half that of the wire 1. That
is because if you halve the diameter then you decrease the area by a
factor of about 3 (A = πr2)



Evaluation
==========

* As mentioned previously, the biggest downfall of the investigation
was the apparent mistakes when choosing the wire, in that they
would appear to be of differing diameters. This did not, in this
case, cause a big problem as the same wire was used for each set
of results so it is known that the results for each wire are
correct.

* Generally speaking, wire 1 would appear to contain the most
accurate results due to the fact that all of its points bar one
sit on the line of best fit for that wire. The only one that does
not is the point at 90cm, which was exactly at the point that the
black mark (mentioned previously) was found to be.

* Wire 2, on the other hand, had three main anomalous results: at
50, 80 and 90cm. They are by no means that far off but in an
experiment such as this, which is generally a very accurate one
anyway, such anomalous results should not be quite so common.
Possible explanations for these anomalies are as follows:

*

* The length of wire for that particular measurement was not
correct. At 50 and 80cm it is possible that the length was
shorter, causing a lower resistance, and at 90cm it is
possible that it was longer, causing a higher resistance. The
solution to this is to measure the lengths more carefully and
ensure that the wire is pulled tight against the metre rule.

* For a particular result, one or more of the connections could
have been faulty, causing extra resistance at the connections.
A solution to this would be to, before each experiment,
connect the connections together without the wire in place and
measure the resistance then. If it is higher than it should be
then the connections could be cleaned.

* Whilst extremely unlikely, it is conceivable that the power
supply was providing a different voltage for some of the
results. This is unlikely to be a problem in this
investigation but it might have been an issue had we used
batteries instead.

NB: If one were to assume that Ohm's Law applies, then another
possible explanation could be that at some points (more likely in the
lower lengths), the wire was not allowed to cool completely so that
the temperature was higher for that measurement. Whilst unlikely (due
to the two sets of results), this would cause a higher resistance as
explained previously. However, it is now known, after researching the
metal alloy "constantan," that the resistivity (the electrical
resistance of a conductor of particular area and length) of this alloy
is not affected by temperature. Therefore, in these experiments Ohm's
Law does not apply.
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