Resistance Coursework Conclusion

Experiment on Electrical Resistance

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Experiment on Electrical Resistance



The electrical resistance of a material is its opposition to the flow
of electric current (slowing the flow of electrons down). Resistance
occurs when the electrons travelling along the wire collide with the
atoms of the wire. These collisions slow down the flow of electrons
causing resistance. Resistance is a measure of how hard it is to move
the electrons through the wire.


A current is the rate of the flow of charge (electrons) and the
resistance controls the amount of current flowing. If we want to
calculate the current flowing through the circuit, we need to know how
much resistance it has. A resistor that has a large resistance only
allows a small current through it and a small resistance allows a
large current through. Resistors are usually long coils of wire, or
small pieces of material that do not conduct electricity very well,
therefore the conductivity of the metals affect resistance. As the
potential difference (voltage) between the ends of conductor is
increased the current passing through it increases. If the temperature
of the conductor doesn't change, the current that flows is
proportional to the voltage applied. This is called Ohms Law.


Ohms Law= Potential Difference x Current or


Potential Difference = resistance x current or

The unit of resistance is measured in Ohms (W).

Measuring Resistance

The voltage across the resistor is measured using the voltmeter. The
current flowing through the resistor is measured using the ammeter.
The resistance can then be calculated using the formula: Resistance =
Voltage

Current

The width, length, material and temperature are factors, which affect
the resistance of a wire.

Temperature: If the wire is heated up the atoms in the wire will start
to vibrate because of their increase in energy. This causes more
collisions between the electrons and the atoms as the atoms are moving
into the path of the electrons. This increase in collisions means that
there will be an increase in resistance.

Material: The type of material will affect the amount of free

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Electrical Resistance         Experiment         Electric Current         Resistor         Affect Resistance         Voltage         Collisions         Conductor         Atoms        




electrons, which are able to flow through the wire. The number of
electrons depends on the amount of electrons in the outer energy shell
of the atoms, so if there are more or larger atoms then there must be
more electrons available. If the material has a high number of atoms
there will be high number of electrons causing a lower resistance
because of the increase in the number of electrons. Also if the atoms
in the material are closely packed then the electrons will have more
frequent collisions and the resistance will increase.

Wire length: If the length of the wire is increased then the
resistance will also increase as the electrons will have a longer
distance to travel and so more collisions will occur. Due to this the
length increase should be proportional to the resistance increase.

Wire width: If the wires width is increased the resistance will
decrease. This is because of the increase in the space for the
electrons to travel through. Due to this increased space between the
atoms there should be less collisions.

I am going to investigate how the length of wire affects its
resistance.

I have done a preliminary experiment to help me make my plan:

Preliminary Work

Diagram:

[IMAGE]




Method:

The apparatus was set up in a circuit as shown in the diagram above. I
used a wire with constantan wire SWG 32. The lab pack was set to
coarse=2.0V and Fine=0.2V. The length of the wire was increased by 5cm
each time. The results were recorded and put into a table.

Results:

Length (cm)

Voltmeter (v)

Ammeter (I)

Resistance (W)

5

0.45

0.66

0.68

10

0.6

0.48

1.25

15

0.7

0.42

1.67

20

0.7

0.38

1.84

25

0.8

0.32

2.50

30

0.8

0.28

2.86

35

0.9

0.26

3.46

40

0.9

0.24

3.75

45

0.9

0.23

3.91

50

1.0

0.22

4.54

55

1.0

0.18

5.56

60

1.0

0.18

5.56

65

1.0

0.18

5.56

70

1.0

0.16

6.25

75

1.1

0.16

6.88

80

1.1

0.14

7.86

85

1.1

0.14

7.86

Conclusion:

From these results I've learnt that as the wire gets longer, the
resistance gets bigger.

The preliminary experiment gives me information on what size wire I
should use, and what the settings on my lab pack are going to be. I
also now know, what type of results I should be getting in my real
experiment.


Prediction

I predict that as the length of the resistance wire increases the
current flowing through the constantan wire decreases and the
resistance increases. This is because when increasing the length of
the wire there is a greater mass of the substance. Therefore there are
a greater number of positive ions. Electrons colliding with the
positive ions, causing the electrons to slow as their kinetic energy
has been transferred to the positive ions, cause resistance. A short
length of wire (5cm) has a large current (0.66A) and a small
resistance (0.68W) but a long length wire (80cm) has a small current
and a large resistance. I can see this from my preliminary experiment.

When the given length is doubled, this means that there is double the
amount of mobile electrons, and so double the chance of a collision.
As an electrical current is passed through the conductor, an electron
has to travel double the distance, and will therefore have two times
the amount of objects in its path. So, as I increase the length of
wire I will increase the resistance, so as I double the length of the
wire I will double the resistance, treble the length, treble the
resistance. From my scientific background I stated that the resistance
is directly proportional to the length.


Planning

In my experiment I am going to use the following apparatus:

§ Constantan Wire SWG 32

§ Ammeter

§ Voltmeter

§ Lab pack

§ Crocodile clips

§ Wires

I am going to set my apparatus in a series circuit, and join the
voltmeter parallel to the resistance wire.

I am going to use 19 different lengths (5cm-95cm):

5cm 25cm 45m 65cm 85cm

10cm 30cm 50cm 70cm 90cm

15cm 35cm 55cm 75cm 95cm

20cm 40cm 60cm 80cm

I will measure these lengths on a metre rule.

I am going to put the lab pack to these settings: coarse=4.0V and
fine=0.4V. This is different to what I used in my preliminary
experiment. I decided to increase the voltage on the lab pack slightly
because the current readings I was getting were quite low, so I wanted
to see if by changing the lab pack settings the current would get
bigger.

I will record my results in a table like the one I used in my
preliminary experiment, and I will then plot a graph of resistance (Y
axis) against Length (x axis).

Safety

· I am going to wear safety goggles and an overall throughout the
practical work.

· If I use a high voltage setting on the lab pack, there will be a
high current flowing through the wire, and therefore, it will heat up,
melt and break, therefore I am going to keep the voltages on the lab
pack quite low (4.0V and 0.4V=4.4V)

Fair Test

· To make my results are accurate and reliable as possible, I am going
to take 3 readings at each length and find the resistance in each 3
readings. Then I am going to find the average (mean) resistance at
each length.

· For a fair test I will need to make sure that the other variables
that I am not testing remain constant. I shall try and keep
temperature constant by only turning on the power pack for short
bursts so as to avoid the wires temperature going up significantly.
The other variables will be very easy to keep constant because I will
not be changing the type of wire that in turn means the thickness will
not change throughout the experiment and I will not change the voltage
I input at all during the experiment.

· I will read off the voltmeter and ammeter readings exactly.



v Obtaining Evidence

I carried out my plan as I stated, but I had to use constantan SWG 30
instead of constantan SWG 32, which I had stated. This was because
there were no more constantan SWG 32 wires left.

Length (cm)

Voltage (V)

Reading 1

Current (A)

Reading 1

Resistance (W)

(Reading 1)

Voltage (V)

Reading 2

Current (A) Reading 2

Resistance (W)

(Reading 2)

Voltage (V)

Reading 3

Current (A)

Reading 3

Resistance (W)

(Reading 3)

5

0.2

0.84

0.24

0.3

0.78

0.38

0.3

0.74

0.41

10

0.4

0.70

0.57

0.5

0.64

0.78

0.4

0.62

0.65

15

0.5

0.56

0.89

0.6

0.50

1.20

0.5

0.54

0.93

20

0.7

0.50

1.40

0.6

0.44

1.36

0.6

0.46

1.30

25

0.7

0.46

1.52

0.7

0.40

1.75

0.7

0.44

1.59

30

0.8

0.40

2.00

0.8

0.34

2.35

0.8

0.40

2.00

35

0.8

0.36

2.22

0.8

0.32

2.50

0.8

0.36

2.22

40

0.9

0.36

2.50

0.8

0.32

2.50

0.8

0.32

2.50

45

0.9

0.32

2.81

0.8

0.28

2.86

0.9

0.30

3.00

50

1.0

0.30

3.33

0.9

0.26

3.46

0.9

0.28

3.21

55

1.0

0.28

3.57

0.9

0.24

3.75

0.9

0.26

3.46

60

1.0

0.26

3.85

0.9

0.24

3.75

0.9

0.24

3.75

65

1.0

0.24

4.17

0.9

0.22

4.09

1.0

0.24

4.17

70

1.0

0.22

4.55

0.9

0.20

4.50

1.0

0.22

4.55

75

1.0

0.22

4.55

0.9

0.20

4.50

1.0

0.20

5.00

80

1.0

0.20

5.00

1.0

0.18

5.56

1.0

0.20

5.00

85

1.0

0.18

5.56

1.0

0.18

5.56

1.0

0.18

5.56

90

1.0

0.18

5.56

1.0

0.18

5.56

1.0

0.18

5.56

95

1.0

0.18

5.56

1.0

0.18

5.56

1.0

0.16

6.25


I repeated the experiment 3 times to get an average reading (like I
said in my plan). I worked out the average resistance by adding all 3
readings resistance at each length together and dividing by 3.

Length (cm) enen

Average (mean) Resistance (W) eeeee

5

0.34

10

0.67

15

1.01

20

1.36

25

1.62

30

2.12

35

2.31

40

2.50

45

2.89

50

3.34

55

3.59

60

3.78

65

4.14

70

4.53

75

4.68

80

5.19

85

5.56

90

5.56

95

5.79

My readings were accurate, because they represent the proportion
relationship between resistance and length. This is because current
flowing through the wire is proportional to the voltage applied.


v Analysis

I kept my readings at the same accuracy through out my experiment. For
resistance I recorded the readings at 2 d.p. , for current I recorded
the readings at 2 d.p. , and for voltage I recorded the readings at 1
d.p. To make it easier to draw my graph I am going to round up the
readings for resistance to 1 d.p.

Length (cm) enen

Average (mean) Resistance (W)

5

0.3

10

0.7

15

1.0

20

1.4

25

1.6

30

2.1

35

2.3

40

2.5

45

2.9

50

3.3

55

3.6

60

3.8

65

4.1

70

4.5

75

4.7

80

5.2

85

5.6

90

5.6

95

5.8

To illustrate my findings I have drawn a graph with a line of best
fit, which is in a straight line going through most of my points. The
straight line shows that ohm's law was present in my experiment;
therefore resistance is directly proportional to length. The length of
the wire affects the resistance of the wire because the number of
fixed ions in the wire increases or decreases as the length of the
wire increases or decreases in proportion. As stated in my plan,
electrical resistance in a wire is caused by collisions between the
free electrons and the fixed ionic structure of the metal. The more
collisions there are, the more difficult it is for the electrons to
pass through and therefore the greater the resistance. By increasing
the length, the number of fixed ions is also increased and
consequently more collisions occur. This has the effect of increasing
the resistance.

My prediction was correct. The resistance of the wire is directly
proportional to its length.

From the graph, we can also find out the gradient, which gives the
value of the resistance per unit length of the wire. This is useful
because it allows me to predict the resistance of any length of this
wire and so make resistors that can be used in circuits by cutting the
appropriate amount of wire

v Evaluation

Overall, my experiment went according to my plan.

From my graph it is clear the results follow a good straight line,
which supports my prediction. There were however, 8 anomalous points
on my graph, which I have circled. These fell slightly off of the best
straight line. There could be many causes for these anomalies:
firstly, by reading the potential difference to 1 d.p. , slight
variations in the P.d. could have been missed; secondly, the ammeters
and voltmeters could have been damaged and reading falsely on both the
meters used (however, this seems unlikely as the results were as I
expected), thirdly, Measuring the lengths of the wire is also a
inaccuracy as the rulers used are not exact, and it is difficult to
get an accurate reading of length by eye, as the wire might not be
completely straight, it may be of different thicknesses throughout the
length, so the length may have been longer than I had measured, lastly
whenever current flows through a wire it will heat up.As I stated in
my introduction, this heating effect will also tend to increase the
resistance. I feel that this last point is the most likely cause of
the errors I have.

To improve the reliability of my experiment, I would ensure that these
possibilities were overcome. I would use a voltmeter that was able to
read to 2 d.p., which would be more accurate. An even better method
for measuring the resistance would be to use a multi-meter to read the
resistance directly. By taking just one reading for the resistance
instead of two (current and p.d.), I will be able to reduce any errors
I have in reading the scales. I would also ensure that the temperature
of the wire stayed as constant as possible. I could do this a number
of ways. One method would be to cool the wire to a constant
temperature by immersing it in ice for all of the readings. A better
method however, would be to ensure that the current flowed in the wire
for as short a time as possible (as I stated in my plan) but this time
I'd try and turn the lab pack off even quicker, and so the heating
effect was as small as possible. By making these improvements, the
reliability of my experiment would be improved and so I could be even
more confident of my conclusions.

I am confident in my data. I took 3 readings for each of my 19 lengths
and so gained an average resistance. It is clear that all of my
results follow the same pattern and so I am confident in my conclusion
that resistance is proportional to length.

To extend my investigation, I would like to examine one of the other
factors from my introduction. As I feel that the heating effect of the
current gave me anomalous results, I would test to what extent
temperature affects resistance. To do this, I would take identical
lengths and thicknesses of wire and place them at different
temperatures using a water bath. In this way I could control the
temperature and by using the same circuit as before, determine the
affect that temperature has on the resistance.



In conclusion, the results for experiment 8.1 were a success in studying resonance of the voltages through the LCR circuit. An ideal system of inductive reactivity is an inductor without resistance. A real conductor, in practice, will have resistance and resonance at VR=VRmax<V0. The voltages across the resistor as a function of frequency of the applied sine wave through the series LCR circuit were indeed determined and a percent error comparing the theoretical versus experimental resonance frequency were established. The success of 8.1 gave rise to a minimal percent error of 2.37%, which indicates that the theory along with the experiment go hand in hand as far as experimental control. Results for 8.2 were also successful in that the measurements found achieved close resemblance to what was provided in the lab manual. The fact that we were able to reproduce similar results means the overall theory and experiment are factual data. Possible sources of error could have been attributed by a malfunction within the PASCO interface system, which would produce results not consistent with what was provided. Another error of course is always human error, as in the procedure of either experiment was not followed precisely.

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