An investigation into the theory of resistance
An investigation into the theory of resistance
Resistance of a wire
An electric current is the flow of electrons through a material. The
Current through a wire is proportional to the potential difference
across it. Plotting a graph of P.D against current would give a
straight line graph through the origin.
P.D
(V)
[image002.jpg] I (A)
The gradient of the line (V/ I) is a constant and is called
resistance. Resistance is measured in ohms (Ohm).
The graph above is an ideal case where there is no temperature change
of the wire during the time that measurements are being taken. This
will not be the case as passing an electric current through a wire
causes it to heat up, as in an electric kettle or electric fire.
By setting the following circuit it is possible to determine the
resistance of a wire:
[image004.jpg] ( [image006.jpg] = wire sample)
Planning
I shall apply an electrical current through a piece of wire one
hundred centimeters long. I will be taking readings of current and
P.d. every 10 centimeters. With the information I gather, I will then
be able to calculate the resistance using the formula:
Voltage (V)
= resistance
(Ohm)
Current (I)
Aim
I aim to carry out an experiment which will enable me to show a
relationship between length of a wire and resistance of a wire. In
this investigation I will see how resistance of a wire varies with the
extending length. The things I could change in this experiment are
called the variables, these are:
- Material of the wire
- Width of the wire
- Starting temperature of the wire
- Current in the circuit
Prediction
I predict that as I take my readings moving further along the wire,
the greater the resistance will become. This is because the longer the
wire, the more times the free electrons will collide with other
electrons, such as the particles making up the metal. From this more
electrical energy should be transferred into thermal energy. This in
short, means less electricity can pass through the wire giving it a
greater resistance. If my prediction appears to be correct then the
results of the resistance against length graph will be directly
proportional and show positive correlation.
Here is a simple diagram showing a metal wire that shall be used:
[image008.jpg]
It is the interaction between these positive atoms that causes the
wire to have resistance.
The inside of the metal has a regular array of positive ions (+ve);
this is when an ion is a metal atom, which has lost its free
electrons. The free electrons can swim about in the space between the
ions like gas molecules. When voltage is applied across the ends of a
wire the negative ions, (-ve) electrons, are attached towards the
positive end of the wire and current flows. Longer wires will cause ...
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[image008.jpg]
It is the interaction between these positive atoms that causes the
wire to have resistance.
The inside of the metal has a regular array of positive ions (+ve);
this is when an ion is a metal atom, which has lost its free
electrons. The free electrons can swim about in the space between the
ions like gas molecules. When voltage is applied across the ends of a
wire the negative ions, (-ve) electrons, are attached towards the
positive end of the wire and current flows. Longer wires will cause an
increase in resistance because the electrons have to travel past more
atoms, because of this, collisions between the electrons and the atoms
are more likely in longer wires then in shorter wires, also because of
more collisions occurring, the wire may heat up, this in turn may
cause an alteration of the results, creating anomalies. Ohms law will
also have an effect on my results. Ohms law states that the following
will happen:
Resistance (Ohm)
[image010.jpg] Length Of Wire (cm)
Also, because the results will be altered through heating, I have
decided to take certain precautions. In an attempt to discard this
alteration I will disconnect the wire for each new reading, therefore
preventing heating up of the wire which should allow the experiment to
obey ohms law, which states that resistance will be directly
proportional to length, in a temperature controlled environment. From
this though, ultimately, increasing the length of wire should increase
the total amount of positive ions inside the wire, resulting in a
higher resistance.
Apparatus
The equipment I will use is:
- 100 centimeter piece of wire
- Ammeter
- Voltmeter
- Crocodile clips
- Connecting wire
- Ruler
Method
1. Collect the required equipment for the investigation.
2. Connect the equipment as shown in the circuit diagram.
3. Place crocodile clips along the wire every 10 centimeters.
4. Take preliminary readings from the voltmeter and ammeter.
5. Record the results shown on voltmeter and ammeter in a table.
6. Calculate the resistance and evaluate.
7. Take note of preliminary results and modify investigation where
necessary.
8. Do the experiment 3 more times and repeat steps 5. and 6. in more
depth.
Pre-Test
I have done a preliminary experiment to allow me to ensure that things
will run smoothly, the results are as follows:
Length (cm)
P.d. (V)
Current (A)
Resistance (Ohm)
0.0
0.03
0.65
0.05
10.0
0.40
0.46
0.87
20.0
0.60
0.30
2.00
30.0
0.67
0.30
2.23
40.0
0.75
0.28
2.68
50.0
0.80
0.23
3.48
60.0
0.96
0.19
5.05
70.0
0.95
0.19
5.00
80.0
0.95
0.18
5.27
90.0
1.17
0.12
9.74
100.0
1.03
0.16
6.44
From this table I have realised that my prediction was actually
correct, the further the length the higher the resistance. My table
reinforces that prediction except for two readings (IN BOLD), these
are the anomalies. These readings at 70cm, which is too low, and at
90cm, which appears to be far too high, could be due to many reasons.
These reasons could be endless, one for example could simply be a poor
connection.
From completing my pre-test trial I have decided I will make no
alterations whatsoever, I believe my preliminary investigation was
quite successful and straight forward. Moving on from this somewhat
simply completed pre-test I will carry out my actual results within
the main experiment, in this main bulk of my investigation I shall
redo the experiment and record my results as shown above 3 times,
calculate the average, draw up a series graphs and evaluate (as
explained in the method).
Results Table
The following table is my recorded three experiments and the
calculated average's and the average resistance:
Length of wire (cm)
Test 1
Test 2
Test 3
Average
Resistance (Ohm)
P.d. (V)
I (A)
P.d. (V)
I (A)
P.d. (V)
I (A)
P.d. (V)
I (A)
0.0
0.05
0.76
0.04
0.70
0.08
0.89
0.06
0.78
0.07
10.0
0.48
0.56
0.51
0.55
0.52
0.56
0.50
0.56
0.89
20.0
0.66
0.43
0.64
0.42
0.68
0.43
0.66
0.43
1.53
30.0
0.76
0.31
0.76
0.33
0.80
0.63
0.77
0.33
2.33
40.0
0.70
0.25
0.74
0.25
0.88
0.29
0.77
0.26
2.96
50.0
0.68
0.15
0.92
0.20
0.91
0.25
0.84
0.20
4.20
60.0
0.87
0.18
0.96
0.21
0.97
0.14
0.93
0.18
5.17
70.0
0.95
0.18
0.99
0.16
1.01
0.20
0.98
0.18
5.44
80.0
0.97
0.14
1.00
0.15
1.03
0.17
1.00
0.15
6.67
90.0
1.00
0.16
0.97
0.15
1.06
0.16
1.01
0.15
6.73
100.0
1.02
0.14
0.98
0.13
1.08
0.15
1.03
0.14
7.36
Conclusion
From my investigation, I have established that the length of a wire
directly affects the total resistance measured in proportion to it. I
have seen that as the length of the wire increases so does the
resistance, this also perfectly backs up my original prediction. In my
prediction I foreseen that if you doubled the length of the wire the
resistance would also double, this is because you are doubling the
number of collisions that would occur between the free electrons and
the atoms in the metal. My results support this as the graph of length
against resistance shows that relationship is directly proportional.
As the points on the graph are very close to the line of best fit,
this supports my prediction. Also as I repeated my experiment 3 times
and obtained very similar results, it shows that this experiment is
repeatable and reliable. So, I conclude that as the length of wire
increases, so does the resistance. I have realised also that double
the length means double the atoms, which doubles the collisions and in
turn, as explained in my prediction, doubles the resistance. This
leads me also to believe that resistance would be less in smaller
wires, this is due to higher current and increased heat.
During the investigation three major changes were brought to my
attention, these changes were:
-> As I increased the length of wire,
a.) The potential difference increased
b.) The flowing current decreased
c.) The resistance in the wire also increased.
I also found that when doubling the length of wire the resistance will
more or less double also. E.g. when the length was 50cm the
resistance was 4.00Ohm,
and when the length was 100cm the
resistance was 8.00Ohm.
Evaluation
The experiment I carried out was completed by means of very basic
school laboratory equipment. Although reliable and trustworthy
evidence was collected, proved by the similar 3 times repeated results
and matching line of best fit to my prediction, I believe my results
could have been far more accurate with a greater time span and some
far more enhanced technical equipment, such as a digital multimeter.
Although during my experiment there were no major anomalies there were
a few variations within my repeats of the experiment. These minor
variations truthfully had no major effect on the overall experiment
due to the diminutive extremity of them. Nevertheless these small
variations may have many similar reasons for appearance of which that
the major anomaly would have on occurrence.
These reasons could consist of such things as:
- Loose connectivity and/or faulty equipment
- Human error (inaccurate readings and/or checks)
- Temperature (collision speed alterations)
To improve the accuracy of my experiment It would have been helpful
if:
- The wire was in a temperature controlled environment, this
is because resistance is affected by temperature.
- The voltmeter and ammeter were difficult to take a reading
off, this is due to the unsettling of the actual readings, they
flicker and change several times before stopping on a final reading.
If you move slightly however, the results will flicker again and
become distorted. To prevent this, a better quality analogue meter
with a built in mirror to prevent parallax could be used to my
advantage.
- Also, if I had more time I could have extended my experiment
and repeated it with shorter intervals of wire. I could have taken
readings every 5cm instead of every 10cm, this way I could gather more
information and add a set of supplementary details to my results.
If I changed all of the above, in theory I should come across far
superior accuracy in my readings. If this theory is correct my results
graphs should show a stronger correlation.
If I were to present extra evidence I could make the following changes
for further experiment.
- Increase length of wire
- Increase the thickness of the wire,
- Change the material of the wire.
If the above three changes were investigated for further experiment, I
would hope that they would only validate my predictions and basically
back up my evidence.
By: Luke Stokes