# Resistance of a Wire

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Resistance of a Wire

We are trying to find out what affects the resistance of a wire.
Resistance is the slowing down of electric flow (flow of electrons)
due to metal ions. The equation to measure resistance is:

Resistance = Voltage Ã· Current

R = V / I

Resistance is measures in 'volts per amps' or, more commonly, 'Ohms'

There are a few things that affect resistance. I think these are:

Â¶ Length of wire

Â¶ Diameter of wire

Â¶ Material/type of wire

Â¶ Temperature

I am going to try and find out how the diameter of the wire affects
the resistance of the wire. I will do some tests find out how the
diameter affects the resistance. I think that if I increase the
diameter the resistance will decrease.

Method
======

1. First I will set up a circuit with a power pack, voltmeter, ammeter
and a space for a 1metre wire.

2. Then I will get a metre ruler and measure 1 metre of the first size
of wire and cut it with wire cutters.

3. I will stick the wire to the metre ruler with two pieces of sticky
tape 2cm away from either end to keep the wire straight.

4. I will then put the wire (attached to the ruler) in the gap in the
circuit and attach it to the circuit.

5. After turning the power pack on, I will record the numbers on the
voltmeter and ammeter.

6. I will then repeat steps 2 to 5 with 4 other different Standard
Wire Gauge sizes of wires.

7. Next I will repeat the whole experiment another few times.

I have chosen this method because it is quick, practical and easy to
do and will produce accurate and reliable results. I think it is the
best because it is the easiest one to do and you don't need that much
equipment but still get good results.

Apparatus
=========

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### Popular Essays

Â¶ Power pack

Â¶ Connecting wires

Â¶ Crocodile clips

Â¶ Voltmeter

Â¶ Ammeter

Â¶ 5 different SWG sizes of

Constantan wire

Â¶ Metre ruler

Â¶ Sticky tape

Â¶ Wire cutter

I have chosen this apparatus because it is what I need for this
experiment to get accurate, good results. It would have been better
for this experiment to use an ohmmeter but we don't have any available
so I will use an ammeter and a voltmeter and use the equation:
resistance = voltage Ã· current I will calculate the resistance using
the equation with a calculator to get precise answers and check then
twice. To make the experiment more accurate I will use a digital
ammeter and voltmeter that measures to two decimal places. I have
chosen to use constantan wire because the changes in resistance can be
seen more clearly in constantan than in some metal wires like copper,
and because constantan has a low temperature coefficient, which means
that it does not heat up much and so the resistance will not be
affected notably by temperature. The connecting leads in the circuit
have their own resistance. However, this will have a very little
effect on the readings taken in my experiment. I will keep the voltage
set on the power pack on 6 volts for all the experiments. I will use a
metre ruler because it is more suitable and accurate for our
measurements than a 6-inch ruler. I will use the same equipment for
all the repeated experiments too.

Variables

To create a fair test some aspects of the experiment will have to be
kept the same whilst one key variable is changed. I am going to change
the diameter so I will need to keep everything else the same.

Variable
--------

Effect

Control

Length of the wire

If a wire is longer than one metre then that wire's resistance is
higher than it should be because if the wire is longer then there are
more metal atoms for the current to pass. More atoms get in the way of
the free electrons, which means that the current (rate of the flow of
the electrons) is less and so the resistance is higher.

I will measure the length of the wire with a metre ruler to 1 metre.

Material/Type of wire

If a different type of wire is used then the resistance will change
because different materials have different resistances and different
reactions to temperature. For example if silver was used for one of
the tests then that resistance value would be a lot lower than it's
supposed to be because it has a low electrical resistance.

I will use constantan for all the tests.

Temperature

If the temperature is different then the resistance will change
because if the wire is hotter the metal atoms vibrate more vigorously
and faster and further from their rest positions. This means that they
are more likely to get in the way of the travelling free electrons. A
metal has more resistance when it is hot.

I will keep the experiment set up in the same place in the room (away
from the radiators) and do all of the experiments within the same
hour.

Safety
======

To make this experiment safe I will: -

Â¶ Place the experiment in the centre of the table so that nothing will
fall off

Â¶ Remove unnecessary equipment from the table i.e. pencil case

Â¶ Remove bags from under the table so that no one trips over them

Â¶ Not touch the wire when the power pack is on!

Â¶ Make sure plugs are pushed in properly and wires are not dangling so
there less chance of being electrocuted

Reliability
===========

To make this experiment as reliable as possible I will try and follow
a fair test and repeat the experiment a few times to confirm my
results. There are only a few flaws in my experiment: -

Â¶ The length of the wire may be very slightly inaccurate because the
wire may stretch slightly when we pull it to get the (originally
curled) wire straight against the ruler.

Â¶ The temperature in the room may change very slightly

Â¶ The connecting leads in the circuit have their own resistance

But by doing the following our results should be fairly reliable: -

Â¶ Measuring accurately

Â¶ Using the same equipment

Â¶ Redoing the experiments

Preliminary Work

I tried this experiment on a digital laptop using the Standard Wire
Gauge values of 28, 30, 32, 36, and 40. These results are theoretical
results programmed in to the computer and can be found in textbooks
too. This is the results table:

Standard Wire Gauge (SWG)

Resistance per metre (Î©/m)

28

4.32

30

6.16

32

8.12

36

16.40

40

41.10

I chose to use this range on the laptop because these are the only
sizes of constantan wires we have in school and so I have to use those
in the actual experiment. For that reason I did those values on the
laptop. I am happy with the range because the results are well spread,
therefore producing a clear graph. From these results and graph, I can
make a prediction for my actual experiment.

Range
=====

I will use the following of Standard Wire Gauge values because they
give me a good range and I am happy with the spread of the theoretical
values they gave me in my preliminary work. There is the right amount
of readings to make an accurate conclusion. I also have to use this
range because these are the only sizes of constantan wires we have in
school. Here are the SWG values and their diameters.

Standard Wire Gauge (SWG)

Diameter of wire (mm)

28

0.3759

30

0.3150

32

0.2743

36

0.1930

40

0.1219

Secondary Data
==============

I used some textbooks at school, the BBC bitesize revision website,
and the Revise for Science GCSE: Suffolk Higher Tier revision book to
help me with my prediction. I also used Lessons in Electric circuits
by Tony R. Kuphaldt, which I found on the Internet, that says:

The formula for calculating the circular-mil area of a circular wire
is very simple:

Circular Wire Area Formula A=d2

Because this is a unit of area measurement, the mathematical power of
2 is still in effect (doubling the width of a circle will always
quadruple its area, no matter what units are used, or if the width of
that circle is expressed in terms of radius or diameter). Electrons
flow through large-diameter wires easier than small-diameter wires,
due to the greater cross-sectional area they have in which to move.

Prediction
==========

Electricity flows in metals. Metal wires are made of millions of tiny
metal crystals. Each crystal's atoms are arranged in a regular
pattern. The metal is full of 'free' electrons that do not stick to
any particular atom. They fill the space between atoms in the metal.
There is an electric current when these electrons move. Metal atoms
get in the way of travelling electrons. This causes electrical
resistance. Some conductors are worse than others because they have
more resistance to current. The free electrons keep bumping into
atoms. A wire's resistance depends on the metal. Constantan is a
copper-nickel alloy with a high electrical resistance and is used as a
resistance wire. The resistance also depends on the wire's size. The
overall resistance is more when you connect the wires in series (twice
the resistance of one wire). The overall resistance is less when you
connect the wires in parallel (1/2 the resistance of one wire) because
more current can pass through two wires, and with an increase in
current the resistance goes down. The Standard Wire Gauge works as so:
The larger the gauge number, the thinner the wire; the smaller the
gauge number, the fatter the wire. This is an inversely proportional
measurement scale. Ohm's law says that 'the current flowing through a
component is proportional to the potential difference between its
ends, providing temperature is constant.'

From this information I predict that as the diameter of the wire
decreases (the SWG increase), the resistance of the wire increases. I
think this is because a wire with a diameter twice the size of another
wire would have 4 times as much wire. This is like having 4 wires in
parallel, which means there are more pathways for the current to pass
through. The more electrons would be able to pass through the larger
wire at any one time and because there is an increase in current the
resistance goes down (because of the equation R=V/I) This means that
there will be Â¼ of the smaller wire's resistance in the larger wire. I
can therefore predict the graph to look like this because if a
diameter of 1mm equalled 16Î©/m, 2mm would equal 4Î©/m, and 4mm would
equal 1Î©/m, giving a curvy graph:

These are my predictions for each of the Standard Wire Gauges: -

Â¶ For a metre of 28 SWG constantan wire I predict that the resistance
will be around 4.32Î©/m because that is the theoretical value I found
from my preliminary work, and because the diameter is very large, and
so a lot of current passes through the wire, so the resistance is
therefore very low.

Â¶ For 30 SWG I predict that the resistance will be around 6.16Î©/m
because the wire is thinner and so the current is a little less,
therefore the resistance is more than for 28 SWG. The theoretical
value shown in my preliminary work is 6.16Î©/m.

Â¶ For 32 SWG I predict that the resistance will be around 8.12Î©/m
because the wire is quite thin and so the current is a less, therefore
the resistance is higher than for 30 SWG. And the theoretical value
shown in my preliminary work is 8.12Î©/m.

Â¶ For 36 SWG I predict that the resistance will be roughly 4 times
more than the resistance of 28 SWG because the diameter is roughly
half of the diameter of 28 SWG. The wire is thin and so the current is
a lot less, therefore the resistance is a lot more than for 28 SWG.
The theoretical value shown in my preliminary work is 16.40Î©/m.

Â¶ For 40 SWG I predict that the resistance will be around 41.10Î©/m
because the wire is extremely thin and so the current is very small,
therefore the resistance is very high compared to 28 SWG. And the
theoretical value shown in my preliminary work is 41.10Î©/m.

Obtaining Evidence

Following my method I have carefully and safely done three experiments
and collected some results. I recorded the results as precisely as
possible.

This is the results table for my first experiment: -

Standard Wire Gauge (SWG)

Voltage (Volts)

Current (Amps)

Resistance per metre (Î©/m)

28

5.55

1.26

4.40

30

5.73

0.87

6.59

32

6.04

0.71

8.51

36

6.15

0.36

17.08

40

6.15

0.15

41.00

This is the results table for my second experiment: -

Standard Wire Gauge (SWG)

Voltage (Volts)

Current (Amps)

Resistance per metre (Î©/m)

28

5.67

1.29

4.40

30

5.76

0.89

6.47

32

6.16

0.72

8.56

36

6.22

0.36

17.28

40

6.14

0.15

40.93

This is the results table for my third experiment: -

Standard Wire Gauge (SWG)

Voltage (Volts)

Current (Amps)

Resistance per metre (Î©/m)

28

5.47

1.29

4.24

30

5.64

0.90

6.27

32

5.81

0.67

8.67

36

5.97

0.35

17.06

40

6.14

0.15

40.93

I have done three experiments to make my results even more accurate
and to make sure I have no odd results.

I worked out the resistance using the following formula:

Resistance = Voltage Ã· Current

The results from the repeated experiments confirm the reliability of
the original data because they are similar results showing a similar
pattern. Using the results a have obtained I can find the average
resistances and use these to produce an accurate and reliable graph.

These are the average resistances of the two experiments: -

Standard Wire Gauge (SWG)

Average Resistance per metre (Î©/m)

Theoretical resistance per metre (Î©/m)

28

4.34

4.32

30

6.44

6.16

32

8.58

8.12

36

17.13

16.40

40

40.95

41.10

This table confirms the reliability of my results because it shows how
close my results are to the theoretical values. I have drawn a graph
using the data in the table above comparing the average and
theoretical results.

I have also worked out the percentage error of my averaged results
using the following formula:

Actual resistance x 100 = % error

Theoretical resistance

These are the percentage errors: -

Standard Wire Gauge (SWG)

Percentage error of results (%)

Percentage change to 2d.p.

28

100.4629630

0.46% over

30

104.5454545

4.55% over

32

105.6650246

5.67% over

36

104.5121951

4.51% over

40

99.6350365

0.36% under

These show precisely how accurate my results were. And the graph backs
this up.

Analysis

I have found from my results that 28 SWG constantan wire has the
smallest resistance on average of 4.34Î©/m and 40 SWG constantan wire
has the largest resistance on average of 40.95. I have found that as
the Standard Wire Gauge increases the resistance increases too, which
means that as the diameter increase the resistance decreases because a
high SWG is a thin wire and a low SWG is a thick wire. The graph
clearly shows this trend with a curve that slopes upwards and gets
steeper at the end. The graph shows a positive correlation between SWG
and resistance. The gradient changes in my graph, as the x-axis (SWG)
gets bigger the gradient becomes steeper. This is because the
resistance multiplies by four when the wire is twice as thin. As the
wire gets thinner the current bumps into more atoms and flows less
easily and so the resistance gets really high. And the resistance gets
higher and higher as the wire gets thinner, each time the resistance
rising by greater amounts.

I have found that the wire's resistance increases as the SWG increases
(diameter decreases). This is related to the fact that more current
can pass through thicker wires because with an increase in current the
resistance goes down.

Â¶ The 28 SWG wire's resistance was 4.34Î©/m on average. This is because
the diameter is very large, and so a lot of current passes through the
wire, so the resistance is therefore very low.

Â¶ The 30 SWG wire's resistance was 6.44Î©/m on average. This is because
the diameter is quite large, and so quite a bit of current passes
through the wire, so the resistance is therefore low.

Â¶ The 32 SWG wire's resistance was 8.58Î©/m on average. This is because
the diameter is thinner than the 28 SWG wire, and less current passes
through the wire, so the resistance is therefore higher.

Â¶ The 36 SWG wire's resistance was 17.13Î©/m on average. This is almost
four times as much as the resistance for the 28 SWG wire because it is
about half the size in diameter. The diameter is small, and only a
small amount of current passes through the wire, so the resistance is
therefore high.

Â¶ The 40 SWG wire's resistance was 40.95Î©/m on average. This is
because the diameter is very small, and so hardly any current passes
through the wire, so the resistance is therefore very high.

The following diagrams show the wires and the flow of the electrons
through them, showing mini hurdles as the resistance.

What I have found out is extremely similar to what I originally
predicted. The results are very close to the theoretical values,
within 10% either way. The shape of my predicted graph is the same as
the one produced from my results and the analysis of my results agrees
with my prediction.

Evaluation

I think that this investigation was successful because my results
collaborated with my prediction. The method I used was good because it
was easy to set up and also straightforward and safe to do. It has
produced very accurate and reliable results. I know this because the
results in all three experiments were very similar and followed the
same pattern. I think that most of my results are accurate enough
because the wires were measured using a suitable ruler and the
voltmeter and the ammeter measured to two decimal places instead of
rounding up to a whole number. I think the procedure was very suitable
for the investigation but the results would have been even more
reliable if we could have used an ohmmeter instead of a voltmeter and
ammeter because I may have read either the voltmeter or ammeter wrong
some of the times (as the numbers often changed all the time).

I didn't have any odd results and all of them are accurate. The graph
shows this by showing how close they all are to the theoretical
values. I didn't have any problems with my investigation and
everything went smoothly as I planned. I followed my method exactly
and tried to measure everything as precisely as possible. I think that
my results are good enough to make a firm conclusion because they seem
reliable. I don't need any more results to make my conclusion more
definite because I have already done the experiment three times and my
graph shows clearly that the results are good.

I have come to the conclusion that the diameter affects the resistance
of the wire and as the diameter of the wire decreases the resistance
of the wire increases. I have also found out that this happens because
the thicker wire has more passage for the current to flow through and
so more current can flow at a time, therefore the current is high
meaning that the resistance is low in a thick wire, and vice versa. I
have been measuring the diameter using the Standard Wire Gauge scale.
To further confirm my conclusion if I had the equipment I could use an
equally spread out range of wires instead of making do with the ones I
had e.g. 28,32,36,40,44 SWG. I could repeat the experiment a few more
times, try the experiment with other materials to make sure the
diameter has the same affect on the resistance on all wires, try the
experiment using American Wire Gauge measurements, or try the
experiment with other diameters.