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How the Length of a Wire Affects Its Resistance

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How the Length of a Wire Affects Its Resistance


Introduction:

I'm going to investigate the relationship between the length of a wire
and it's resistance. A few things determine the resistance of a wire.
Firstly and possibly the most important is the length. A material of
long wire has more resistance than a short wire. For example take a
straw and put some water in mouth, and try to push it through the
straw. Then cut ¾'s of the straw off and try again. It should be much
easier this time (i.e., less resistance). The ohmic resistance per
atom for any given material is the same, so the length of wire can
affect the resistance of a wire because there are more atoms in a
longer wire for the electrons to pass through than a shorter wire.

Secondly the cross-sectional area of the wire. Because there is more
room for electrons to pass through. The thicker the wire the less
resistance.

Thirdly the material of wire can affect the resistance of a wire
because some materials resist the flow of electrons more than others.
It determines the conductivity of substance. For example the best
conductor is copper and the second best conductor is aluminium.
Aluminium is used more because not only does it conduct electricity
exceptionally well. But it is cheaper and easier to use. Copper is
expensive but has a longer life expectancy than aluminium and is
guaranteed to deliver the best source of electricity that it can
provide. Aluminium is a good conductor of electricity and is also
cheaper than copper but aluminium is not expected to have as long a
life expectancy as that of copper. For every 2% of aluminium used 1%
of copper is used. This property of materials is known as resistivity.

Theory:

I know from my textbook and class-note that the resistance varies as
the length increases, because when the current that consist of charge
carriers (that is electrons) passes through a wire the electrons
undergo collision. If the wire is short the electrons travel through a
short distance. If the wire is longer the electrons go through long
distance, undergo more collision. i.e. the more the resistance.

From introduction I can deduce the following facts:

1: resistance increases as the length increase.

2: resistance decreases as the cross-sectional area increase.

3: resistance also depend on the resistivity of different materials.
It increases as the resistivity increases.

If I indicate the resistance with (R), the length of the wire with
(l), cross-sectional area with (A) and resistivity with a Greek letter
rho (r) I get the following formula.



R=rl/A
======

If I rearrange the formula and compare it with straight line formula
(y = mx + c)

Than I have;


R=p/Axl + 0
-----------

Now I got two variables one is R- resistance and second one is l-
length, where length is independent variable and R is dependent
variable. For a fair test I have keep the other quantities constant
apart from the one that I vary. They are the resistivity,
cross-sectional area and the current (the current changes the
temperature of the wire).

Prediction:

I predict that the resistance will be proportional to length and the
graph R vs l will give a straight line that passing through all
origins.

From the comparison of the resistance formula (R=p/Axl) with
straight-line formula (y = mx + c) I can predict that p/A will me the
gradient of the graph.

Plan:

I'm going to carry out an experiment to investigate that how the
resistance varies with the length of a wire.

I was provided with a meter long Constantan wire taped on a meter
rular. First I will measure the diameter of wire in three different
points and find the average diameter. I will chose micrometer to
measure the diameter of the wire, because it can measure 10 times more
accurate than the varnier calliper i.e.. Before I connect the circuit
I'll measure the resistance of wire for different lengths by using the
ohmmeter at room temperature. I'll place the crocodile clips at the
either ends of the 1-meter wire and record the reading of ohmmeter on
my result table an than I'll decrease the length to 80cm, 60cm, 40cm
and 20cm and record the reading for each length on my result table.


Result 1:

Diameter of wire (mm)= 0.43 0.42 0.44

Average diameter of wire = 0.43mm

Room temperature, q = 25 C

Length (cm)

20

40

60

80

100

Resistance (ohm)

1.2

1.7

2.3

3.0

3.6

Apparatus:

Tow 1.5v batteries

Variable resistor

Ammeter

Voltmeter

Circuits wires

Crocodile clips

1-meter constantant wire

Safety:

Before I start the experiment I have to follow the instruction listed
bellow.

- I'll make sure that the circuit is connected properly before turning
on the power supply.

- I won't touch any testing materials and naked wires during the
experiment or until the power supply is switched off.

- I will not perform my experiment in wet area, as water is a very
good conductor.

- I'll not switch on the power pack where there is no resistant wire.

Diagram:

Method:

I have to collect the apparatus listed above and connect them as shown
in the diagram. Before I switch on the power supply I want to mention
that I will keep the current constant each length and after each
experiment I will turn off the power supply, because as the current
passes through the wire the electrons (charge carriers) collide with
the atoms of the wire and the atoms vibrate which cause heat producing
and the heat affect the resistance of the wire.

How to keep the current constant?

The variable resistor is used to keep the current constant by pushing
the panel on the back of the resistor up and down.

As the wire provide was wiggly not straight wire. i.e. I can't get the
accurate length, so I'll place the crocodile clip in three different
points and record three values for the voltage and average them to
three significant figures to get the more accurate reading.

I will place the crocodile clip on one end of the wire and switch on
the power supply and place another crocodile clip on 10cm length of
the wire on the ruler in three points and record three reading of
voltmeter on the result table.

As I mentioned above that I'll switch off the power supply and
increase the length by 10cm that is 20cm follow by 30cm, 40cm, 50cm,
60cm, 70cm, 80cm, 90cm and 100cm.

I will repeat the procedure for each length and record three values of
the voltmeter. After these all experiments I'll disconnect the circuit
and do the following calculation.

R = V/I

I going to divide each voltage by the current that I have kept
constant for each length, thus I will get three reading for the
resistance of each length. I will also average the values of
resistance and plot a graph of length to resistance (lxR) and do some
calculations to find out the result.

Result:

Current I = 0.195 amps

Volts in (V)

Resistance in (ohm)

Length (cm)

V1

V2

V3

R1

R2

R3

R (ave)

10.0

0.050

0.055

0.054

0.260

0.280

0.280

0.270

20.0

0.109

0.112

0.115

0.559

0.574

0.590

0.570

30.0

0.174

0.175

0.171

0.892

0.897

0.877

0.890

40.0

0.233

0.231

0.232

1.20

1.19

1.19

1.19

50.0

0.302

0.291

0.291

1.55

1.49

1.49

1.51

60.0

0.352

0.351

0.351

1.81

1.80

1.80

1.80

70.0

0.414

0.416

0.414

2.12

2.13

2.12

2.13

80.0

0.471

0.47

0.468

2.42

2.41

2.4

2.41

90.0

0.529

0.53

0.529

2.71

2.72

2.71

2.71

100.0

0.582

0.584

0.584

2.99

3.00

3.00

2.99

Graph:

[IMAGE]

Conclusion:

As I predicted that my graph will be a straight line passing through
the origins. I can see that from the plotted values of R vs l.
Therefore I conclude that resistance is proportional to length i.e.
Rxl.

If I compare the resistance formula R=rl/A with straight-line formula
(y = mx + c) will get R=p/Axl + 0. It gives me the gradient m= p/A my
intercept is zero (c=0) and the resistivity is p=gradient x A

My error bars are too small to plot on the graph i.e. (+/-0.01)

Evaluation:

I had a couple of problems through out the experiment. First the wire
provided was wiggly and the crocodile clips also couldn't grip on one
point of the wire, because it had two sides of the teeth and griped on
two point s of the wire as shown below.

Therefore I was placing the crocodile clip on three point of the wire
and recorded three reading for the voltmeter so that I deduced three
values for resistance and averaged them. Than I used experimental
errors method to deal with the straight-line accuracy as I had
predicted. I got my error bars too small to plot then on the graph.
Therefore I believe that I covered this problem correctly.

2: The diameter and resistivity of the constantant wire provided in
the data book of Griffen Education page 129 were respectively 0.45mm
and 3.02-ohm m at 20 C temperature and 1 atm pressure, but my result
was slightly different from this because I did my experiment at room
temperature 25C and the temperature affect the diameter resistivity of
the wire. At low temperature the kinetic energy of the atoms of the
materials decrease and the materials squeeze down while at high
temperature the more the KE the more the atoms vibrating and the
materials volume increase.

3: The method of measurement of the resistance. There are two possible
ways to measure the resistance. By using ammeter and second from the
R=V/I formula. I preferred the formula one, because it gave me the
answer to three decimal places which I believe that it is more
accurate then the reading of ammeter.

They could be improved by using more accurate apparatus such as a more
straight wire with precise diameter and the crocodile clips with a
single sided teeth.

Bibliography:

I have used the following sources to complete my coursework.

1: My class-note

2: Textbook (OCR Physics 1)

3: The world of Physics/ second edition/

4: www.coursework.help.co.uk

5: www.coursework.info.co.uk

6: www.earthsky.com

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"How the Length of a Wire Affects Its Resistance." 123HelpMe.com. 24 Apr 2014
    <http://www.123HelpMe.com/view.asp?id=121201>.




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