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The Effect of Length of a Wire on Its Resistance

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The Effect of Length of a Wire on Its Resistance

Background Knowledge:

An electric current is the flow of charge that is measured in Amperes
using an Ammeter. Current in a metal is due to the flow of electrons
that are repelled from the negative terminal and flow towards the
positive terminal. The terminals are made positive and negative
because of the chemicals in the battery. The nichrome wire that the
electrons have to pass through is made of atoms. Each of these atoms
consists of a nucleus, which is made up of protons and neutrons. In a
metal the atoms are held tightly to the nucleus. Some of the outer
electrons are called 'free electrons' because they can be knocked out
of place easily. When a free electron leaves an atom, the atom becomes
an 'ion' because the charge is not equal. Ions that are left are
vibrating in a fixed place, this is called a lattice. Free electrons
have to pass through a lattice.

The temperature of the wire would increase if the current was high so
when I do the experiment I must keep it low.

[IMAGE]If I double the length of the wire then I will be doubling the
amount of resistance. This is because the free electrons are pushed
around the circuit because there is an electric field in the nichrome
wire. The battery sets up this electric field from the positive
terminal to the negative terminal. If the electric field goes through
a short wire then it will be strong and it will push the free
electrons with a big force and so a lot of electrons will go through
the short wire. If the wire is twice as long then the electric field
will be half as strong as the shorter wire ,hence there will only be
half the force pushing the free electrons and so half the current. In
fact I will have doubled the resistance.

[IMAGE]



The structure of an atom
========================

Variables:

Dependant- Resistance of the wire

Independent-Length of the wire

Control- Temperature, material of wire, Cross-sectional area of the
wire

I need to keep the temperature constant because if it was to increase
then the resistance would increase so I must keep the current low.

I need to keep the material of the wire the same because each metal
has a different resistance so I must use the same type of wire each
time- I am going to use Nichrome wire from the same reel to ensure
this.

I need to keep the cross-sectional area of the wire the same because
thick wire has less resistance than thin wire and for my experiment I
will use SWG 32 Nichrome wire.

Predictions:

· (Qualitative) If the length of the wire is longer then the
resistance will be bigger.

· (Quantitative) Doubling the length of the wire would double the
resistance.

If resistance is directly proportional to the length of the wire then
my graph that I would draw from my results would look like this:

[IMAGE]


Resistance/W

[IMAGE]


Length of wire/cm

A directly proportional graph is a straight line graph that goes
through the origin.

[IMAGE]If I double the length of the wire then I will be doubling the
amount of resistance. This is because the free electrons are pushed
around the circuit because there is an electric field in the nichrome
wire. The battery sets up this electric field from the positive
terminal to the negative terminal. If the electric field goes through
a short wire then it will be strong and it will push the free
electrons with a big force and so a lot of electrons will go through
the short wire. If the wire is twice as long then the electric field
will be half as strong as the shorter wire ,hence there will only be
half the force pushing the free electrons and so half the current. In
fact I will have doubled the resistance.

This is my table which I would set up to show my results:

Length of wire/cm

Current/A

Voltage/V

Average Voltage/V

Resistance/W

1

2

3

10

20

30

40

50

60

70

80

90

100

Preliminary Work:

I did three preliminary experiments and I have included them with this
work.

Proposed Method:

How will my preliminary work inform the plan:

In my preliminary work I used three different circuits to measure
resistance. I found that the third experiment was the most effective
because of the potential divider. With a potential divider you can get
much more accurate control of the current of voltage.

In the light bulb experiment, I noticed that the filament got hot and
so the resistance increased and therefore it is important to prevent
the nichrome wire from getting hot and I will achieve this by keeping
the current low.

Making the test fair:

I need to keep the temperature constant because if it was to increase
then the resistance would increase so I must keep the current low.

I need to keep the material of the wire the same because each metal
has a different resistance so I must use the same type of wire each
time- I am going to use Nichrome wire from the same reel to ensure
this.

I need to keep the cross-sectional area of the wire the same because
thick wire has less resistance than thin wire and for my experiment I
will use SWG 32 Nichrome wire.

Safety Precautions:

I need to take the following safety precautions during the experiment:
ensure that I have dry hands whilst dealing with the electricity to
prevent me from being electrocuted, wear gloves when changing the
length of the wire so I won't burn myself, keep a low voltage current
to prevent the wire burning or getting hot and I must wear safety
glasses when cutting the length of the wire to protect my eyes.

Detailed Procedure:

[IMAGE]


[IMAGE][IMAGE][IMAGE][IMAGE][IMAGE][IMAGE]

[IMAGE]


[IMAGE]

V

[IMAGE]

A

Results:

Length of wire/cm

Current/A

Voltage/V

Average Voltage/V

Resistance/W

1

2

3

10

0.41

0.79

0.78

0.84

0.80

1.95

20

0.41

1.64

1.59

1.57

1.60

3.90

30

0.41

2.50

2.58

2.44

2.51

6.12

40

0.41

3.32

3.28

3.38

3.33

8.12

50

0.41

4.18

4.12

4.08

4.13

10.07

60

0.41

5.05

4.88

4.91

4.95

12.07

70

0.41

5.87

5.80

5.77

5.81

14.17

80

0.41

6.66

6.63

6.63

6.64

16.19

90

0.41

7.63

7.52

7.41

7.52

18.34

100

0.41

8.27

8.39

8.30

8.32

20.29

Analysis:

Interpretation of results:

My graph of resistance against length is a straight line that goes
through the origin, which leads me to the conclusion that resistance
is proportional to the length as I stated in my prediction:

If resistance is directly proportional to the length of the wire then
my graph that I would draw from my results would look like this:

[IMAGE]


Resistance/W

[IMAGE]


Length of wire/cm

A directly proportional graph is a straight line graph that goes
through the origin.

[IMAGE]If I double the length of the wire then I will be doubling the
amount of resistance. This is because the free electrons are pushed
around the circuit because there is an electric field in the nichrome
wire. The battery sets up this electric field from the positive
terminal to the negative terminal. If the electric field goes through
a short wire then it will be strong and it will push the free
electrons with a big force and so a lot of electrons will go through
the short wire. If the wire is twice as long then the electric field
will be half as strong as the shorter wire ,hence there will only be
half the force pushing the free electrons and so half the current. In
fact I will have doubled the resistance.

This fully supports my original prediction, bearing in mind that I
have only worked with one type of wire (Nichrome) and one thickness of
wire (SWG 32) from 10cm to 100cm.

Evaluation:

I measured the length of the wire from 10cm to 100cm using a metre
ruler with 1mm graduations. Because the metre ruler was calibrated at
1mm I could measure the length of the wire to one tenth of a
centimetre.

This would introduce an error of about 1%

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