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Resistance and Length of a Wire

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Resistance and Length of a Wire

Aim: To see whether the length of a wire affects its resistance.

Prediction: I predict that the longer wire the more resistance will be
encountered due to the increased number of positive ions present so
the electrons will have further to travel to make it through the wire.
If we double the length of the wire we will double the probability of
the electrons hitting the ions. My research was carried out in the
A-level textbook "advanced physics for you" I found this equation

RESISTANCE (ohms) =P (ohm metres) X LENGTH (m)

CROSS-SECTIONAL AREA (sq m)

So where p= resistivity this is the equation you would discover the
resistance measured in ohms of a wire etc. I predict that the wire
will act like a long resistor. I also predict that the graph will
result in something like this sketch below. Also below is a sketch of
resistance and how it works as you can see the electrons have to get
through the wire and have to make it past some positive ions, because
they are charged the way they are the positive ions attach themselves
to the electrons so they cannot pass through. The longer a wire is the
less chance the same amount of electrons will get to the other side
unlike a shorter wire. But this is not true for thick ness the thicker
the wire the wider space there is for passing electrons.

Diagram:

Plan: I will measure the resistance of 7 different lengths of nichrome
wire using the ammeter-voltmeter method. For the first length of 10 cm
I will measure the current and voltage. I will repeat this step up to
70 cm. each time I will find the resistance of the wire using ohms law
(resistance= voltage/current). At each length I shall move the
rheostat so we can work out the average resistance of each length,
also to prevent errors. I shall record my results in 3 tables as I am
going to perform the experiment 3 times to seek out anomalous results.

Safety: I will ensure that none of the wires are frayed and that there
is no water near any electric equipment; as in all electrical
experiments. Also I will only run current through my circuit for a
short period of time as if the wire becomes heated then particles
begin to expand thus increasing resistance

Method: Firstly I will collect my apparatus then set it up in the
circuit shown above. I placed the crocodile clips 10 cm apart on the
wire for my first test and slid my rheostat to one end. Now I was
ready to record my first reading so I turned on my power pack set at 4
volts, recorded the readings then snapped off the power, slid my
rheostat halfway then once again recorded the reading then repeated
with the rheostat on full after this I turned off the power then
repeated these 3 steps 6 more times up to 70 cm. once I had done the
experiment 3 times with all of my recorded results, I cleared the
apparatus away then gathered all of the relevant data. From this I can
conclude my results from what the graph is showing. There are also
certain things that need to be kept the same or change throughout the
experiment these are called variables. The exact same wire for each
experiment needs to be used as any variation could lead to an
inaccuracy in results due to more/less positive ions. The current
needs to be changed 3 times for each length using the variable
resistor/ rheostat so I can work out an average resistance for each
length. The same thickness of wire needs to be used because it really
affects resistance so it wouldn't be a fair test. The same temperature
will need to be kept as if we have particles expanding and contracting
the test is no good, so it would be preferable for the experiment to
be done as quickly as possible on the same day. The input variable is
the length of wire and can be changed by adjusting the crocodile
clips. The outcome variable is voltage (volts) and current (amps) and
will be measured by a voltmeter and an ammeter. The range of values I
will use is from 10 cm to 70 cm moving up 10 cm each time. I will
repeat my experiment 3 times using exactly the same equipment to
ensure a fair test and no anomalous results.

Apparatus List: Wire- This nichrome wire is what my experiment will be
conducted on. It will theoretically vary in length but stay the exact
same wire throughout.

Power Pack- this is needed to supply 4 volts of power to the circuit.

Croc Clips- form part of the input variable and will be moved apart to
a maximum of 70cm on the wire.

Wires- these insulated wires will be conducting the electricity
through the circuit.

Ammeter- forms part of the outcome variable as it will change current
readings across the circuit as the experiment progresses.

Voltmeter- also is a part of the outcome variable as the voltage
across the wire will change.

Variable resistor/rheostat- used to provide 3 different voltages for
each length so we can work out a fair average.

Analysis: In this part of the write I am going to discuss my results
and what they tell us firstly though the graph that I drew up from my
results, the line of best fit tells us that the average resistance and
the length go up by the same ratio so if we doubled the length of the
wire then theoretically according to our results the resistance should
double. This is also stated in ohms law. From this graph if you had
enough paper to write the units on you could predict any length of our
nichrome's resistance within reason. When plotting my tables I needed
to keep to the same degree of accuracy and not deviate which was two
decimal places. As you can see in my results table I discovered an
anomalous result that didn't make sense but worked the other 2 times
when we did the experiment. When I was working out the averages I
omitted this result. This could have been caused by a number of
reasons, faulty equipment mostly. The results from every experiment
have gone as predicted in the hypothesis and have obeyed all of the
previous information that is displayed in the prediction. Now using
our results graph we could predict the resistance of a 15 cm wire
using the line of best fit. It would be 1 ohm of resistance. In my
prediction I said that "if we double the length of the wire we will
double the probability of the electrons hitting the ions" this theory
has been proved correct by our results graph.

Conclusion/Evaluation: Now that I have obtained my results from the 3
experiments I performed I can go on to draw a conclusion and seek out
what went wrong and what needs to be improved. I think that our
results fit the pattern very well, this can be determined by looking
at how strong the positive correlation is on the graph and on my
tables as the number patterns arise. Whether this investigation has
been a success can only be determined by the accuracy of the results.
Without scientifically accurate results, the investigation would be
meaningless and disruptive to the person acting upon it. The results
shown in this investigation are true and are believed to be correct.
In this sentence 'correct' is also meaning as accurate as can possibly
be attained. There are many ways in which this investigation could
have improved its scientific standing. One way to improve the
reliability and accuracy of the results would be to repeat the
experiment 'n' times so that a true average could be obtained. The
experiments were repeated to obtain an average but they were only
repeated twice. This is more reliable than conducting the experiment
once or twice but still more results would have given more accurate
averages. If I was to do this experiment again I would be persuaded to
seek out more accurate professional equipment as to improve the
accuracy of our results. Such as university standard crocodile clips
as well as more accurate voltmeter/ammeter that go up to 4 decimal
places. Also we could use some low resistance wires and components
once again to improve accuracy. As I had one anomalous result this
could have occurred due to faulty equipment but also after we had
performed experiment 2 and totaled up the results from all three
something didn't look right, it was found that the rheostat for that
experiment was faulty so that was properly accounted for. Although
this display of controversy is founded, the experiment was very
reliable and efficient. There is no way to improve the method of the
experiment used as a basis for all of the experiments. It was a
perfect method of calculating resistance although there are some
negative technicalities, which were explained above. For the purpose
of allowing the equation…

R = V / I

...to be calculated there is no better substitution although
scientific knowledge of how resistance is calculated to extreme
military precision is regrettably absent. The experiment was simple,
quick and effective. Possible changes in the investigation were noted
earlier. The results are true and so is the conclusion. How I could do
more experimental work is by doing investigations such as more lengths
of wire, different types of wire e.g. copper, aluminium also I could
see at different temperatures, how that directly affected results as
well as seeing how resistance is inversely proportional to area so
using a thicker wire, the possibilities are endless. Apart from the
above brief demonstration of negativity, the investigation was a
success. After examining the basic out come of each experiment in the
summary. Overall it was a success. The aim was to see whether "the
length of a wire affects resistance" and among other factors I think
we can safely say yes it does. The following equations have been
verified:

R = V / I

(Resistance (Ω) = Voltage (V) / Current (I))

R µ L

(Resistance is proportional to length)

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"Resistance and Length of a Wire." 123HelpMe.com. 25 Apr 2014
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