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# An Investigation into how the resistance of a piece of graphite paper is affected by the width of the graphite paper.

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Introduction

An Investigation into how the resistance of a piece of graphite paper is affected by the width of the graphite paper.

Planning

I will be investigating how the resistance of a piece of graphite paper is affected by the width of it. The aim of the investigation is to carry out a suitable experiment to find various different resistances for various different widths of graphite paper.

Preliminary Experiment

The purpose of the preliminary experiment is to find a suitable length of graphite paper to use in the real experiment. For this experiment we will be using a 0-1mA shunt as I think it will give the best deflection. Ideally we wanted to find a length of graphite paper that can allow the 0-1mA shunt to reach a reading near to or exactly 1mA. Hence if we are going to do this we need a shunt that has the best deflection for this kind of experiment and that shunt is a 0-1mA. The circuit below is the circuit or series that I used in the preliminary experiment and the one I will be using in the real experiment.

+    -                       Clips     Graphite Paper  V The Apparatus

• Battery
• Voltmeter
• Ammeter
• 0-1mA shunt
• Wires connecting apparatus
•  Ruler
• Scissors
• Graphite paper
• Clips holding the graphite paper

The Method

• One followed the above diagram to attach all the wires to the different pieces of apparatus.
• I attached the clips to each end of the graphite paper.
• I attached the 0-1mA shunt to the ammeter.
• I read from the ammeter each time I cut down the length by using scissors. I did this till the ammeter got a reading near enough to 1mA.

Safety Precautions

• As I used scissors one should have handled them properly at all times for one could have been cut by the blade.
• One should check the circuit or series at the start to check that it hasn’t been short-circuited.

The Results

 Length (cm) V1 (V) I1  (A) V2  (V) I2  (A) 40 1.61 0.76 1.60 0.73 35 1.50 0.91 1.49 0.90 32 1.47 0.93 1.46 0.94 30 1.45 0.95 1.44 0.96 29 1.42 0.98 1.42 0.98 28 1.41 1.1 1.41 1.1

From the various measurements of paper we found that from each of the connector points of the clips the ideal length of paper for the experiment that will take place is 29cm. This is because as one can see from the table of results above the ammeter reads 0.98mA for 29cm which actually is the closest result we could find nearest to the bench mark of 1mA. To prove my find I did the same experiment for 28cm and for both the preliminary experiment and the repeat the reading on the ammeter came out to be higher than 1mA (near to full-scale deflection). Hence I can’t use it as my length and so I will use 29cm.

Now if I take the formula R=V/I I can find the resistance of a piece of graphite paper with 29cm as its length.

R= 1.42/0.98

R= 1.45ohms

R= 1450ohms

The Experiment

Now I have found my length that I will use in the real experiment we can carry on with the investigation by performing the real thing.

The Apparatus

• Battery
• Voltmeter
• Ammeter
• 0-1mA shunt
• Wires connecting apparatus
•  Ruler
• Scissors
• Graphite paper
• Clips holding the graphite paper

The Method

• One should follow the diagram earlier in the planning section of the investigation and attach all the wires to the different pieces of apparatus.
• I will attach the clips to each end of the graphite paper. I will start the measurement of 29cm from clip to clip.
• I will attach the 0-1mA shunt to the ammeter.
• I will read from the ammeter each time I cut down the width by using scissors. I will do this for 7 different widths and repeat the experiment.
• I will take the voltage reading and the ammeter reading.
...read more.

Middle

I will be keeping the other input variable (the length) constant because if we change the length as well as the width in the same experiment we won’t get accurate results for the experiment we are carrying out. Also if we change the length the experiment would become unfair, as different lengths would have different widths would just make the whole investigation pointless, as no solid conclusions would come out of it at the end. In the experiment I will measure current from the ammeter and the voltage from the voltmeter. It is imperative that I do this because if I don’t I will not be able to find the resistance of the graphite paper for various different lengths. As both the voltage and the current are output variables I have no control over them. To get a rounded result and to also check that my results are right I will repeat the experiment again. If I don’t do this then my results could be wrong without me knowing. I am also going to have seven different widths of the graphite paper so there is a wide variety of results and thus I will be able to make more justifiable conclusions.

Safety Precautions

•  I will use scissors and in the experiment one should handle them properly at all times for the blade could cut one.
• One should check the circuit or series at the start to check that it hasn’t been short-circuited.

The Theory

Electricity is conducted through a conductor and in the case of this experiment our conductor will be a piece of graphite paper. Electricity is conducted by the means of free electrons however the number of free electrons really depends on the material (in this case the graphite paper). The more free electrons in a chosen material means a much better conductor, i.e. it will have less resistance. For example, the metal named gold has more free electrons than lets say iron. If one takes the statement above gold must be a better conductor. Free electrons are given energy and as a result of this they move and collide with neighbouring free electrons. In this investigation that we are carrying out the following statement will take place across the width of the piece of paper and thus electricity is conducted. The concept is described as the result of energy loss in the form of heat. The concept involves collisions between the free electrons and the fixed particles in the chosen metal, other free electrons and impurities. These collisions change the energy that the free electrons are carrying into heat. The following diagram helps to explain the concept:                   Free electrons This diagram explains the collision of free electrons. The two bonded electrons have collided.

The resistance of a uniform conductor (in this case the graphite paper) depends on the length, the area of the cross section and the material. The longer the conductor is in length, the greater the resistance will be. The narrower the conductor (this is what I am investigating), the greater the resistance will be. Another rule is that metals are much better conductors than non-metals. Copper is known to be the best conductor of electricity. Numerous amounts of tests do show that the length of a conductor is proportional to its resistance. However in this experiment we will not need that fact as we are testing the effect the width has on resistance. Tests also show that a conductor is inversely proportional to the area of its cross section.

In this experiment the resistance of the width of the piece of paper is calculated by measuring the current that is present in that circuit or series. Also one must calculate the voltage across the piece of graphite paper (in parallel). From these measurements we can work out the resistance using the below formula.

V= Voltage

I= Current

R= Resistance

So if V= IR the formula can be re arranged to make resistance the subject: R= V/I.

## The Predictions

• I predict that if I half the width of the piece of graphite paper I will half the current and thus double the resistance. This is because as I half the width of the graphite there will be less space for the current to travel through the medium and also there is the concept that as one halves the width one will also double the resistance. In this case the variation of the width is the input variable and the output variables happen to be the variation of both the resistance and the current.
• I also predict that if I decrease the width of the graphite paper in centimetres then the current will decrease and thus the resistance will increase. This prediction goes by the same ideas as the first prediction. Hence as I decrease the width in centimetres of the graphite paper I will automatically decrease the size of space for the particles to flow through. Hence the resistance of the flow of current will increase, and thus the current flow will decrease.
...read more.

Conclusion

As there are no anomalous results then the evidence is almost certain to justify a firm conclusion. The conclusion is that for the width is inversely proportional to the resistance. Hence as the width of any given metallic object decreases the resistance increases.

If one wants to do further work into this topic one could do an experiment into the affects the temperature of a piece of graphite paper will have on its resistance. Prior to the experiment I would have done a preliminary experiment, testing different temperatures and seeing which set of temperatures I will work with in the real experiment.

The Apparatus

• Battery
• Voltmeter
• Ammeter
• 0-1mA Shunt
• Graphite Paper
• Guillotine
• Wires Connecting Apparatus
• Clips
• Thermometer
• Immersion Heater
• Beaker
• Water

The Method

• Set up the apparatus accordingly with all the wires connected in the right places. ( Same principles as the main experiment only the graphite paper is not flat but raped round a beaker)
• I will chop the pieces of graphite paper up in the guillotine.
• Once heated, put the immersion heater into a beaker full of water.
• Rap a piece of graphite paper round the beaker.
• Clip the clippers onto the graphite paper.
• Put the thermometer into the beaker.
• At 10 degree intervals note down the ammeter reading and the voltage from the voltmeter.
• I will repeat the experiment twice over to check my results.

Immersion Heater                       Clip Graphite Paper Beaker The Prediction

• If the temperature of a given metallic object increases the free electrons contained in the metal will increase in speed. Hence the higher the temperature the bigger the resistance will be.
• I also predict that if I increase the temperature by 10 degrees I will double the resistance.

...read more.

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