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I am going to investigate what the resistivity is of a pencil lead. Pencil lead is made from a combination of finely ground graphite and clay, mixed with water and pressed together at high temperatures into thin rods

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Finding Out The Resistivity Of Pencil Lead



I am going to investigate what the resistivity is of a pencil lead.  Pencil lead is made from a combination of finely ground graphite and clay, mixed with water and pressed together at high temperatures into thin rods. Graphite is largely made up of carbon, which is quite a good conductor of electricity, but clay is not.  This means the more clay that is mixed within the pencil lead the higher the resistance will be.  The resistivity of a material is an individual property.  It does not depend on the dimensions of the component only the materials from which it is made.  To do this I will first have to find the resistance of the pencil lead.  For the resistance I expect the graph to look something like this:



The reason I predict the graph to look like this is because I think, and assume, that pencil lead will be an ohmic resistor.  The graph will therefore look like this because the characteristic of an ohmic graph is that of above (a straight line).  This means that current is directly proportional to the voltage.  The gradient of the graph is also the resistance of the pencil lead.  The gradient will then be taken along with the cross-sectional area and the length of the pencil lead and put into the resistivity formula.  However I think that there is a distinct possibility that the pencil lead may have the characteristics of a semi conductor, as carbon is a semi conductor.  This means that the graph could look like this:







However, pencil lead also contains clay that is a good insulator of electricity so may affect this characteristic but if the graph were to look like this it is because carbon is a semi conductor.

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The temperature of the pencil lead will affect the resistance.  It is especially important that this remains the same as materials that are ohmic resistors, at high temperatures, can change the characteristic of the material (no longer is an ohmic resistor).  The higher the temperature the higher the resistance because the electrons move faster and the positive ions vibrate more due to an increase in kinetic energy.  This means that there are more collisions between them leading to an increase in the resistance.  To achieve keeping the temperature of the pencil lead constant I will let the pencil lead cool for a couple of minutes after each reading as well as keeping windows closed to try and keep the room temperature constant.

  1. I will first of all measure the diameter (using a micrometer as this is an accurate piece of equipment) of the pencil lead and the length (using the mm ruler).  I will be measuring the diameter of the pencil lead three times throughout the experiment to try and make sure that I get an accurate reading that remains constant.
  2. I will then setup the circuit that is displayed above.  The reason why I will be using a potential divider circuit is because I can get a higher range of voltages as well as it also helps in getting the voltage more accurate.  I will place the crocodile clips on the end of the pencil lead and take the width of the clips off the total length of the lead.  The reason I will do this is because the crocodile clips will be conducting the electricity at the points where they are attached so the lead is only conducting past these clips.
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-6.  If I were to use a more accurate voltmeter the percentage error could have been cut down drastically meaning that my actual result would have been more accurate.

If I repeated the experiment I might also use a different piece of lead.  The piece of lead could be of a different softness/hardness, a different diameter or a different length.  I would then take one of these variables and see what happens to the resistance and then the resistivity of the lead.

Note:  The actual resistivity of graphite is 7.84x10-6.  There are many reasons why my result does not match up with that of the actual figure.  There are three main reasons:

  1. The percentage error of this experiment was large and so would have probably had a huge effect on the outcome of the result.  In a laboratory there would be much more accurate equipment which would have meant that the percentage error would practically be 0%.
  2. The actual resistivity of constantan will be in controlled conditions.  This means that the pressure would have remained constant along with the temperature etc.
  3. The final main reason is that the pencil lead that I used does not just contain graphite.  In fact it contains a variety of materials including clay.  This would have a large effect on my result.

*When I measured the diameter all three readings read 2.725mm.

Richard Burn                The Resistivity Of A Pencil Lead

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