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Investigating the relationship between the length of a pencil lead and its electrical resistance.

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Investigating the relationship between the length of a pencil lead and its electrical resistance.


  • The aim of the experiment

The aim of the experiment is to establish the relationship between the length of a pencil lead and its electrical resistance.

  • List of the apparatus to be used
  • Pencil lead of a length of about 10-15cm
  • Power supply
  • Ammeter (3SF)
  • Voltmeter(3SF)
  • Micrometer +/- 0.01 mm
  • Metre Ruler (0-100 cm)  +/- 0.1 cm
  • Standard connecting wires
  • Crocodile clips
  • Sandpaper
  • Protection resistor
  • The Diagram

  • Method

During my experiment I will:

  1. Set up apparatus as shown in the diagram.
  2. Measure the resistance of the protection resistor with the multimeter and record its value above the table
  3. use the sand paper to remove the upper layer of coating from the rod, moving the paper wrapped around the lead along the full length of it.
  4. Measure the diameter of the rod with the micrometer taking measurements in 5 or 6 places (changing the angle, at which we are measuring, too). Record the values. Average them and record the average.
  5. put one of the crocodile clip at the end of the pencil lead, leaving about 0.5 cm at the end. Put the second crocodile clip at the other end.
  6. Measure the inside distance between the clips. Record in the table.
  7. turn on the power supply. Read of the values of the voltage and current. Record in the table.
...read more.


  • Sensitivity of the measuring instruments

In my experiment I will be using different measuring instruments.

The first measurement will be the diameter of the pencil lead. I will measure it with the micrometer accurate to 0.01mm (3SF). I will measure the diameter in about 5 or 6 places along the rod, to make sure that the cross sectional area does not differ a lot in different areas of the lead.

The second thing I will be measuring will be the length of the graphite rod. It will be measured on the insides of the crocodile clips (since it is the shortest way that the current can flow through). This will be measured with a ruler to the nearest mm (2SF).

I will also be measuring voltage and current using multimeters, which are accurate to 3SF.

  • Outline of the relevant theory

“Ohm'slaw, states that the potential difference between two points on a metallic conductor and the current I flowing through it are proportional (at a set temperature): V=IR where R is a constant called the resistance of the conductor. The law also applies to some nonmetallic conductors.”

I believe that the pencil lead, which is made of graphite (which is an electrical conductor), will obey ohm’s law, as long as the temperature and cross sectional area will be kept constant.

...read more.



I think that that the errors in the experiment weren’t very big, because by using very small currents I have prevented my pencil lead from heating up, which would make my results to some extent unreliable. However because I have been using so small currents and voltages, my values of V are accurate only to 2 SF.

I think that the error in measurements of the length wasn’t very big since I have always made sure that the clips were perpendicular to the rod, and that I am measuring the distance along the lead anstead at the ends of the clips.


The systematic error that has made my values of R increase is about 0.6Ω. The error in reading the values of the current and voltage is about 0.3 mA (~2%) and 0.001V(~2%) respectively (the voltage was changing much less than current), So the error bounds for R should also be 2%., But as can be seen on the graph, all values fall within these bounds.


By using a better connections (eg. shorter wires) or cleaning the clips and wire connections thoroughly a systematic error can be reduced. If the temperature of the lead may have been kept constant (eg. using an oil bath) the voltages may have been bigger, what would improve the precision of the experiment. This might have also been improved by using more sensitive meter or a mV scale.

Joanna Meldner               PHYSICS - As Practical Assessment 2        Page         

...read more.

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