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# An investigation into the relationship between resistance, cross-sectional area and Resistivity.

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Introduction

John Bussey Physics Investigation

An investigation into the relationship between resistance, cross-sectional area and Resistivity.

## Research

The equation for finding resistance is

R= V/I

Where V = potential difference (volts) and I = current (amps)

Current is the rate of flow of charge. An amp = 1 coulomb/second. The coulomb is the standard unit of charge. Potential difference is the amount of electrical energy transferred per unit of charge between two points. It is measured in joules per coulomb, or volts.

The opposition to the flow of charge is resistance, measured in ohms (Ω). The larger a materials resistance, the greater the amount of potential difference needed to make a current flow through it. A material such as steel will have a relatively high resistance compared to that of gold. Some materials, known as superconductors have no resistance whatsoever!

When a potential difference is applied to a conductor, all the free electrons in it move in the same direction. When the electrons ‘move’ through the conductor they collide with the atoms in the material, so they are continually accelerating and decelerating. Because of this the electrons do not have a constant velocity, so we give them an average velocity, known as the drift velocity.

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V is directly proportional to I: If there is an increase in V there will be an increase in I. The best wire for this experiment is one with a relatively high resistance per unit length but also one which will not overheat with higher resistance (a wire with good temperature stability.) In my experiment, I will use nichrome wire, because it displays both of the above qualities. I will use 0.5 amps through 30cm of wire.

I will carry out my experiment as fairly as possible, but there are bound to be errors and inaccuracies. Many of these will be due to the measuring equipment. The most accurate ammeters and voltmeters available to me are accurate to ±0.01Amp (or Volt). This will affect the accuracy of my readings for p.d and current and more importantly, my calculated resistance, where the associated percentage errors will be added together, increasing the overall %error. The metre rule used to measure the wire is accurate to ±0.001m. The micrometer used to measure the diameter of the wire is accurate to ±0.01mm. Although a hundredth of a millimetre is a very small inaccuracy, we must remember that we are using

Conclusion

Evaluation

When doing my experiment, I tried to make my work as accurate as possible by using the best equipment available to me. However there were still small discrepancies in my work. I took an average value for resistance by measuring three different lengths of wire within a metre of wire taped to a metre ruler. To improve the accuracy of my work, I could have chosen three separate lengths of wire, maybe from different coils, which would have given me a better average. Also, when I recorded the data, I did it in two sessions; a number of conditions that could have affected my experiment could have changed, for example the heat.

The actual value for resistivity, given by the catalogue the wire was obtained from is 1.13 x10-6Ωm. All my values for resistivity lay slightly below this value, but my closest value, taken from my maximum gradient was 1.0909 x10-6Ωm, which is only 0.0391 x10-6Ωm.

I believe that my experiment was of a good level of accuracy and I regard it a success.

This student written piece of work is one of many that can be found in our GCSE Electricity and Magnetism section.

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