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Investigating the resistivity of an unkown wire

Extracts from this document...

Introduction

Michael Ofori

Introduction

The aim of this investigation that I am about to embark on is to research into the resistivity of a wire found on an ancient mummified Persian princess who according to one translation is a daughter of the King Xerxes which was about 2,600 years ago.

After I have found the resistivity of this wire, I will compare and contrast it with other resistivities of the different types of contemporary wires available today in order to interpret and conclude whether it is made from a modern alloy.

Theory

An electric current in a wire is the passage of moving charge through the material. Charge is carried by particles such as electrons and ions. In some materials such as a metal, the charge is carried by electrons. In other materials such as salt solution, the charge is carried out by ions. If charged particles are moving, a current is produced. Electrons moving in a circuit are negatively charged. They move from the negative terminal to the positive one. In spite of this, the direction of the current in a circuit is taken as being from positive to negative.

A current in a wire is due to the movement of free electrons. A wire consists of millions of atoms which have electrons tightly bounded to the atomic radius by the electrical attractive force between the positive nucleus and the negative electrons. In solids, one or two of the outer electrons surrounding each atom are used to form the bonds between atoms that hold the solid itself together.

Middle

• Firstly, measure the diameter of the wire at 6 different lengths using a micrometer and workout the mean diameter of the wire.
• Set up experiment as shown in the diagram
• Connect power supply to ammeter (using connecting wires) and from the ammeter to the research wire using a connecting wire clip
• Connect the other end of the research wire to the variable resistor (again using a wire clip) and from the variable resistor to the power supply
• Connect the voltmeter in parallel to the wire (as voltmeters have high resistance and will not let current through if connected in series).
• Make sure the ammeter and voltmeter reading is zero before turning on power supply
• After power supply is turned on, change the resistance of the circuit by the use of the variable resistor and take accurate measurements of the current and voltage using the ammeter and voltmeter when resistance is changed.
• If the wire gets hot after when measurements have been taken, wait until the wire cools down before taking next measurement in order to prevent biased data.
• Carry out 8 experiments and repeat any test if necessary.
• When all measurements have been taken, insert them into a well structured table containing units, headings etc and draw a correlation graph to work out median resistance (R=V/I) and also observe the relationship between voltage and current.
• Using the calculated mean diameter of wire, calculate the radius and cross-sectional area of wire using the formula πr2 and work out the resistivity of the wire using the formula (ρ = RA / L)

Safety

Conclusion

Percentage error =  Error in reading

Average value

Micrometer

% error = 0.001mm

0.565mm

= 0.176 %.

This is percentage error is not significantly high as it is under 1% so therefore the micrometer measurements were quite accurate to my surprise. However, because they do not correspond to my expectations in determining the percentage error of my calculations which was due to the instruments that was given to me, I will also calculate the percentage error for the voltmeter and ammeter as well to see which instrument carried the most percentage error which ultimately resulted in variation of my data with published data values.

Voltmeter

% error = 0.01

0.05

= 20 %.

The concludes that the voltmeter carries a slight degree of error associated with the voltmeter measurements I took and this ultimately causes a clear distinction between published data values and my value. In future experiments, I will use a different and a more accurate voltmeter for precise measurements.

Ammeter

% error = 1mm

25mm

= 4%

Although this percentage uncertainty value is also not significantly high, it also contributes to variation between data sheet values and my value. This percentage error in opinion was caused from using an analogue ammeter to measure the current. I had to manually measure the current with my eye considering the parallax error and factors of that nature although I had considered these factors earlier in my plan. Because an analogue ammeter was used, I was unable to measure the current to a satisfying degree of accuracy. In future experiments, I will improve the measurements of current using a digital ammeter.

Bibliography

1. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html
2. AS physics, isbn: 0435628925
3. http://hyperphysics.phy-astr.gsu.edu/HBASE/Tables/rstiv.html

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