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Determining the resistivity of a piece of wire

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Introduction

Chris Barr        Determining the resistivity of a piece of wire        March 2004

Determining the resistivity of a piece of wire

Resistivity

Resistivity is a property of a wire linking the cross sectional area and lengths of a piece of wire. Resistivity is the measure of resistance to flow on a molecular level.

“It is a measure of the resistance to the flow of current from a microscopic level, that is, as explained in terms of the atoms, the basic building blocks of all solid materials. The resistivity, ρ  (Greek letter rho), depends on the behaviour and number of free, or conduction, electrons and not on the shape of the conductor, as does resistance.”

(http://mst-online.nsu.edu/mstonline/electronic/electronic2.htm)

As explained above it differs from resistance as it takes into account the properties of the material. Resistance does not do this it is merely the ratio of Voltage to current through a material/component.

Resistivity (ρ) is defined through the equation below where resistance is R length is l and cross sectional area is A.

                                ρ =  R A

                                          l

The unit of resistivity can be show below

                                ρ =  R A

                                          l

                                ρ =  x m2

                                        m

                                ρ =  Ωm

So the Si unit of resistivity is ohm meters (Ωm)

The piece of wire to be used will be an alloy called Nichrome. It is an alloy of Nickel and Chromium. The exact compositions of the alloy Nichrome are 80% Chromium and 20% Nickel.

...read more.

Middle

Micrometer readings of the wires’ diameter are used to calculate the cross sectional area by using the formula

                                        A = π d2

                                                 2

Results

The results table shown overleaf contains the raw and manipulated data from the experiment. During the experiment the current was not altered and was always kept at 0.50A. This was a suitable value as in a previous experiment the current was kept at 0.50A and this did not heat the wire suitably to alter the results. The length was however changed for each trial. The length was measured at 10cm intervals. Voltage changed was measured. There were two trial runs for each length of wire. The voltages were measured and recorded as V1 and V2. As the error on the ruler was ±0.001m the maximum and minimum values that the reading could’ve been are shown. This also applied to the voltmeter and ammeter which had errors of ±0.01V and ±0.01A respectively. Knowing these errors a maximum and minimum were recorded taking into account both V1 and V2.

E.g. in the fist reading at l=1.00m V1=7.74V and V2=7.23V this meant accounting the random error of ±0.01V the minimum and maximum voltages are 7.72V and 7.75V respectively. All raw data must be recorded to 2 decimal places as this is the greatest accuracy of the equipment. Minimum and maximum also have 2 decimal places as they are not manipulated data.

...read more.

Conclusion

x10-6Nm ±1.6x10-7Nm

This is close to the accepted value of 1x10-6Nm


Evaluation

A few problems arose during the experiment. These were mainly to do with the difficulty of setting the current to 0.50A each time. Towards the larger lengths of wire the current was increasingly difficult to alter accurately. Once a suitable current value was set the voltage reading then was not static. It was constantly changing making it very difficult to measure. This problem was not solvable and thus the error bars for the higher resistance values are fairly large. One further difficulty was the necessity to measure the wire and alter the current and hold the jockey at the same time. This was near impossible at first where the wire was loose next to the ruler. To overcome this problem sellotape was used to affix the wire to the ruler this then made it relatively easy to measure.

If I did the experiment a further time I would change only one piece of equipment and that would be the power supply. If this was changed it would maybe keep the voltage at a much more constant level. The rest of the experimental procedure was very substantial however. Therefore if the experiment was repeated the method and the equipment (power supply excluded) need not be changed.

For an extension to the experiment the resistivity of other wires could be measured. This could include copper, steel and other metal/metal alloy wires. Another extension would be to change the diameter of the wire to see what affect that had on the resistivity.

...read more.

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