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# Resistivity of a Wire.

Extracts from this document...

Introduction

Dipesh Mistry                Physics Assessment

PHYSICS ASSESSMENT – RESISTIVITY OF A WIRE

## PLANNING

PRELIMINARY RESEARCH

What is resistivity? - Resistivity is a fundamental parameter of the material making up the wire that describes how easily the wire can transmit an electrical current.  High values of resistivity imply that the material making up the wire is very resistant to the flow of electricity.  Low values of resistivity imply that the material making up the wire transmits electrical current very easily.

Ohms law states that if the cross section of the wire is uniform, then the resistance is proportional to the length and inversely proportional to the area of the cross section.  There are four variables that affect the resistance of a wire.  These factors are thickness/diameter, length, material and temperature.  The two factors I am going to look at are thickness and length because the effect on the resistance is more measurable than the effect of resistance with material and temperature.

The thickness/diameter of the wire will have an affect on the resistance of a wire.  This is because the electrons have to squeeze together more to pass through a thin wire than they do to pass through a thick wire.

The length of a wire affects the resistance because if you double the length you double the resistance.  So for this experiment, it would be sensible to keep the length of the wire constant so you are calculating one set resistance value for the wire.

Middle

0.1

0.003

0.003

0.003

0.003

0.003

0.2

0.007

0.006

0.007

0.006

0.007

0.3

0.011

0.011

0.009

0.010

0.010

0.4

0.015

0.014

0.014

0.013

0.014

0.5

0.017

0.015

0.016

0.017

0.016

0.6

0.020

0.020

0.020

0.021

0.020

0.7

0.023

0.021

0.023

0.023

0.023

0.8

0.025

0.025

0.025

0.026

0.025

0.9

0.028

0.029

0.029

0.029

0.029

1.0

0.031

0.030

0.030

0.031

0.031

When taking my current readings, I rounded the figures off to 2 significant figures as I thought it was a sensible choice from the scale of my ammeter and voltmeter.  I have also stated the units underneath or next to the column headings.

The length of wire used was 0.75m +/- 1mm, which is the exact measured length.  This measurement is an important factor, as I shall need it in order to calculate the resistivity.

Diameter (mm)

D1

0.38

D2

0.38

D3

0.38

D4

0.38

D5

0.38

D6

0.38

## Average

0.38

Above you can see the results for the diameter measurements.  I took readings at 6 evenly spaced places along the wire and then calculated an average.  The average diameter was calculated to be 0.38mm, which is also an important reading, which will be used to calculate the cross-sectional area.

Now that I have a value for the diameter, I shall now calculate the cross sectional area using the equation πd2/4, as shown below.

Cross sectional area = πd2/4

Cross sectional area = π × (0.38 × 10-3m )2 /4

Cross sectional area = 0.113411494 × 10-6m2

Cross sectional area = 1.1 × 10-7m2(2s.f)

This cross sectional area value is an important factor, as it will be used later on to calculate the resistivity.

As you can see from the previous page, I have drawn a graph of my results.  Both the axis have been labeled stating the correct unit of measurement.  Once my points were plotted, I then drew a line of best fit going through the origin.

Conclusion

• Crocodile clips used in the experiment may have added resistance to the circuit and therefore add to error

Random errors:

• In my results table the readings I repeated for the current were not always the same – implying that there is a certain random uncertainty in my data so that for any given voltage the current might fluctuate (solution – repeat readings which were carried out)
• Diameter of wire – if this is not constant; the result will be flawed (solution – repeat readings to identify uniformity, which I did).  The repeats I took could have shown that the diameter was not the same throughout the wire, again indicating that there is a possibility of random uncertainties in the value of the diameter and hence the cross-sectional area.

IMPROVEMENTS

If I were to carry out this experiment again, I would use more accurate equipment to minimize errors throughout the experiment and therefore making my calculations and final resistivity value as close as I can to the actual value.  For example I could use a computer program that controls the voltage so that I can increase the voltage and take readings at set intervals.  For the experiment I carried out, the potentiometer I used was on a non-linear scale, so I couldn’t get an exact value from my multimeters when reading the current and voltage.  So if I were to carry it out again, I would try using a potentiometer on a linear scale to give exact values for voltage and current readings.  I could also use better connections such as soldering the connections, which would also reduce errors in my experiment.

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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