To investigate the factors which effect the resistance of a metal wire.

Hannah Clapham Physics Coursework 2003

To investigate the factors which effect the resistance of a metal wire

Aim: To find how different factors affect the resistance of a metal wire.

Hypothesis: For this investigation I think that the thinner the wire the higher the resistance of the wire. This is because the electrons in the wire can flow more easily when the wire is thicker because there are less collisions and therefore less resistance so when the wire is therefore thinner there are more collisions and the electrons flow more slowly creating more resistance.

Knowledge that I already have is Ohms law and how to measure resistance using a voltmeter and an ammeter. Ohm's law states that the amount of current flowing in a circuit made up of pure resistances is directly proportional to the electromotive force impressed on the circuit and inversely proportional to the total resistance of the circuit. The law is usually expressed by the formula I = E/R, where I is the current in amperes, E is the electromotive force in volts, and R is the resistance in ohms. This enables us to work out

the resistance using the current and voltage.
R=V/I.

Theory: Atoms are made up of a positively charged nucleus surrounded by negatively charged electrons. In solids, one or two of the electrons in each atom are used to form the bonds between atoms that hold the solid together. In a metal these bonding electrons are free to move through the entire solid. These are often referred to as “free electrons”. An electric current is a flow of charged particles and when a voltage is applied to a metal, the free electrons can flow through the metal.

When a metal wire is placed in an electric circuit the voltage makes the electrons flow through the wire. As they do so, they collide with the metal ions and this process slows down the flow. The collisions between the electrons and the atoms cause the electrons to move slower, which in effect causes resistance. Resistance is a measure of how easily the electrons can move through the metal, therefore a low resistance means the electrons can move easily.

Electric current is a measure of the charge that flows per second. The formula for this is:

Current = charge ÷ time

Since the charge on each electron is the same, current represents the number of electrons flowing per second. If the resistance is high, the flow of electrons is slowed down and so the number of electrons per second is reduced meaning that the current is reduced. Now, the factors that affect the resistance of a wire are going to be described.

Firstly, temperature is a factor. If the wire is heated, the atoms will move around more because there will be an increase in energy. This would cause more collisions between the atoms and the electrons. The increase in collisions would cause the resistance to rise. This would be very hard to do, because the equipment needed to do this experiment effectively has not been given to us.

Secondly, the width of the wire is a factor. This will cause resistance to decrease because of the increase in space in the wire. The increase in space means that there is more space for the electrons to flow freely because there would be fewer collisions with atoms. I could do this by using different widths of a wire; for example thin, medium, or thick copper could be used as well as different diameters of constantan.

Thirdly, the material used would be a factor. If the material being used contains atoms with a large number of electrons on the outer shells, then this means there are more electrons available. So, in theory, if the material has a large number of atoms, there should be less resistance, because of the higher number of electrons .If the atoms in the wire are closely packed, then this will cause an increase in resistance, due to frequent collisions. To do this I would use the same length and width of many different wire materials, using the same amount of voltage each time.

Finally, the length of the wire is a factor. The longer the wire, the longer it will take electrons to get to the end of the wire. This is because there will be more collisions between electrons and atoms. So, in theory, the length of the wire should be directly proportional to the resistance. This would be very easy to do, and give accurate results. I have chosen to do the width of the wire as my factor because I think that this would be interesting to do and there are also many ways to develop and increase the accuracy of this factor.

Variables: The variable that I am changing in my experiment is the diameters of the wire. It will range from 18 SWG to 38 SWG. The dependent variable that I am measuring is the resistance of the wire. This will be measured in ohms (Ω) with a multimeter. The rest of the experiment will be the same. I will use a total length of 50cm of wire. The experiment is done at room temperature. I will keep the following variables the same:

Temperature- I will keep the temperature of the wire at a constant temperature. In my first method I used a multimeter which uses a current that is so small that it does not affect the temperature of the wire. Later in the second method using a variable resistor o will keep it the same by using a variable resistor to keep the amps at 50.0ma which will not heat up the wire. I cannot say that it will definitely not affect the temperature as there is no apparatus that I am aware of to test this, but I have been ...

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Length of the wire- I will make sure that I use the same length of wire for each experiment, which will be 50cm long.

Increase in diameter- I will increase the diameter of the wire by the same value of SWG each time, which will mean that the wire will increase by 2 SWG each time although this does not relate to the diameter of the wire.

Measuring the resistance - I am going to use the same multimeters and later on, variable resistor, for my entire experiment as different pieces of apparatus may vary the accuracy of my results. This is because the measurements may slightly vary between multimeters and variable resistors, although the zero error of the multimeter will be taken before doing each stage of the investigation.

Safety and precautions: There are no specific safety hazards during this experiment as there are no toxic solutions involved. Whilst measuring the length of the wire I need to take care that the end of the wire does not poke in anybody’s eyes. As was stated in my planning section of the coursework, I had to keep all of the different non-variables the same, to make sure that none of them affected the results of the experiment in any way. I will make sure that I set up the experiment away from any hazards, so it does not get altered or any interference from other equipment. I will keep the desktop that I am working on as clean as possible, so that there is nothing on the desk, except for the apparatus needed experiment.

Pilot Experiment: I conducted a preliminary experiment. For this experiment I used a multimeter as an ohm meter (diagram and method below), which was less accurate for the thicker wires. I also began by doing a trial experiment to decide which metal to use from Copper and Constantan. The results I obtained were as follows:

These results clearly showed me that Copper had a very low resistance and would not give me any real results therefore I chose Constantan as these results were very different from the copper and although I only did 3 diameters of wire a pattern was already starting to develop.

I then continued to do a second pilot investigation. For this I used a 50cm length of wire with multiple diameters of Constantan. The results were as follows:

Although these results were quite good, if I increased the length of the wire I think that this would give me more accuracy as in theory the result should double. I would collect the data for diameter and resistance 3 times so I can improve accuracy by taking an average.

Apparatus List:

Multimeter (ohm meter)

2 connecting wires

2 crocodile clips

Metre ruler

Various diameters of Constantan wire ranging from 18 SWG to 38 SWG in 2 SWG intervals.

Micrometer

Method:

Firstly collect all of the apparatus listed above.
Put the 2 connecting wires into the multimeter in the terminals, which allows the meter to work as an ohm-meter. Put the 2 crocodile clips on either end of the connecting wires.
Turn on the multimeter and turn the dial to 200Ω, which reads to 0.1Ω, therefore meaning the ohm-metre can read to more accuracy. Some multimeters have a zero-error, which will alter the results. To find out this zero error clip the two connecting wires together and turn on the metre. This will give you a zero error, which can be negative or positive. You only need to note down this value but when writing up the results this value needs to be added or subtracted from the resistance value.
Collect the diameter of Constantan wire that you want to measure and straighten out 1 meter of it.
Put the left crocodile clip on the beginning of the wire and place this at 0m on the ruler, and place the right crocodile clip further down the wire at 1m making sure the wire is as straight as possible.
Switch on the multimeter on and record the resistance on the screen. Repeat this reading a further 2 times therefore enabling an average to be taken.
Repeat steps 1-6 with other diameters of wire so you eventually have results for wires 18 SWG to 38 SWG.

Diagram:

Micrometer:

To find the diameter of a wire I used a specialized piece of equipment called a micrometer.

The micrometer is exceptionally accurate measuring instrument and the reading error is 1/200mm= 0.005mm.

The tick marks along the barrel of the micrometer represent halves of millimetres. Every revolution of the knob will expose another tick mark on the barrel, and the jaws will open another half millimetre. There are 50 tick marks wrapped around the moving barrel of the micrometer. Each of these tick marks represents 1/100 millimetre.

To read the distance between the jaws of the micrometer, simply add the number of half-millimetres to the number of hundredths of millimetres. For example the above diameter is 2.62mm (2.50+0.12mm)

Method for measuring the diameter of the wire:

Put the wire you want to measure between the jaws of the micrometer.
Use the ratchet knob to close the jaws on the wire until it clicks. When it clicks it is sufficiently closed.
Look at the fixed barrel and the moving barrel and record the two numbers. Now add these two numbers together and this is the diameter of the wire.
Take away the zero error of the micrometer. To work out the zero error you close the jaws using the ratchet knob until it clicks. You then read off the measurement as though you would for a wire.
Repeat the reading a further 2 times to improve accuracy by taking an average of the 3 readings.

Fair Test: To make sure it is a fair test I will use the same length of wire each time. I will also make sure that I use the same multimeter throughout my experiment to avoid any inaccuracy in changing equipment. The only thing that will change is the diameters of the wire.

The Data: I am going to collect data on the different resistances of varying diameters of wire. I will increase the diameter of the wire each time by 2 SWG, so the diameter will range from 18 SWG to 38 SWG. Once I have collected the data I will format a table of my results.

The Results:

The zero error is the error on the apparatus which has to be added or taken away from the reading. These were:

Micrometer: -1

Multimeter: +2

Graph 1

This graph shows that there is a correlation although it is in the form of a curve, which therefore means it is not directly proportional. I also noticed that the thicker wires were less accurate so I will therefore use another method which will increase the accuracy. This method uses a variable resistor which is as follows:

Variable Resistor Method

Apparatus List:

Power Supply

Variable resistor

2 multimeters (1 ammeter, 1 voltmeter)

7 connecting wires

2 crocodile clips

Metre ruler

Various diameters of Constantan wire ranging from 18 SWG to 38 SWG in 2 SWG intervals.

Micrometer

Method:

Firstly collect all of the apparatus listed above.
Plug in the power supply and turn the knob to 6V but do not turn on. Put 2 of the connecting wires into the power supply in the D.C terminals.
Plug the connecting wires into the variable resistor. Using 2 more of the connecting wires, plug one in at the end terminal of the variable resistor and the other into the first terminal via the existing connecting wire.
This connecting wire then needs to be plugged into a multimeter set to work as an ammeter on 200 A. Plug in another of the connecting wires to the multimeter in the correct terminal for it to be used as an ammeter.
Connect a crocodile clip onto the end of the connecting wire that is plugged in at the end of the variable resistor and into the back terminal of this connecting wire insert another, which will connect to the second multimeter.
Finally to complete the circuit add a final connecting wire into the second multimeter and connect with the connecting wire coming from the ammeter and attach a crocodile clip to the end. Set the second multimeter to work as a voltmeter on 200 V. The circuit should then look similar to the following circuit diagram:

Some multimeters have a zero-error, which will alter the results. To find out this zero error clip the two connecting wires together and turn on the metre. This will give you a zero error which can be negative or positive. You only need to note down this value but when writing up the results this value needs to be added or subtracted from the value.
Collect the different diameters of wire (18 SWG until 26 SWG). Begin with the thickest wire (18 SWG) and straighten out a 100 cm length of wire. Attach it to the 2 crocodile clips.
Put the left crocodile clip on the beginning of the wire and place this at 0m on the ruler, and place the right crocodile clip further down the wire at 1m making sure the wire is as straight as possible.
Turn on the power supply (6V) and the multimeters. Move the variable resistor until the ammeter reads 50 milliamps (you will need to change this for each diameter of wire). Read off the values from the voltmeter and repeat the reading a further 2 times therefore enabling an average to be taken.
Repeat steps 8-10 with other diameters of wire so you eventually have results for wires 18 SWG to 26 SWG.
Measure the diameter of the wire using a micrometer. (See method on page 4).

Diagram:

The Data: I am going to collect data on the different resistances of varying diameter of wire. I will increase the diameter of the wire each time by 2 SWG, so the diameter will range from 18 SWG to 26 SWG. Once I have collected the data I will format a table of my results from the variable resistor method in which I will calculate myself the resistance. This will enable me to see whether the diameter of the wire affects the resistance of the wire.

The Results:

This method was a lot more accurate as the multimeter was not calculating the resistance, which therefore meant the voltmeter and ammeter values were a lot more accurate as they were 4 figure numbers. I then calculated the resistances myself which therefore meant the values were more accurate because the voltmeter figures were to 3 decimal places which meant that I could also calculate the resistances to 3 decimal places.

To show the correlation more clearly I will divide 1 by the diameter, which will hopefully allow me to plot a linear trend line with data that has a strong correlation. I used the data from the variable resistor method for the thicker wires to increase the accuracy of my original data.

This data on the following page was used to create graph 2.

Graph 2

As you can see from this graph there is an inverse correlation between the diameter of the wire and its resistance, although it is not straight therefore diameter is not directly proportional to resistance. This graph shows me that the thicker the wire, the higher the resistance but the values for diameter on this graph are inverted although do not give a straight line so I will create another graph comparing the inverse of the cross sectional area against the resistance and this will give me the resistivity of the wire, which I think will show me that the cross sectional area is directly proportional to the resistance.

Increasing the area of a wire will quadruple the space in the wire and therefore the resistance will increase.

As I can see that the results from the variable resistor method are more accurate I will continue to use these results when creating my graph of the inverse of cross sectional to ensure that the best possible results were achieved.

To work out the cross sectional area of the wire I used πr2 where r is the radius (½ diameter) of the wire. The data to produce this graph is as follows:

This graph shows me that my data is good and accurate as the R2 value is 0.9981 and this is very close to 1.

The line has good correlation and shows me that the resistance of a wire is inversely proportional to the cross sectional area. From this graph I can work out the resistivity.

Resistivity is defined as the resistance of a cylinder of the material 1 metre long with a cross-sectional area of 1 m2.

The equation for working out the resistivity is:

Resistivity=Resistance (Ω) x Cross sectional area (m2)

Length (m)

The resistivity (ρ) of constantan wire is 49 x 10-8. This formula can be rearranged to read R= ρ l x 1/A which is the same as y=mx + c. This then enables me to use the y value on my graph to analyse the resistivity of constantan in my experiment. My graph reads y = 0.4774x + 0.081 so if I translate this into y = mx + c this means that the y-intercept (c) is 0.081. This is a very good value as I would ideally expect the line to intercept at the origin and this is a value close to this, which means my data was quite accurate. The mx value on my graph shows me the resistivity of constantan wire in my experiment. This value is 0.4774 and if I were to put this into exponential form it would read 47.74 x 10-2, but my measurements were in millimetres2 and resistivity is measured in metres2 so this value needs to be divided by 1 million. The resistivity of constantan is therefore 47.74 x 10-8. This value is quite close to the theoretical value for the resistivity of constantan so my resistivity value is quite good as it is fairly close to this. The percentage accuracy of the resistivity is 97.4%, which means are data is almost perfect.

Conclusion: On the graphs on the previous pages there are distinct correlations. The thicker the wires the lower the resistance of the wire. The results show that there is a linear relationship between resistance of a wire and its diameter therefore its cross sectional area. This means that there is an inverse relationship between diameter and resistance, as when the diameter increase the resistance decreases. The cross sectional area is directly inversely proportional to the resistance as this gives me almost a perfectly straight line with an accuracy of 99.81% which is excellent.

My hypothesis stated that “For this investigation I think that the thinner the wire the higher the resistance of the wire. This is because the electrons in the wire can flow more easily when the wire is thicker because there are less collisions and therefore less resistance so when the wire is therefore thinner there are more collisions and the electrons flow more slowly creating more resistance." The results from this experiment have shown that this statement is almost correct. The reasoning for it not being perfect is that although it is true that the thinner the wire the higher the resistance, it is not directly proportional can be seen from my second graph. This is why I then went on to investigate whether the resistance was directly proportional to the cross sectional area and I found that this was directly inversely proportional.

The first set of data I collected using a multimeter for the thicker wires (18 SWG to 26 SWG) was less accurate as it only measured the resistance to 0.1 Ω. This is why I carried out these results again with a different method increasing the accuracy of my data, which therefore reduced the risk of anomalous data. The resistivity results show that the resistivity of the constantan wire is 47.74 x 10-8 which means that the wire I used in my experiment is slightly impure. From this experiment I have found out that resistance is not directly proportional to diameter as I first thought but is directly inversely proportional to cross sectional area.

Evaluation: The results I obtained from this experiment were initially not quite as clear as I had hoped, but after changing my method for the thicker wires this caused the results to become a lot more accurate. The accuracy of my results was very good as when using the variable resistor methid the results were taken up to 3 decimal places and then measuring the diameter the micrometer reads to 100th of a millimetre. Although some of my data was not 100% accurate the graphs did not show these results to be anomalous as they fitted almost perfectly to the best fit line. By taking each of the readings 3 times I increased my accuracy as this meant I coul d take an average of my results and would decrease any anomalous results.

My experiment went well although there are a couple of areas which could be improved if I were to do this experiment again. The first of theses is the straightening if the wire. When straightening out a 1 metre length of wire I found it very difficult to get the thicker wires straight which could have lead to some inaccuracy. To improve this I could use the follwing method. Clamp one end of the wire and place a weight on the other other to stretch out the wire hopefully straightening out any bends and kinks in the wire. Although doing this would straighten the wire the wire may also stretch. I would therefore take the diameter reading after straightening the wire as if the wire had stretched with the weight the diameter may have decreased.

I would repeat this investigation I would investigate more factors such as heat and length so that I could see how these affect the wires resistance. I would also carry out this investigation further and compare the properties of other conductive metals so I could see how each factor affects metals with varying resistivity’s.

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