I have chosen that my independent or “input” variables will be the length and the diameter of the wire. I have chosen to investigate these factors because it is simple to measure the length and diameter using a ruler and record my findings. When altering this variable my results could show a connection between the independent variable and the resistance given by the wire.
The dependant or “output” variables in this experiment will be the current and voltage of the circuit. I have chosen this because to find the resistance of a wire I need to know the current and voltage. Also the current and voltage in this experiment will hopefully differ with the different lengths and diameters of wire and therefore they are dependant on the independent variables.
To ensure the experiment is fair and make certain that only length, thickness and resistance are being investigated, I will have to control the temperature and material of the wire. I will do control the temperature of the wire because if it heats up it can increase the resistance and affect my results. It will be difficult to control the temperature as the heat of the wire cannot be measured by a thermometer. However, I will try to keep the temperature low by carrying out the experiment in the same room each time, do not leave the circuit on for any longer than is needed and keep the current below 0.5 amps.
The other variable I will control will be the material of the wire. The material of the wire is Constantan because this will not affect my results. By using the same material my results will be accurate and mean something.
The Apparatus and Method
For my investigation I will use a simple circuit that can be used to find the resistance of any test object.
The power supply in this experiment will be a ‘power pack’ which will provide the voltage needed to push the current around the circuit.
The variable resistor will be used in my circuit to alter the amount of current flowing through the circuit which will enable me to have a variety of current values and make my results more accurate.
The constantan wire is my test object which will be a range of lengths and diameters to allow me to investigate how the resistance of a wire varies.
The voltmeter measures the voltage across my test object and is measured in volts. In a circuit the voltmeter is always connected in parallel with the test object as it needs to measure the voltage across it. The voltmeter will give me a reading for the potential difference which will allow me to work out the resistance of the wire.
The ammeter measures the current flowing around the circuit in amperes (amps). Unlike the voltmeter the ammeter is connected in series and will allow me with the voltmeter reading to work out the resistance.
Other apparatus used in this experiment will include:
 A meter ruler – to measure the length and diameter of the wire.
 Crocodile clips – to connect the test wire into the circuit.
 And various other wires to connect the above items together and complete the circuit.
Method
I will set up the apparatus from the previous page in the circuit I have explained. The wire I am testing will be attached to the meter ruler. The positive crocodile clip will be attached at 0cm and the negative clip is moved up and down the wire stopping at the measurements I will take. I will measure the resistance of five different lengths and five different diameters of the constantan using the reading from the ammeter and voltmeter. I will measure the current going through the wire and the voltage going across the wire for each length and diameter. I will then find the resistance of each different length and diameter I will measure using Ohms Law; R = V/I. I will repeat the process for each length and diameter I will test three times to prevent any errors occurring. The three measurements will then allow me to find an average resistance of my data. I will use the average resistance to plot a graph of length against the average resistance and a graph of diameter against the average, which will allow me to make any conclusions and analyse my data.
Measurements
I plan to range my observations from 10 to 90cm. I will do this as measurements are unable to be taken below 10 and above 90 due to the bolts which attach the wire to the ruler. I will take the measurements every 20cm. The measurements will be: 10cm, 30cm, 50cm, 70cm and 90cm. I have chosen these lengths because they are easily measured by the meter ruler and give a good range of results. I have also chosen five diameters which will be much smaller than the lengths due to it being difficult to measure large diameters. The measurements for the diameter of the wire will be 0.19mm, 0.23mm, 0.28mm, 0.31mm and 0.37mm. I have chosen to take a range of five lengths and five diameters because it will allow me to plot an accurate and interesting graph. I have also chosen to repeat the experiment on each length and diameter three times so an average can be taken and ensure no extreme values will effect my results.
It could be possible that my results may contain figures which are out of place because, although I will try to avoid them as much as possible, errors can occur. Errors which could occur are:
 A rise in temperature this could cause the resistance to increase making my results slightly inaccurate.
 The ammeters and voltmeters I will use may contain slight error values, they may have been damaged or they may just simply be old could result in inaccurate readings.
 The wire I will be testing may not be completely straight making it difficult to get an accurate reading by eye. Also the wire may be of a different thickness throughout the length.
Any of these may contribute to causing an error in my results so hopefully by repeating my experiment and taking averages my results will be as accurate as possible.
I have chosen to use a voltage of 3 volts to ensure the variable resistor and the rest of my circuit does not heat up too much. However, if I choose to move to higher currents I may have to increase the voltage to the current can be pushed around the circuit.
I have not chosen a set current to use in my circuit to allow me to collect a range of results. I will use the variable resistor control how much current flows through the circuit. I will record my results in the following sample tables.
My Predictions
I predict that if the length of the wire increases then the resistance of the wire will also increase.
I predict that if the thickness of the wire is increased then the resistance will decrease.
These predictions are backed up by the preliminary experiment that I have done and included the results of in this plan of my investigation.
According to the AQA Physics Revision Guide resistance occurs when the electrons traveling through the wire collide with the atoms of the wire. These collisions slow down the flow of electrons causing resistance. Resistance is a measure of how hard it is to move the electrons through a wire. For example imagine water flowing down various pipes. For the water to flow down these pipes we must use a pump to push the water along. If any of the pipes are narrowed the flow of water is reduced. In this water model the pump represents the power supply in an electrical circuit, the water flowing down the pipes represents the current and the narrow pipes represent the resistor. Using this model helps me understand the flow of electricity better.
I think that the longer the wire, the higher the resistance because if the wire is long it will contain more atoms and so the more likely the electrons are going to ‘collide’ with the atoms. Therefore the longer the length of wire the more molecules there are to oppose the flow of electrons. The cascade theory explains this. Electrons have negative charges which cause them to repel each other and cascade resulting in other electrons being pushed instantaneously. The electrons are pushed instantaneously to keep the flow of electricity going and as one leaves the wire another electron enters to replace it.
The above diagram shows that electrons are attracted to the nucleus of the atoms in the wire. The electron has to avoid collisions with the atoms and does this by the electron behind it pushing it causing the electron to travel through the wire correctly. If the length of the wire is doubled, the resistance will be doubled because the electrons have to travel past twice as many atoms in twice the so double the energy will be needed it push the electrons.
The thicker the wire the more channels the electrons in the wire have to travel down and the resistance decreases as the energy is spread out. According to one of my resources it can be represented by the ‘door model’. The people represent the electrons and the door represents the diameter of wire. If the door is wider, the more people can get through, more easily. If the door is small, people have more difficulty to get through and not as many people are able to walk in or out of the door. It is the same principal for the electrons in a wire. If the diameter is thicker more electrons can go through the wire, therefore reducing the resistance.
The diagram above shows that by increasing the diameter of the wire by a factor of 2, the particles increase by a factor of 4. Therefore the resistance decreases by a factor of 4 because the electrons have four times as many gaps to travel through the wire and is four times as easy to pass through. So if the diameter doubles, the area quadruples, particles quadruple, gaps quadruple and the resistance quarters.
When analyzing my results I will plot them in graphs with the independent variables, the length and diameter of the wire, on the xaxis and the resistance on the yaxis. If my predictions are correct the graph for length should show a straight line through the origin because there should be a direct proportionality between the length and the resistance. If my prediction is correct for diameter, the graph should show a curved line beginning at the top because the diameter squared is inversely proportional to the resistance, or D = 1/R
Safety
Whilst doing this investigation, it is important to take safety into consideration. Firstly I must ensure I follow the safety rules of the laboratory by not running around the laboratory, do not eat and drink in the laboratory and clean up any spillages, keeping water away from any electrical equipment.
The scissors I will use to cut the wire to the appropriate measurements should only be used for that and no other reason. It is important to be careful whilst using the power supply and to prevent any accidental shocks I will make sure the power pack will be at 0 volts before using it. It is essential to be careful when using live wires and I will check none are frayed or dangerous before using them to prevent any accidents or my experiment being ruined. I will also try to keep the current to below 0.5 amps to prevent the wires from heating up, which is a safety factor and will also prevent my results being distorted.
Preliminary Work
The Resistance of Black Putty
For my coursework I will carry out a preliminary experiment to test the resistance of black putty.
In this experiment I will use the following apparatus, in the circuit which I will use in my main experiment.
Apparatus
I will use the following apparatus in my preliminary experiments:

Ruler – to measure the length and diameter of the black putty

Black Putty – my test object which can molded in to the different lengths and diameters I will test.

Power supply – kept at a constant 3 volts to ensure my results are as accurate as possible

Crocodile clips – to connect the black putty being investigated to the rest of the circuit.

Voltmeter – to measure the potential difference and help me to figure out the resistance of the putty.

Ammeter – to measure the current and help with the potential difference to figure out the resistance of the putty.

Variable resistor – to allow the current to be changed

Wires – to connect the above items together and complete the following circuit.
For Experiment 1, investigating the connection between length and resistance I will firstly set up the apparatus I have just explained.
I will measure four different lengths of putty; 15cm long, 10cm long, 5cm long and 2.5cm long, keeping the diameter of the putty at a constant 1cm thick.
I will note down the voltage and current in the following tables and use these readings to help me work out the resistance.
This experiment will be repeated three times to give me an average resistance, which will be more accurate as errors are limited.
Experiment 2 will investigate the relationship between diameter and resistance.
The circuit will be set up the same and the experiment will be repeated three times just as in experiment 1.
However I will use the following diameter measurements and keep the length a constant 8cm: 1cm thick, 1.5cm thick, 2cm thick and 2.5 cm thick.
The following tables show the results of my experiments.
Conclusion
My results show that as the length of the black putty decreases the resistance also decreases. When the diameter of the black putty increases the resistance decreases. This conclusion will help me with my plan and predictions and prepare me for my main experiments.