* Wires with wider diameter have more free electrons because the cross-section surface area is larger in proportion to the length, so the wider the wires are, the less reactive they would be. Resistance is proportional to the cross-section are of the wire given that the length and the material should be the same.
* Longer wires will cause an increase in resistance because the electrons have to travel past more atoms and collisions between the electrons and the atoms are more likely then in shorter wires. Resistance should also be proportional to the length of the wires.
Methods
The equipment needed consists of:
* A variable DC power pack
* Ordinary wires
* An ammeter
* A voltmeter
* 2 crocodile clips
* Assorted wires for tests
Then a circuit is set up in the same way as the illustrated diagram below.
* Connect the wire to the circuit by the crocodile clips
* Take the voltage and current readings from the meters
* Increase/decrease the supply from the power pack and take the readings again
* Repeat the experiment with different pieces of wire
Safety precautions
* Make sure that the circuit is properly connected before turning the power supply on, and do not touch the apparatus, especially the tested, naked wires until the power is switched off
* The changing of the tested wires should only occur when the power is off
* Do not carry out the experiment in wet areas, as water is a very good conductor.
* Do not switch on the power pack when there is no resistant wire and do not turn the power supply up too high because normal laboratory wires may melt
Background knowledge
Using a circuit such as this one on the left, an important general relationship can be seen. The variable resistor is used to control the current in the circuit and the voltmeter measures how the potential difference (voltage) across the resistor varies. Provided that the temperature does not change significantly, the results give a graph looking like this. This means that the current is proportional to the p.d. The relationship is called Ohm's law. Ohm's law only applies if the temperature is constant, and does not apply to all electrical components.
We can write Ohm's law in symbols:
V ??I
Or
V = IR
And R is the resistance of the resistor. It can be rearranged so that R is the subject, hence:
R = V/I
The larger the resistance, the greater the gradient will be. Gradient of the graph gives the value of resistance.
Ohm's law does not always apply. A light bulb in place of the resistor in the circuit gives a different pattern for the current and voltage relationship, as shown in the graph. Here the current and voltage are not proportional. The bulb obviously gets hotter and hotter. Since "resistance" is measured by the gradient of the graph, we have here an example where the resistance is increasing.
A heat-dependent resistor or thermistor gives the opposite pattern. Its resistance decreases as the temperature rises
But obviously we are dealing with "normal" resistors in this investigation, so the gradient of the graphs obtained should be the same throughout - in a linear fashion - and the resistance should remain constant as the voltage/current is altered.
I am investigating how resistance is affected by different variables.
Some variables that will be relevant in this investigation:
¨ Length
¨ Thickness
¨ Temperature
¨ The amount of fixed ions
¨ Current
¨ Resistance
¨ Material
The thing that I am going to change is the length of the wire. The other variables (thickness, temperature, current and material) will have to be kept constant in both experiments to make sure that only the length and resistance is investigated.
Metals conduct electricity because the atoms in them do not hold on to their electrons very well, and so creating free electrons, carrying a negative charge to "jump" along the line of atoms in a wire. Resistance is caused when these electrons flowing towards the positive terminal have to "jump" atoms. Therefore if we double the length of wire the amount of atoms in the wire doubles, so the number of jumps double, so twice the amount of energy is required: There are twice as many jumps if the wire is twice as long. Therefore the pattern of results I expect to find is that the longer the length of wire, the higher the resistance. It will be of direct proportion.
From a previous experiment I already know that the thinner the wire is the less channels of electrons in the wire for current to flow, so the energy is not spread out as much, so the resistance will be higher: We see that if the area of the wire doubles, so does the number of possible routes for the current to flow down, therefore the energy is twice as spread out, so resistance might halve.
i.e. Resistance = 1/Area.
This can be explained using the formula:
R=V/I
Where there is two times the current, and the voltage is the same, therefore the Resistance will halve. I did some research in a book called "Ordinary Level Physics" By A.F. Abbott. It says that "doubling the area will therefore halve the resistance". In other words the resistance of a wire is inversely proportional to its area.
Method
The apparatus I shall need to do the experiment is; a jochy, a voltmeter, an ammeter and a meter bridge.
This is a diagram of how I will set it up:
I will take measurements at intervals of ten centimetres. To make it a fair test I will be careful to keep the current, thickness and temperature all the same, and to make sure I place the jochy exactly on the centimetre mark. Of course I will keep the same meter bridge so the amount of fixed ions and the same material will be kept the same. However, the temperature will rise once the current is passing through it, which will cause the atoms in the wire to vibrate, and so obstruct the flow of electrons, so the resistance will increase creating an error. I will try and make sure the wire does not get to hot for safety precautions.
Results
Experiment 1
Experiment 2
Analysis
The graphs I have drawn have a straight line through the origin, which means the Resistance is directly proportional to the Length. This means that if the Length is 50cm, and the resistance is 1.00 Ohms, then if the length doubles to 100cm then the resistance also doubles to 2.00 ohms.
This is because of the scientific idea, stated in the planning that if you double the number of atoms in it, so doubling the number of atom "jumps", which causes resistance: The results support my predictions very well, they turned out the way I had anticipated, they match my prediction line almost exactly. I had predicted a straight line through the origin, which means "R", is directly proportional to "L".
Evaluation
The experiment was very accurate. There are three (highlighted in blue) errors in the first experiment and one (also highlighted in blue) error in the second experiment. These errors could be down to the measurement of the wire or a temperature rise. Measuring the length of the wire is an inaccuracy because the rulers used on the meter bridges are not exact, and it is difficult to get an accurate reading of length by eye, as the wire might not be completely straight, it may be of different thickness throughout the length. These results would be difficult to improve on as they were very accurate, and there were no anomalous results. But if I were to do the experiment again I would a more accurate method of measurement and take a much wider range of readings and more readings so that a more accurate average can be taken.
I would also investigate other factors, such as temperature, thickness, current, and material to see how these effect resistance. I would also do the experiment under different conditions such as temperature and pressure to see if they make any difference to the resistance.
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