An crystal lattice, and so the electrons in

An electrical conductor is a substance through which electrical current flows with little resistance. Electricity is passed through a conductor, in this case a length of wire, by means of free electrons. In metals the atoms are arranged in a regular crystal lattice, and so the electrons in the outer shells of the atoms are free to move through the metal, even if it is a solid. It is this ‘sea’ of mobile electrons that allow the conduction of electricity. The number of free electrons depends on the material due to the varying amounts of electrons in the outer shell.

The more free electrons the better the conductor, i. e. it has less resistance. (An example of a possible metal crystal lattice with a ‘sea’ of mobile electrons) For example, by using the periodic table we can work out that Copper will be a better conductor of electricity than Iron. Copper has more electrons in the outer shell of its atoms, its electronic structure being 2,8,8,11 meaning that there are 11 electrons in the outer shell of each atom in the metal. Iron’s electronic structure is 2,8,8,8 meaning that there are only 8 free electrons compared to copper’s 11.

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When the free electrons in a wire are given energy, they have the ability to move and collide with neighbouring free electrons. This happens across the length of the wire, and so electricity is conducted. In each collision between the free electrons against fixed particles of the metal, impurities in that material and other freely mobile electrons, some of the electrical energy is converted into heat energy. The property that converts electrical energy into heat, in opposing electrical current, is resistance.

The electrical resistance of a wire can be defined as the ratio of the voltage applied to the electrical current at a constant temperature that flows through the wire. Ohm’s Law states that: V = IR Where: V is the voltage I is the current R is the resistance of the conductor This formula can be rearranged so that Resistance becomes the subject: R=V/I This means that the resistance of a wire conductor will remain constant provided that the temperature also remains constant. It would also be correct to assume that as the temperature of the wire increases the resistance will also increase.

At higher temperatures the mobile electrons will have more energy, and so will be moving at an increased speed therefore increasing the possibility of collisions. More collisions means more electrical energy being converted into heat energy, thus the resistance will increase. Resistance, measured in Ohms (R) is also equal to the resistivity of the wire (? ) multiplied by the length (l), and then divided by the cross-sectional area of the wire (A). R = ? l /A “The resistivity of a material is the resistance which a sample of it would have if its length was 1 metre and its area of a cross-section was 1 metrei??.

” -Quote from “Physics in outline” by Richard Candlin. Variables: There are four variables that I can investigate: 1. Length of wire 2. Cross-sectional area of wire 3. Temperature of wire at beginning of experiment 4. Material of the wire Changing all of these will result in a change in the following: a. The temperature of the wire b. Voltage across the wire c. Current in circuit d. The resistance of the wire I will need to take readings from both the voltage across the wire and the current in the circuit to work out the resistance of the wire.

The two variables I have chosen to investigate are the length of the wire and the cross-sectional area of the wire, as I feel that these will provide me with a clear and accurate set of results from which I can obtain a suitable analysis. Predictions: In the experiment with varying length, I predict that as the length of the wire increases, the resistance will also increase. As the length increases, the number of particles also increases, so that there are more mobile electrons and so a greater number of collisions will occur, meaning that more heat will be lost and that the resistance will rise.

The formula for the resistance (R) of the wire is R = ? l /A. As the material, the starting temperature and the cross-sectional area of the wire will be kept constant throughout this experiment, ? /A will be constant and hence R will be directly proportional to l. This means that if the length doubles the resistance of the wire will also double. Furthermore, increasing the cross-sectional area of the wire will result in a decrease in the resistance. As the width doubles, the chance of possible collisions is halved, as there will be two times the amount of space for the particles to travel in.

For example, take a road with a certain number of cars on it. If the road has only one lane, it will easily become congested, and so the cars will move slowly. Add an extra lane, and the cars will be able to spread out between the two lanes, therefore the cars can travel quicker. The same happens with metal conductors. The more electrons in the wire, the more crowded it becomes. This indicates that there will be more collisions so the resistance will increase. If the same number of electrons is given more space (doubling the cross-sectional area) they are able to move without too many collisions, so the resistance goes down.

Say, for instance, that there are ten cars in one lane. Add another lane and the number of cars in each goes down to five, so the cars will be able to move twice as quickly due to half the amount of congestion. When the cross-sectional area of a wire is doubled, the electrons have twice the amount of space to travel in, and so the resistance is halved. This implies that resistance is inversely proportional to the cross-sectional area. Experiment One: Investigation into how varying the length of a wire will affect its resistance Fair Test:

In order to ensure that the experiment is as fair as possible, only one factor will be varied: the length of the wire. The other factors will be kept constant as shown below: The cross-sectional area will be kept constant (at 38 SWG (standard wire gauge) or 0. 0181mmi?? ), as this factor will be explored in Experiment Two. The material of the wire will also need to be kept constant throughout, and I have chosen to use Constantan wire, as this was the material that provided me with a larger quantity of widths to test in the experiment investigating the cross-sectional area due to lack of resources.

The temperature of the wire at the start must be the same to make it a fair test, and so each test should be done in the same environment at room temperature, as if there was a fluctuation in the starting temperature the electrons would have more energy and so this would have an effect on the resistance. The current passing through the circuit must also be kept the same, as a change in the current may cause a sudden rise or drop in temperature that would end in a confusing set of results. Method: Safety: Precautions must be taken so that no water gets near any of the electrical appliances.