## Resistivity: cooled to extremely low temperatures, some conductors

Resistivity: It is a characteristic property of each material, and is useful in comparing various materials on the basis of their ability to conduct electric currents. High resistivity designates poor conductors. Resistivity () is proportional to the resistance (R) of a wire, multiplied by its cross-sectional area (A), and divided by its length (l). = RA / l. Since lengths are measured in centimetres in this experiment, resistivity would be expressed in units of ohm-centimetre. Conductivity is the reciprocal of resistivity, and it, too, characterizes materials on the basis of how well electric current flows in them.

Good electrical conductors have high conductivities and low resistivities. Good insulators have high resistivities and low conductivities. (Britannica CD 2000 Deluxe Edition) Resistance: It is the property of an electric circuit that transforms electric energy into heat energy in opposing electric current. Resistance involves collisions of the current particles with the fixed particles that make up the structure of the conductor. The electromotive force or voltage (V) across a circuit, divided by the current (I) through that circuit, defines the amount of electrical resistance (R).

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R = V / I. Ohm is the common unit of electrical resistance, equivalent to one volt per ampere. The resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area. Resistance also depends on the material of the conductor, as better conductors have less resistance seeing as electricity can flow through them more easily. The resistance of a circuit element generally increases when temperature also increases. When cooled to extremely low temperatures, some conductors have zero resistance.

(Britannica CD 2000 Deluxe Edition) What affects the resistance of a wire? There are four main factors that govern the resistance of a wire: 1. Length – this is what we are investigating, to see how the length of a wire affects its resistance. 2. Cross-sectional area – if the cross-sectional area is larger then the resistance will be higher because it means there is more wire for the current to travel through. Therefore there are more atoms there, to obstruct the flowing electrons, which poses a greater resistance to the current. 3.

Material – since a better conductor means that it allows current to flow through it more easily, it is obvious that they have less resistance. This means that as conductivity increases, resistance decreases. 4. Temperature – as the temperature of the room or specifically the wire itself, increases, its atoms will vibrate with greater frequency and therefore obstruct the flowing electrons more. This increases the resistance, and shows that as temperature rises, so does the resistance. Prediction The coursework we are carrying out is investigating how the length of a wire affects the resistance.

I predict that the longer the wire, the higher the resistance. Since current is a flow of electrons, these electrons will collide with the atoms of the wire, when travelling through the circuit. If the wire is longer then there are obviously more atoms in the wire. So there are subsequently more collisions between the atoms of the wire and flowing electrons, when trying to complete the circuit from the negative to positive terminal. Therefore there are more atoms getting in the way of the current, which means there is a higher resistance to the flow of current.

So as the wire gets shorter, the numbers of atoms available to resist the flowing electons decrease. Therefore, there is then a lower resistance. This explains the trend that as the length of the wire increases so does the resistance. Also, looking back at the formula for resistivity we can see that = RA / l. So in this experiment, is constant throughout as we are using wire of the same material. Also, the current (A) is kept the same during the experiment, which is at 0. 20 Amps. So given that and A are constant, R must be proportional to l.

Therefore since the resistance is proportional to the length of the wire, the graph derived from the results will be a straight line. This means it will be a linear graph. Theoretically the line should also go through the origin, because when there is no wire in the circuit, there is no resistance against the flowing electrons. resistance length I will obtain a graph similar to this by drawing the line of best fit through the points I plot, with an even distribution of points about the line.

A curved graph requires more findings than a straight lined one, to ensure that it is plotted accurately and displays a prominent trend. Nevertheless I have decided to obtain readings at every 5cm, because more points will enhance my graph and any anomalies can be identified easily, as these will be distant from the line of best fit. Safety In preparation of the coursework practical, I have vigilantly considered the safety implications involved. In general, I will first concentrate on setting up the apparatus carefully so that I am not vulnerable to any danger caused by the electrical equipment.

We have been allocated the large power packs that have a facility incorporating a light that shows when the circuit is overheating. So if there is any danger we can immediately see that the circuit is overheating. I have decided that the current will be kept at a relatively low value, and subsequently it will keep the voltage low. This is to prevent the wire from heating up, as a larger current would begin to generate heat. But keeping the current low throughout the experiment, raises no further issue of the wire overheating, and will minimise any possible danger with the wire.

I am sure that all these safety precautions will minimise exposure to any potential hazards when carrying out the experiment. Preliminary Results Before going ahead with the coursework practical, we had to decide which material would be best to use. In order to make that decision accurately, based on a scientific foundation, we carried out a preliminary experiment, which compared the resistance of two different wires.

We did the experiment using a copper wire and a constantan wire, taking the readings at every 10cm. The results were recorded: CURRENT = 0.20 AMPS Length (cm) Copper Wire Constantan Wire PD (V) Resistance () PD (V) Resistance () From this experiment it can be clearly seen that copper is a better conductor than constantan, as the resistance changes very little as the length changes. However, length has a much greater effect on the resistance of constantan as the readings vary much more.

So, to obtain a set of results that prominently show the affect of length on resistance, it is best to use constantan wire. This is why we have decided to use wire from this material for our coursework. Prior to carrying out the real practical, we did a practice one, which was intended to show us the kind of results that are expected. It would also indicate a good number of readings to take for when it comes to do the actual coursework practical. The apparatus were set up and the results were recorded:

These results evidently show us that as the length decreases, so does the resistance. This, therefore, supports my initial prediction. We can also see that the readings for both sets of results were exactly the same except for when the wire was 100cm. This was merely a slight random error. Apart from that we can see that all the readings agreed, and a definite trend can be noticed.

Fair Test In order to certify that the resistance is depending totally upon the length of the wire, which is what we are investigating, we have to control all the other variables that would otherwise affect the resistance. This is so that this experiment remains a fair test. Cross-sectional area – this will remain the same throughout the experiment because we will initially cut just one piece of wire 1 metre long, and then employ the various lengths using crocodile clips at the different points on the metre stick. So since the wire will be the same for the entire investigation, the cross-sectional area of that wire will be the same.

Material – the wire being used for the experiment will be of constantan material, and this will not change at any time. This is important because different materials would give different resistances, depending on their conductivity. Temperature – we intend to keep this constant throughout, as the entire experiment will be carried out under room temperature. We are doing this because a change in temperature in the surrounding would affect the resistance, as the wire would also change temperature. So controlling the temperature keeps it a fair test, as the temperature will not alter performance of the resistance.

Current – since it is the potential difference across the wire that is being measured, we have to make sure the current is kept the same for every reading. Again this is because if the current is not controlled, an increase would cause the wire to heat up and this would have an affect on the resistance. So I have chosen 0. 2 Amps as the standard current reading across the circuit. Accuracy All round accuracy is very important when carrying out an experiment, so that the results obtained are reliable and then truthfully display the trend that should be seen.