An Investigation into the Resistance of Wire.

An Investigation into the Resistance of Wire

Plan

Our aim is to measure the resistance of a given piece of wire choosing just one variable out of temperature, width and material.

To help us predict the result of the actual investigation we first did a prelim experiment using length as our variable. We set up a circuit as shown below:

We cut the wire by 25cm each time making the length smaller and recorded the amps and voltage measurements. We found out that the shorter the wire became the lower the resistance became as shown in the table below:

This helps us with our prediction and other information and research about electrons and ohms law also help us predict what the results will be like. Ohm showed that doubling the voltage doubles the current. Treble the voltage will give treble the current, and so on. The larger the resistance, the greater the voltage needed to push each ampere of current through it. This led to the definition of one ohm, “A resistor has a resistance of one ohm, if a voltage of one volt will drive a current of one ampere through it.” The resistance of a resistor is the voltage per unit of current so R = V/I. When components are connected in series the total resistance is equal to the sum of the individual components i.e. the wire. It is found that the resistance of a conductor depends on the material from which it is made, its length, its cross-sectional area, and its temperature. For constant temperature the resistance, R in Ohms, of a uniform wire is given by R = ρL/A where L is the length of the wire in meters, and A is its cross-sectional area in square meters. The proportionality factor ρ is known as the specific resistance of the conductor. It is constant for a given temperature and depends only on the nature of the material. Therefore the resistance of the wire is the resistance per unit length for a unit cross-sectional area. In order to find ρ it is necessary only to determine the resistance of a known length of wire of given radius. The resistance is then calculated from the equation.

Using this knowledge we predict that the resistance of the wire will decrease the more length is cut off. If the length of the wire is increased, then the resistance will increase. This is due to the electrons having a longer distance to travel and so more collisions will occur. Due to this, the length increase should be directly proportional to the increase in resistance. Each electron must travel further throughout the wire and are therefore exposed to more electrons, which is equivalent to more resistance. If there is less time it will be because there is less wire ...

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First, the power pack was set up with wires leading out of it. The power pack was set at 6v. The wire was connected to an ammeter and then to a resistor by crocodile clips. The voltmeter was placed parallel to the resistor. Then, the wires were joined up and run back into the power pack. The circuit looked the same as the one in the preliminary experiment.

We used just over 1m of wire to allow room for the crocodile clips. When we got readings from the voltmeter and the ammeter, we turned the power pack off. We did this as quickly as possible and then resized the length of the wire using a 1m ruler and cut the length with a pair of wire cutters to be just over 0.90, again allowing for room for the crocodile clips. Then, the power pack was turned on again and the readings from the voltmeter and the ammeter were taken down. Once again we turned off the power pack and shortened the length by cutting to just over 80cm in length. We continued taking off 10cm every time until the length of the wire was down to 10cm long and as we went along, we noted down the results. We repeated this method twice to give us an average, so we could get more accurate results.

We made this experiment a fair test by keeping the voltage going through the circuit the same every time. Also, the same wire was used every time so that the diameter and the material of the resistor were the same. This would have kept the experiment a fair test, as there was no advantage or disadvantage for each experiment that was taken.

Observation

Analysis

The results from the graph (see back page) and the results table give a clear indication of how the resistance compares to the wire length. There is a very strong positive correlation on the graph. This means that when the length of the wire decreases, the resistance also decreases or as x got smaller y got smaller. The results are also directly proportional, which therefore supports our prediction. If there isn’t any wire there can’t be any resistance, again proving our prediction. The larger the resistance, the greater the gradient will be. The gradient of the graph gives the value of resistance. The gradient of my graph is. The line of best fit passes through zero supporting my hypothesis when saying if there is no wire then there can be no resistance. Assuming the temperature was kept constant and the material is kept the same we can add a constant sign into the equation giving us

The results are so because in any metal wire, there are a number of atoms and free moving electrons. Electricity is the movement of these electrons through the wire. Resistance is caused when the free electrons moving through the wire collide with the atoms making their path through the wire more difficult. This means that if there are more atoms in the way to collide with the free electrons the resistance is increased. In a length of wire there will be a number of atoms, and in a wire twice the length, there will be twice the number of atoms. This will lead to there being double the number of collisions between the electrons and the atoms increasing the resistance by 2. This explains why the results were directly proportional. For example a wire that was 10 cm long may have 500 atoms blocking the electrons. Therefore in a wire 20 cm long, there would be 1000 atoms meaning that the resistance had doubled. The results can be proven so by the information given in the plan also.

Evaluation

I feel our experiment was very successful since there were no anomalies, but there may have been minor errors. We made sure we didn’t over heat the wire and worked very quickly in the turning on and off of power, but our measuring and cutting of the wire may have been slightly inaccurate. Next time we would make the measuring more accurate, even though the results came out the way we predicted.

To learn more about the resistance of wire we could look at the different factors that affect it, such as temperature. If the wire is heated up the atoms in the wire will start to vibrate because of their increase in energy. This causes more collisions between the electrons and the atoms as the atoms are moving into the path of the electrons. This increase in collisions means that there will be an increase in resistance. However, I would not be able to carry out a fair test because it is extremely difficult to produce and control the range of temperatures needed without the correct equipment.

The type of material will affect the amount of free electrons, which are able to flow through the wire. The number of electrons depends on the amount of electrons in the outer energy shell of the atoms, so if there are more or larger atoms then there must be more electrons available. If the material has a high number of atoms there will be high number of electrons causing a lower resistance because of the increase in the number of electrons. Also if the atoms in the material are closely packed then the electrons will have more frequent collisions and the resistance will increase. If I chose to measure the difference in the resistance in different materials I would chose a number of different materials and using the same voltage of 6. I would record the resistance given by each wire of the same length and width.

If the wires width is increased the resistance will decrease. This is because of the increase in the space for the electrons to travel through. Due to this increased space between the atoms there should be less collisions. To measure the wire width I would use different widths of the same length and same material of wire e.g. thin, medium and thick copper wire. To record the difference in widths I would use the same voltage and measure the resistance for each thickness.

For all of these experiments I would use the same circuit shown in the investigation for the resistance of wire, determined by the length. I would keep a constant voltage of two. I would have to be very careful again in not over heating the wire. I would be able to therefore work out the resistance and determine which materials, length and width of wire would be most useful in certain circumstances.