Resistance of a Wire Investigation

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FIRST

Before starting my coursework I have decided to choose a factor that will affect the resistance of a wire. I shall do this by going through all of the factors that affect the resistance of a wire and how I would measuring each factor to find out which would be the most effective and easiest factor to measure. Below is a list of factors and reasons why they affect the resistance of a wire. From this list of factors I  shall only pick one factor to investigate. To explain the how the factors would affect the resistance of a wire I have drawn a diagram to show how resistance occurs.

GAP

To chose which factor I am going to investigate I am going to consider how I would measure each factor and which factor would be the best and easiest to record. To measure the wire width I would use different widths of the same length and same material of wire. To record the difference in widths I would use the same voltage and measure the resistance for each thickness. Although it would be easy to obtain and record the data the graphs that I would be able to draw up would not be interesting. For the temperature of the wire 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. 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 I would record the resistance given by each wire of the same length and width. Although once again it would be simple to record these results the graphs that could be drawn would not show any connection between the material and the resistance because of the limited number of materials I could test with the equipment available .The final factor is the length of the wire. To measure and record the findings for this factor would be simple and the results collected could show a connection between the length of the wire and the resistance given by the wire. This is why I have chosen to investigate this factor.

GAP

Preliminary Method

In this preliminary experiment I will select a wire that will be used in my main experiment when Investigating the connecting between the length of the wire and the resistance of the wire. To ensure a fair test whilst carrying out my preliminary experiments I am going to be very careful When selecting my independent variables which are the width of the wire and the wire material. I am Going to use a constant voltage of 2 volts and a constant length of 50 cm.

Apparatus:

  • Meter ruler ¡V To measure the wire being tested to ensure a fair test.
  • Selection of wires ¡V Different materials and widths but the same length. Crocodile clips ¡V To connect the wire being investigated to the rest of the circuit.
  • Voltmeter & Ammeter ¡V To measure the resistance.
  • Wires ¡V To connect the above items and to complete the circuit.
  • To measure the resistance of the wire I am going to use the equation

RESISTANCE=VOLTS

CURRENT I will obtain the voltage and current readings from the voltmeter and ammeter. Below is a circuit diagram for my preliminary experiment.
                                

POWER SUPPLY

VOLTS
AMMETER

VOLTMETER
CROCODILE CLIPS

WIRE

METER RULER

To ensure a fair test I shall keep the power supply at 2 volts and I shall keep the length of the wire at 50 Cm.

Preliminary Results

Below is a table of results which I have collected from my preliminary experiment.

From these results I have chosen to use thin Constantine for the wire I am going to use in my main Experiment. I have chosen this wire as it has the highest resistance and so it will be easier to notice any Difference in resistance in my main experiment


Main Method

Before I start my main experiment I have chosen to do a risk assessment which is shown below.

Risk Assessment:

I will handle the power supply carefully. I am going to only use a voltage of 2 volts. I will be careful when handling live wires.

Apparatus:

Power Supply

Ammeter
Voltmeter
Thin Constantine wire

Meter Ruler

Crocodile Clips

Connecting Wires

I have chosen to use thin Constantine wire because from my preliminary results I found that this wire had the highest resistance, because it has the highest resistance it will be easier to measure any change in resistance. To collect the data for my graph I have chosen to take a range of 5 lengths. I have chosen a range of 5. As to plot an accurate graph I will need at least 5 points to mark on the graph . I have also chosen to. Take 3 repeats at each length and then take an average. I have chosen this so that if I have any Anomalous results they will not show when I plot the averages on the graph. The lengths that I have

Chosen are as follows : 20cm , 40cm , 60cm , 80cm, and 100cm. I have chosen these lengths because They are easily measured by the meter ruler and give a good range.

        

Below is a circuit diagram of the circuit I am going to use in my main experiment:

                                 

POWER SUPPLY

2 VOLTS

AMMETER

VOLTMETER

CROCODILE CLIPS

WIRE

METER RULER

In my main experiment instead of using an ohmmeter I have chosen to use an ammeter and voltmeter ,

I have done this so that instead of relying on the ohmmeter to give the resistance I will calculate the

Resistance of the wire , I shall calculate the resistance of the wire using the equation below.

RESISTANCE         =       VOLTS

AMPS

I have chosen to use a meter ruler because the lengths that I will be measuring are too big for a smaller Ruler and the meter ruler can be accurate to +1mm.

From these results I have drawn a graph of the length of the wire and the resistance of the wire.

Analysis

From the graph on the previous page I can see that the resistance of the wire is proportional to the length of the wire. I know this because the Line of Best Fit is a straight line showing that if the length of the wire is increased then the resistance of the wire will also increase.

Conclusion
In my prediction I said that: if the length increases than the resistance will also increase in proportion to the length. From my graph I have shown that my prediction was correct, as the Line of Best Fit is a straight line proving that the resistance of the wire is proportional to the length of the wire. The length of the wire affects the resistance of the wire because the number of atoms in the wire increases or decreases as the length of the wire increases or decreases in proportion. The resistance of a wire depends on the number of collisions the electrons have with the atoms of the material , so if there is a larger number of atoms there will be a larger number of collisions which will increase the resistance of the wire. If a length of a wire contains a certain number of atoms when that length is increased the number of atoms will also increase. This is shown in my diagrams below:

Electron
Atom

In this diagram the wire is half the length of the wire below and so has half the number of atoms, this means that the electrons will collide with the atoms half the amount of times. In addition, if the length of the wire was trebled or quadrupled then the resistance would also treble or quadruple.

Evaluation
From my results table and graph I can see that my results that I collected are very reliable. I know this because my results table does not show any individual anomalous results this means that I did not have to leave any results out of my averages because they were anomalous. In addition, on the graph I can see that none of the averages plotted are anomalous because all the averages lie along the same straight line. During my experiment I have noticed several modifications I could make to improve on the Investigation if I was to repeat it. The first of these modifications would be the circuit that I would use. To be more accurate with my results I would use the circuit layout below:


POWER SUPPLY

2 VOLTS

AMMETER

VOLTMETER

WIRE

METRE RULER

Instead of connecting the voltmeter to the main circuit I would connect it to the wire which is being tested. I would do this so that the voltmeter is measuring the voltage of just the wire being tested and not the wires of the main circuit as well. To also improve on my results I would use a digital voltmeter instead of an analogue meter. I would do this because a digital voltmeter is a lot more accurate than an analogue because if the needle in the analogue voltmeter is bent then the readings given off will be false whereas a digital voltmeter does not rely on a needle or any other manual movements. The next modification I would make would be to use pointers instead of crocodile clips ; I would do this because pointers would be more accurate. The pointers would be more accurate because the tips have a much smaller area than the crocodile clips giving a more accurate measurement of the length of wire. As well as making these modifications I would also improve my Investigation by testing the same wire but different widths of that wire. I would do this to expand on my Investigation.

SECOND

The resistance of a wire depends on certain factors. Investigate the effect of two of these factors - Planning

Some variables that will be relevant to this investigation are:

  • Length
  • Thickness
  • Temperature
  • Voltage
  • Resistance
  • Material

 

Of these the variables will be input and output voltages in experiment one, and length and resistance in experiment two. The other variables (temperature, material and voltage) will have to be kept constant in both experiments to make sure that only length, thickness, and resistance are investigated. In experiment 1 the same bit of wire and the same thickness need to be kept constant. In experiment 2, the length will need to be kept constant to make sure only the variables indicated are investigated to ensure a fair test.

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 'jumps' atoms. So if we double the length of a wire, the number 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.

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 2X the current, and the voltage is the same, therefore R will halve. I did some research and 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, or R ? 1/A , but we are measuring diameter, so if the area is: ?r2 = ?(d?2) 2 A= ?d2 ? 4 Where A is area and d is diameter.

Method

Experiment One - First a length of wire over a metre long is sellotaped to a metre rule. The positive crocodile clip is attached at 0cm. In addition, the negative is moved up and down the wire, stopping at 20, 40, 60, 80, and 100cm. Each time reading the ammeter and voltmeter to work out resistance R = V/I. This is using 30 SWG wire. Other variables, voltage, thickness, and temperature will be kept constant, although the temperature will rise once 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.

In both experiments constantan wire is used because it does not heat up as much as copper, so the resistance is not effected as much.

Experiment Two - The circuit is set up is the same, as is the method apart from the length is constant at 50cm, and the thickness is changed between 28, 30, 32, 34, 36, 38 and 40 SWG. For both experiments the voltage will be kept the same at 2V dc from a power pack. Both experiments will be done twice with different ammeters in case of any damaged or old equipment to gain more accurate results.

Analysis

GAP

Evaluation

Evaluation Experiment one: This experiment was quite accurate, as when it is compared to the manufactures line which is on the same graph, we can see that this line is at most only 0.4? Different form the manufactures line. This is a percentage difference of approximately 8%, using the formula: Difference ? Original X 100 This shows that the results were good, as 8% is a very small margin of error. The error bars on the graph show that the most inaccurate result was the 60cm result. This could be down to an error in the measurement of the wire or a temperature rise. The two results for 100cm are the same, and it is near to the manufacture's line, so this is the most accurate point.

The other three readings have almost the same inaccuracy, an average of 10%, which again, is fairly accurate. The inaccuracy could have been because of the wire coming from a different manufacturer to the predicted results, as there is some discrepancy between the amount of copper and nickel in different brand's wire. The ammeters and voltmeters could have been damaged and reading falsely on both the meters used.

Measuring the lengths of the wire is also a inaccuracy as the rulers used 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 would have contributed as well to the error. These results would be difficult to improve on as they are reasonably accurate, and there were no anomalous results. However, if I were to do this experiment again, I would use newer, more accurate ammeters and voltmeters, 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, voltage, and current, and see how these effect the resistance. I would also do the experiments under different conditions such as temperature and pressure to see if it makes any difference to resistance. As these results had a range of only 5 readings, from 0-100cm, and were only repeated twice, and that the results are not 100%, accurate due to the errors discussed earlier, then I would say that these results are not strong enough to base a firm conclusion on because there are so many sources of error, which are explained earlier.

Experiment two - These results were not as accurate as experiment one. I had predicted that the resistance should halve as area doubles, which it does, however not to the predicted curve. When the resistance is 24 ohms, the % inaccuracy is 6%, and when the resistance is 6 ohms, the inaccuracy is 8%. These inaccuracies are fairly large. The error bars, however, are too small to be drawn accurately on the graph. They are at most 3% inaccurate, using the same formula as before. This suggests that the inaccuracies were not experimental, but permanent errors due to problems with the measuring equipment.

These results were this inaccurate as the tool used for measuring the diameter of the wire were very inaccurate due to a zero error on the screw reading, i.e. the mark given for zero mm was not the real mark, hence throwing all the results off by the same amount. The ammeters and voltmeters could have been damaged and reading falsely on both the meters used. Measuring the lengths of the wire is also a inaccuracy as the rulers used 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 would have contributed as well to the error.

There was one slightly anomalous result, at 0.25mm2. This could have been due to a unique error in the measuring and or reading of the meters, or a temperature change. These results could be done better. If I were to do this experiment again, I would use newer, more accurate ammeters and voltmeters, 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, voltage, and current, and see how these effect the resistance. I would also do the experiments under different conditions such as temperature and pressure to see if it makes any difference to resistance.

As these results had a range of only 7 readings, from 0.1 mom, and were only repeated twice, and that the results are not 100% accurate, due to the errors discussed earlier. I would say that these results are not strong enough to base a firm conclusion on because there are so many sources of error, which have been explained earlier.

THIRD

A. Planning

Plan of the method to be used: -

The resistivity of Nichrome can be determined using the equation ??=?RA/L
Where:
R:- Is the resistance of the wire in ?”Ohms“ and can be determined using the equation R=V/I where ”V“ is voltage in volts and ”I“ is current in
amperes.

L:- Is the length of the Nichrome wire used in metres.

A:- Is the cross-sectional area of the wire in metres square and can be determined using the equation A= ??D2 where ”d“ is the diameter of the wire.

Join now!

If I plot a graph of length on the x-axis against resistance on the y-axis. From the relation R = ? L /A which corresponds to the st. line equation ?
Y=max the graph should be a st. line passing through the origin where ”m“ is the gradient of the st. line graph and corresponds to ?/A. Since the cross-sectional area of the wire can be found by knowing it’s diameter. Therefore the resistivity of Nichrome can be calculated. ?

Diagram of the circuit used in this experiment

List of the apparatus used: -

  1. Power pack supply ...

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