# Resistance and Wires

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Introduction

Tom Bell

## 21st Century Additional Science

Written Science Experiment - Resistance and Wires

How is the resistance of nickel-chrome wire affected by its length and diameter?

How is the resistance of nickel-chrome wire affected by its length and diameter?

## Introduction

This investigation determines how changing the length of Nickel-Chrome (nichrome) wires, when passing an electrical current through them, affects their resistance. It also determines how resistance is affected by a change in the diameter of the wire used. Resistance is "the property of failing to conduct electrical or thermal energy".

Resistance is a force which opposes the flow of an electric current around a circuit so that more energy is required to push the charged particles around the circuit. The circuit itself can resist the flow of particles if the wires are either very thin or very long, e.g. the filament across an electric light bulb.

Resistance is measured in ohms. A resistor has the resistance of one ohm if a voltage of one volt is required to push a current of one amp through it.

George Ohm discovered that the emf (electromagnetic force) of a circuit is directly proportional to the current flowing through the circuit. This means that if you triple one, you triple the other. He also discovered that a circuit sometimes resisted the flow of electricity. He called this, resistance. He then came up with a rule for working out the resistance of a circuit:

V÷I = R, V= I×R and R=V÷I

V –Voltage (volts)

I – current (amps)

R – resistance (ohms)

In conducting this experiment I examined the resistance of Nickel-chrome wire. I am investigating 2 variables that affect the resistance of the wire in this investigation. They are the diameter of the wire and the length of the wire.

Middle

9.4

70

6.42

10.9

80

6.45

12.4

90

6.47

13.9

100

6.45

15.5

Mean

6.31

This graph tells us what ‘n’ would be to enable the formula y=nx, to work for each result. This is useful to us in that it enables us to see in detail, the accuracy of our results. This is because the results appear to be in exact proportion between their length and resistance. This calculation tells us that that is in fact not completely true for this experiment. As shown in the table, the results do tend to increase. This should not be the case if the two variables are in direct proportion to each other. This increase in the value of ‘n’, can however be explained. My explanation for this is similar to the reason for the range bars increasing in size of scatter as length is increased. I assume that it is due to the fact that I conducted the tests chronologically from the shorter length of wires, to the longer lengths. Due to the fact that I used the same wire each time, the temperature could have increased marginally despite the fact that I momentarily turned the power off between each recording. This amount of time when the power pack was off, may not have been long enough. The heat could be building up in the test wire, causing an increase in resistance and shown on the diagrams on page 3b in the introduction section. If drawn on a graph, and if the results had been more accurate by me waiting for the wire to cool down for longer, the results for ‘n’, in the equation y=nx, would have shown an exactly straight line because the relationship between length and resistance is directly and exactly proportional as calculated below.

I calculated the mean value of ‘n’ by using the values of ‘n’ for the various lengths. I calculated the value of the mean by adding up all the 10 values for ‘n’, and dividing that sum by the amount of results which was 10. This gave me 6.31. This mean is not however accurate due to the results not being completely accurate as mentioned above. A much more accurate way of calculating a value of ‘n’ that should would work in the equation y=nx would be to use the value of ‘n’ for the result taken first in chronological order because here there is no unfairness in the result caused by heat because the wire could not have been heated. This value is 5.88. Obviously this value is not 100% accurate, partly due the fact that the calculations of ‘n’ were only taken to 2d.p, but it is the most accurate reading of ‘n’ that I can conclude with. This value of ‘n’ can be used for any length due to the fact that the relationship between length (y) and resistance (x) is always directly proportional.

Therefore this value of ‘n’ can be used to calculate the resistance of any length of wire. For example if ‘n’ is always 5.88, then y=5.88×x. So 5.88×x will always give the length of wire that has that specific resistance. And y/5.88 will always give the amount of resistance that that length of wire has. This value of ‘n’ only is relevant to wires with the same diameter as that of which ‘n’ was calculated (34mm). For example, if I were to find the value of the resistance of a wire with a length of 250cm I would use the calculation 250/5.88. This would give me an answer of 42.5ohms. Or if I were to calculate the length of wire with a diameter of 34mm when the resistance was 5ohms, I would use the calculation 5.88×5. This would give me an answer of 29.4cm. This can be proved to be reasonably accurate when plotted on the graph. I have done this as shown on the graph. The reading given by the graph is 31cm, which considering the possibly inaccuracy of the value of ‘n’, is evident to support the reliability of the equation and the accuracy of the recorded results.

It is possible to calculate the amount of resistance 10cm of wire has by reading the graph to measure how much resistance increases every 10cm along the wire. To calculate the amount of resistance that 10cm of wire has, I simply read across the graph from the mean point of 10cm to the ‘y’ axis and found the resistance to be 1.8ohms. Then I did the same for the recording of 20cm, and found a measurement for 3.3ohms. To calculate the resistance change I deducted 1.8 from 3.3 which revealed a change in resistance of 1.5ohms. This is therefore shown to be the amount of resistance that 10cm of the wire has because the different in resistance between 10cm and 20cm (10cm difference in length) is 1.5ohms.

I calculated the resistance of 15cm of the wire, by reading the resistance in ohms when the length of wire is at 25cm. The graph shows how I read the recording. The graph showed that at 25cm, there was a resistance of 4.0ohms. By deducting the previous recording for 10cm of 1.8 from 4.0, 2.2ohms remains. ). 2.2ohms is therefore the amount of resistance that 15cm of wire has because the difference between 10cm and 25cm is 15cm. This method can be used to find the amount of resistance for any length of wire, providing it is nickel-chrome wire with a diameter of 0.34mm. This method will only be accurate with a wire with these properties because the wire used to record this data did have these properties. Any change in these properties would resistance to be different and therefore each length of wire would have a different resistance.

As briefly mentioned before, these results, on the whole are very accurate due to the fact that careful consideration was taken in planning to produce results with very small parameters, shown by the narrow range bars. Accuracy is also shown as each mean results is almost an exact fit into the ‘line of best fit’ of the graph.

Despite this accuracy, the results from higher lengths of wire are shown to have a wider parameter in the range bars. This indicates slight inaccuracy in the recordings. A possible reason for this could be that despite me turning off the equipment in between each recording, the wire could have heated up, and retained some of the heat from the previous recording. This theory fits the pattern because the range bars become wider as the length of wire is increased. Due to the fact that the shorter amount of wire was measured first, an increase in heat over time could have caused a gradual increase in resistance, which produced the increase in the size of the range bars. This is not a certain reason, however it is probable. Assuming that this idea is correct, the lower parameters would have been recorded first at a lower temperature, and the higher parameters of the range bars would have been recorded later on when the wire was hotter.

If I were to conduct this experiment a second time, I would increase the amount of time that the power was turned off, to ensure a sufficient amount of time to allow the wire to fully cool down. This would mean that each range bar would be of a more similar size and they would not increase as length was increased.

As shown on the graph, the line of best fit if kept straight would not go through the point (0, 0) on the graph. It is assumed that the graph may go through this point; however this is not indicated by the graph. This could either be due to a recording error or a lack of detail in the recordings. The idea of a recording error can be tested by re-conducting the experiment. A much more likely explanation is that the measurements were not detailed enough to show a slight curve in the beginning of the ‘line of best fit’. Assuming that the results are in the correct positions, the remaining explanation would be that if the gaps between the independent variables were smaller, e.g. every 1cm, results could have revealed a slight curve in the trend of results. This would answer this question.

It is possible that as shown with the current data, the results, despite a lack of detail, do not appear to curve towards (0, 0), but instead continue to around (0, 0.004).This could be possible because at the instant that the length reaches the ‘Y’ axis, the resistance could drop to 0 ohms. This is surely the case because no wire, has no resistance, however the minutest amount of wire could begin at a certain amount of resistance, without following a proportional ‘line of best fit’ from (0, 0), at a rate of increase of 2.6ohms per 10cm. The presence of a small amount of wire could result in a disproportional amount of initial resistance.

## Conclusion

In conclusion of this experiment, the results show that as the length of the nichrome wire is increased, the resistance of it increases. The amount of resistance caused by a certain length of wire being added on can be calculated by measuring the difference in resistance between two values of length with a difference of the amount of wire that is being measured for resistance. For example to find the resistance of 10cm of the 34mm nichrome wire the calculation would subtract the resistance of 20cm of wire with the resistance of 10cm to reveal the resistance of 10cm of wire. As shown above, this difference in resistance is 1.5ohms. Therefore it is clear that for every 10cm of wire added on with the same diameter, 1.5ohms of resistance will be added. These results support my initial prediction and so my prediction about the relationship between resistance and length was indeed correct.

There are, however some limitations to the conclusion due to the scatter in the range bars. The scatter or size of range bars increases quite a large amount as the length of wire is increased. This increase in the amount of scatter is not coincidence and there is no certain explanation for this. As explained above the simplest explanation is that between each recording, a fragment of heat had been built up in the wire, despite the precaution of turning off the power pack between each reading. No definite conclusion can be drawn from this due to the fact that the reason for this scatter is unsure. This limits the amount or detail of the conclusions that can be made, and therefore decreases the complexity of the investigation, however if I were to re-conduct this experiment, it would be possible to leave more time for the wire to cool down. If then, there was not an increase in the range of scatter, it would give sufficient evidence to support this previously described explanation and therefore a more confident conclusion could have been made and supported with accurate data.

To extend this part of the investigation further I could have drawn a graph that would have shown the results of the calculations of the nth term. This would have enabled me to analyze further, the reasons and causes for the slight increase in the value ‘n’ as length is increased. It would also have more graphically displayed the trend. I would have also been able to include the mean value of ‘n’ on the graph. I could have annotated the graph to explain in more detail how this equation works.

## Experiment 2

In the second part of the investigation I am going to use several lengths of nickel-chrome wire with different diameters to find out any change in resistance between the different diameters of wire.

In this second experiment I chose to use only 2v DC of voltage because the test wire was that much shorter than in the first experiment.

To ensure that the results are as accurate as they can be, each reading will be taken 3 separate times and a mean will be calculated from them. The diameter of each wire will be calculated 3 times and a mean taken to ensure an accurate reading. This will improve the accuracy and reliability of the recorded data.

## Preliminary Test

I have conducted a preliminary test, to ensure that the second part of my experiment will work and have clear results which show a definite trend. The width of the nickel-chrome wire will make a difference in the resistance of the wire because in a thin wire, there are a lot of electrons which have to travel in a proportionally small channel. This causes a lot of collision with other electrons. This collision causes friction, which produces heat. This heat energy which is produced causes resistance because electrical energy from the current is being transferred into heat energy. These facts are backed up with the data results from my preliminary test, shown below. Resistance was calculated using the formula V÷I = R.

Diameter of wire (mm) | Voltage (Volts V) | Current (Amps) | Resistance (Ohms) |

Thick | 0.21 | 1.55 | 1.34 |

Thin | 0.64 | 0.3 | 2.13 |

As I was conducting this preliminary test I made absolute certain, that my results were accurate by ensuring that each length of wire was exactly the same length, and I reduced the voltage input from 12v DC down to 2v DC in order that the wires, particularly the thinner wire, did not heat up. This would have altered the resistance of the wire because the more heat energy that the wire has, the faster atoms move in the wire, and so the electrons in the current have more collisions. This causes friction, which produces heat (see figure 1 on page 3b, in the introduction section). Heat is produced using energy from the electrical current. This causes the overall resistance to increase because there is energy being taken from the electrical current. These results show that a thicker wire has a much smaller resistance than a thinner wire. This preliminary data supports my initial prediction which stated that thinner wire will have more resistance than thicker wire. I calculated the resistance of each wire using the formula, R=V÷I. R is resistance in Ohms, V is voltage or potential difference in Volts and 'I' is current, measured in amperes/amps. The higher that the number of Ohms is, the higher the resistance of the wire is. In conducting the preliminary test, I used the following instruments: power supply (set to 2V), 5 copper wires, 2 crocodile clips, an ammeter, a voltmeter, and the nickel-chrome wires both thick and thin.

## Method

- Collect apparatus: a voltmeter, an ammeter, 5x wires, 2 crocodile clips, 7 nichrome wires with different diameters and a power pack.
- Set apparatus up as shown:

DRAW DIAGRAM OF CIRCUIT 2

- Set the power pack on as low a voltage as possible, 2v. (So that the voltage doesn’t cause the wire to heat up.)
- Place the nichrome between the two crocodile clips to complete the circuit.
- Turn on the power pack and record the current from the ammeter and the voltage from the voltmeter.
- Turn off the power pack.
- Repeat this process for all the diameters of wires.
- Work out the resistance for all the results using Ohm's law. V = I*R
- Record the results on a graph.

My results are shown to be accurate because I conducted the test 3 times and calculated the mean to 2 decimal places. The results above are the mean values. I also conducted the short experiment using only 2v DC to ensure that neither of the wires began to heat up.

To increase the accuracy of the measurements taken of the diameter of each wire, I conducted an experiment whereby each wire was measured using a micrometer 3 times. A micrometer works by clamping the wire between the spindle face and anvil face. They are adjusted by rotating the ratchet. This moves the spindle and thimble down the sleeve. The sleeve has numbers on it which displays the wires diameter when tightened. The table of results from the measurement of the wires is shown below:

Diameter (mm) (2d.p) | |||

Test 1 | Test 2 | Test 3 | Mean |

0.25 | 0.26 | 0.22 | 0.24 |

0.35 | 0.32 | 0.34 | 0.34 |

0.54 | 0.58 | 0.58 | 0.56 |

0.71 | 0.69 | 0.69 | 0.69 |

0.88 | 0.89 | 0.88 | 0.88 |

0.90 | 0.89 | 0.90 | 0.90 |

1.20 | 1.19 | 1.21 | 1.20 |

Conclusion

This investigation has clearly shown that resistance changes proportionally as length increases, and as diameter is increased, resistance rapidly decreases. These two statements are both supported by the results from the enclosed graphs and have been analyzing in their following paragraphs. These two statements also compliment my initial prediction which stated exactly that.

Due to the fact that there is very little scatter in my results, it gives me very little to right about in my conclusions. If the range bars had been bigger or had more scatter, I could have suggested reasons why the results were as they were and attempt to justify the inaccuracies using scientific terminology and detailed explanations or theories as to why the results were as they were. I have explained in detail the reason for the increase in the size of the range bars in the first experiment. Due to the fact that the scatter is so small in the second experiment there is very little to be mentioned. If the results had been inaccurate of had more scatter I could have critically discussed the cause for this.

Bibliography

I used the following websites only for research into resistance:

http://www.bbc.co.uk/schools/gcsebitesize/science/add_aqa/electricity/

There was no other resource or external source of data used other than these. All other data was from the results of the experiments and knowledge of this subject.

This student written piece of work is one of many that can be found in our GCSE Electricity and Magnetism section.

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