# What affects the resistance of a wire?

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Introduction

What affects the resistance of a wire?

### Planning

## Introduction

We are trying to find out what affects the resistance of a wire. Resistance is the slowing down of electric flow (flow of electrons) due to metal ions. The equation to measure resistance is:

Resistance = Voltage ÷ Current

R = V / I

Resistance is measures in ‘volts per amps’ or, more commonly, ‘Ohms’ (Ω).

There are a few things that affect resistance. I think these are:

- Length of wire

- Diameter of wire
- Material/type of wire
- Temperature

I am going to try and find out how the diameter of the wire affects the resistance of the wire. I will do some tests find out how the diameter affects the resistance. I think that if I increase the diameter the resistance will decrease.

## Method

- First I will set up a circuit with a power pack, voltmeter, ammeter and a space for a 1metre wire.
- Then I will get a metre ruler and measure 1 metre of the first size of wire and cut it with wire cutters.
- I will stick the wire to the metre ruler with two pieces of sticky tape 2cm away from either end to keep the wire straight.
- I will then put the wire (attached to the ruler) in the gap in the circuit and attach it to the circuit.
- After turning the power pack on, I will record the numbers on the voltmeter and ammeter.
- I will then repeat steps 2 to 5 with 4 other different Standard Wire Gauge sizes of wires.
- Next I will repeat the whole experiment another few times.

I have chosen this method because it is quick, practical and easy to do and will produce accurate and reliable results. I think it is the best because it is the easiest one to do and you don’t need that much equipment but still get good results.

## Apparatus

- Power pack
- Connecting wires
- Crocodile clips
- Voltmeter
- Ammeter
- 5 different SWG sizes of

Constantan wire

- Metre ruler
- Sticky tape
- Wire cutter

I have chosen this apparatus because it is what I need for this experiment to get accurate, good results. It would have been better for this experiment to use an ohmmeter but we don’t have any available so I will use an ammeter and a voltmeter and use the equation: resistance = voltage ÷ current I will calculate the resistance using the equation with a calculator to get precise answers and check then twice. To make the experiment more accurate I will use a digital ammeter and voltmeter that measures to two decimal places. I have chosen to use constantan wire because the changes in resistance can be seen more clearly in constantan than in some metal wires like copper, and because constantan has a low temperature coefficient, which means that it does not heat up much and so the resistance will not be affected notably by temperature. The connecting leads in the circuit have their own resistance. However, this will have a very little effect on the readings taken in my experiment. I will keep the voltage set on the power pack on 6 volts for all the experiments. I will use a metre ruler because it is more suitable and accurate for our measurements than a 6-inch ruler. I will use the same equipment for all the repeated experiments too.

Variables

To create a fair test some aspects of the experiment will have to be kept the same whilst one key variable is changed. I am going to change the diameter so I will need to keep everything else the same.

## Variable | Effect | Control |

Length of the wire | If a wire is longer than one metre then that wire’s resistance is higher than it should be because if the wire is longer then there are more metal atoms for the current to pass. More atoms get in the way of the free electrons, which means that the current (rate of the flow of the electrons) is less and so the resistance is higher. | I will measure the length of the wire with a metre ruler to 1 metre. |

Material/Type of wire | If a different type of wire is used then the resistance will change because different materials have different resistances and different reactions to temperature. For example if silver was used for one of the tests then that resistance value would be a lot lower than it’s supposed to be because it has a low electrical resistance. | I will use constantan for all the tests. |

Temperature | If the temperature is different then the resistance will change because if the wire is hotter the metal atoms vibrate more vigorously and faster and further from their rest positions. This means that they are more likely to get in the way of the travelling free electrons. A metal has more resistance when it is hot. | I will keep the experiment set up in the same place in the room (away from the radiators) and do all of the experiments within the same hour. |

## Safety

To make this experiment safe I will: -

- Place the experiment in the centre of the table so that nothing will fall off
- Remove unnecessary equipment from the table i.e. pencil case
- Remove bags from under the table so that no one trips over them
- Not touch the wire when the power pack is on!
- Make sure plugs are pushed in properly and wires are not dangling so there less chance of being electrocuted

## Reliability

To make this experiment as reliable as possible I will try and follow a fair test and repeat the experiment a few times to confirm my results. There are only a few flaws in my experiment: -

- The length of the wire may be very slightly inaccurate because the wire may stretch slightly when we pull it to get the (originally curled) wire straight against the ruler.
- The temperature in the room may change very slightly
- The connecting leads in the circuit have their own resistance

But by doing the following our results should be fairly reliable: -

- Measuring accurately
- Using the same equipment
- Redoing the experiments

Middle

30

0.3150

32

0.2743

36

0.1930

40

0.1219

## Secondary Data

I used some textbooks at school, the BBC bitesize revision website, and the Revise for Science GCSE: Suffolk Higher Tier revision book to help me with my prediction. I also used Lessons in Electric circuits by Tony R. Kuphaldt, which I found on the Internet, that says:

The formula for calculating the circular-mil area of a circular wire is very simple:

Circular Wire Area Formula A=d2

Because this is a unit of area measurement, the mathematical power of 2 is still in effect (doubling the width of a circle will always quadruple its area, no matter what units are used, or if the width of that circle is expressed in terms of radius or diameter). Electrons flow through large-diameter wires easier than small-diameter wires, due to the greater cross-sectional area they have in which to move.

## Prediction

Electricity flows in metals. Metal wires are made of millions of tiny metal crystals. Each crystal’s atoms are arranged in a regular pattern. The metal is full of ‘free’ electrons that do not stick to any particular atom. They fill the space between atoms in the metal. There is an electric current when these electrons move. Metal atoms get in the way of travelling electrons. This causes electrical resistance. Some conductors are worse than others because they have more resistance to current. The free electrons keep bumping into atoms. A wire’s resistance depends on the metal. Constantan is a copper-nickel alloy with a high electrical resistance and is used as a resistance wire. The resistance also depends on the wire’s size. The overall resistance is more when you connect the wires in series (twice the resistance of one wire). The overall resistance is less when you connect the wires in parallel (1/2 the resistance of one wire) because more current can pass through two wires, and with an increase in current the resistance goes down. The Standard Wire Gauge works as so: The larger the gauge number, the thinner the wire; the smaller the gauge number, the fatter the wire. This is an inversely proportional measurement scale. Ohm’s law says that ‘the current flowing through a component is proportional to the potential difference between its ends, providing temperature is constant.’

From this information I predict that as the diameter of the wire decreases (the SWG increase), the resistance of the wire increases. I think this is because a wire with a diameter twice the size of another wire would have 4 times as much wire. This is like having 4 wires in parallel, which means there are more pathways for the current to pass through. The more electrons would be able to pass through the larger wire at any one time and because there is an increase in current the resistance goes down (because of the equation R=V/I) This means that there will be ¼ of the smaller wire’s resistance in the larger wire. I can therefore predict the graph to look like this because if a diameter of 1mm equalled 16Ω/m, 2mm would equal 4Ω/m, and 4mm would equal 1Ω/m, giving a curvy graph:

These are my predictions for each of the Standard Wire Gauges: -

- For a metre of 28 SWG constantan wire I predict that the resistance will be around 4.32Ω/m because that is the theoretical value I found from my preliminary work, and because the diameter is very large, and so a lot of current passes through the wire, so the resistance is therefore very low.

- For 30 SWG I predict that the resistance will be around 6.16Ω/m because the wire is thinner and so the current is a little less, therefore the resistance is more than for 28 SWG. The theoretical value shown in my preliminary work is 6.16Ω/m.

- For 32 SWG I predict that the resistance will be around 8.12Ω/m because the wire is quite thin and so the current is a less, therefore the resistance is higher than for 30 SWG. And the theoretical value shown in my preliminary work is 8.12Ω/m.

- For 36 SWG I predict that the resistance will be roughly 4 times more than the resistance of 28 SWG because the diameter is roughly half of the diameter of 28 SWG. The wire is thin and so the current is a lot less, therefore the resistance is a lot more than for 28 SWG. The theoretical value shown in my preliminary work is 16.40Ω/m.

- For 40 SWG I predict that the resistance will be around 41.10Ω/m because the wire is extremely thin and so the current is very small, therefore the resistance is very high compared to 28 SWG. And the theoretical value shown in my preliminary work is 41.10Ω/m.

Obtaining Evidence

Following my method I have carefully and safely done three experiments and collected some results. I recorded the results as precisely as possible.

This is the results table for my first experiment: -

Standard Wire Gauge (SWG) | Voltage (Volts) | Current (Amps) | Resistance per metre (Ω/m) |

28 | 5.55 | 1.26 | 4.40 |

30 | 5.73 | 0.87 | 6.59 |

32 | 6.04 | 0.71 | 8.51 |

36 | 6.15 | 0.36 | 17.08 |

40 | 6.15 | 0.15 | 41.00 |

This is the results table for my second experiment: -

Standard Wire Gauge (SWG) | Voltage (Volts) | Current (Amps) | Resistance per metre (Ω/m) |

28 | 5.67 | 1.29 | 4.40 |

30 | 5.76 | 0.89 | 6.47 |

32 | 6.16 | 0.72 | 8.56 |

36 | 6.22 | 0.36 | 17.28 |

40 | 6.14 | 0.15 | 40.93 |

Conclusion

I didn’t have any odd results and all of them are accurate. The graph shows this by showing how close they all are to the theoretical values. I didn’t have any problems with my investigation and everything went smoothly as I planned. I followed my method exactly and tried to measure everything as precisely as possible. I think that my results are good enough to make a firm conclusion because they seem reliable. I don’t need any more results to make my conclusion more definite because I have already done the experiment three times and my graph shows clearly that the results are good.

I have come to the conclusion that the diameter affects the resistance of the wire and as the diameter of the wire decreases the resistance of the wire increases. I have also found out that this happens because the thicker wire has more passage for the current to flow through and so more current can flow at a time, therefore the current is high meaning that the resistance is low in a thick wire, and vice versa. I have been measuring the diameter using the Standard Wire Gauge scale. To further confirm my conclusion if I had the equipment I could use an equally spread out range of wires instead of making do with the ones I had e.g. 28,32,36,40,44 SWG. I could repeat the experiment a few more times, try the experiment with other materials to make sure the diameter has the same affect on the resistance on all wires, try the experiment using American Wire Gauge measurements, or try the experiment with other diameters.

Emily Cookson 11N 11.05

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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