# An Investigation to Find the Resistivity of Wires

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Introduction

Anthony Gullan Physics Coursework

An Investigation to Find the Resistivity of Wires

## The Experiment

The experiment that was used to obtain the results was very simple. The voltage and current were measured whilst varying the length of wire. The results for voltage and current were recorded along with the diameter of the wire. This allowed for a range of other values to be calculated, including cross-sectional area and resistivity.

The Equipment

- A power supply
- A voltmeter and an Ammeter
- A jockey
- A micrometer
- A 1 meter ruler
- Wire
- Connecting cables

## What is Resistivity?

The resistance of a conductor depends on three factors:

- The material
- The size of material (eg length)
- The temperature

The equation for Resistance is:

R = ρl

A

In this equation the constant is called resistivity, ρ. This is governed by the nature of the material and is affected by temperature. Resistivity varies for different materials, but stays constant for a given material. Below is a table illustrating a few materials resistivity

The equation for resistivity therefore is:

ρ = RA

L

The units for resistivity are Ωm (ohm-metres).

## Conductivity

The opposite of resistivity is conductivity. This can be calculated by using this formula:

σ = 1/ρ

The units are Ω-1m-1.

Predictions

I think that the results that I work out will show these patterns:

- As the length increases the resistance will also increase – there is more wire resulting in more energy needed for the same results
- As the Cross-Sectional Area increases the resistance will decrease – the wire is ‘wider’ resulting in more electrons being able to flow at any one time

Middle

40.00

3.34

50.00

3.66

60.00

4.95

70.00

5.74

80.00

6.60

90.00

7.18

100.00

8.24

This graph is a straight diagonal line. This shows that Resistance and Length are directly proportional. In other words if one value increases by a certain amount then the other value will increase by a proportional amount.

Although in this experiment there are a few anomalies, caused either by technical problems or through human error, this graph shows a strong picture of the relationship between length and resistance of a wire.

Resistance against Area and 1/Area

Resistance (Ω) | 1/Area (m-2) |

0.00 | 0.00E+00 |

11.18 | 2.21E+07 |

8.27 | 1.62E+07 |

6.15 | 1.24E+07 |

4.35 | 8.40E+06 |

0.26 | 4.98E+05 |

Resistance (Ω) | Cross Sectional Area (m2) |

0.00 | 0.00E+00 |

11.18 | 4.52E-08 |

8.27 | 6.16E-08 |

6.15 | 8.04E-08 |

4.35 | 1.19E-07 |

0.26 | 2.01E-06 |

To start with I will analyse Resistance against 1/Area. This graph shows that the cross-sectional area and the resistance of a wire are inversely proportional. At first the shape of the graph suggests that the two values are directly proportional. However, as the area is displayed as 1/area this makes it inversely proportional. This is because the equation for something that is inversely proportional is:

A α 1/B, or in this case Resistance α 1/Area

Conclusion

From the data I have made three observations:

- The length of the wire has a proportional effect on the resistance of the wire
- The cross-sectional are is inversely proportional to the resistance of the wire
- The length of the wire divided by the area of the wire and the resistance of a wire are proportional. Having plotted a graph of these values the resistivity of the wire can be found out by calculating the gradient of the line.

These observations can also be written as:

- R α L

- R α 1/A

- ρ = RA/L

Evaluation

I think that the results that were obtained were good. There were a few anomalies in the graph, however these did not seem to affect the calculations too much. The graphs that I could produce with the data showed how each aspect was related to the others. The experiment used to calculate the results could have been better. For example, more readings could have been taken – i.e. every 5cm. However with the data I was given it was possible to show the relations between resistance, length, cross-sectional area and resistivity.

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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