# Investigate how length affects the resistance of a wire.

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Introduction

## Physics AS Coursework

## Planning

Aim

The aim of my investigation is to investigate how length affects the resistance of a wire. Resistance is the force, which opposes the flow of an electric current around a circuit so that energy is required to push the charged particles around the circuit. Resistance is measured in ohms. Resistance occurs when the electrons travelling along the wire collide with the atoms of the wire. These collisions slow down the flow of electrons causing resistance. Resistance is a measure of how hard it is to move the electrons through the wire.

Plan of the method to be used:- The resistivity of a wire can be determined using the equation P= 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 wire used in metres. A: - Is the cross-sectional area of the wire in metres square and can be determined using the equation A= π(d/2 x10 ³)² where d is the diameter of the wire in mm. I will plot a graph of length on the x-axis against resistance on the y-axis. From the relation R = PL /A which corresponds to the straight line equation y=mx+c the graph should be a straight line passing through the origin where m is the gradient of the straight line graph that corresponds to P/A. Since the cross-sectional area of the wire can be found by measuring its diameter.

Middle

Justification

I am going to conduct the experiment in this way to get a resistance (R), value across a length of nickel chromium wire. This R value along with the length (L) will allow me to plot a graph of R= P L Resistivity (P) Area (A)

A

Y=m x +c making the gradient P allowing me to find P as I know the values of R, L, and A.

A

Results

Length of wire cm | 1.) Voltage Volts | 2.) Voltage Volts | 3.) Voltage Volts | Average Voltage V | Current Amps | Resistance Ohms |

100.0 | 1.21 | 1.24 | 1.24 | 1.23 | 0.18 | 6.83 |

90.0 | 1.10 | 1.11 | 1.11 | 1.11 | 0.18 | 6.17 |

80.0 | 0.98 | 0.99 | 0.99 | 0.99 | 0.18 | 5.50 |

70.0 | 0.86 | 0.87 | 0.87 | 0.87 | 0.18 | 4.83 |

60.0 | 0.73 | 0.74 | 0.74 | 0.74 | 0.18 | 4.11 |

50.0 | 0.61 | 0.62 | 0.62 | 0.62 | 0.18 | 3.44 |

40.0 | 0.49 | 0.50 | 0.49 | 0.49 | 0.18 | 2.72 |

30.0 | 0.36 | 0.37 | 0.35 | 0.36 | 0.18 | 2.00 |

Results of testing the diameter of Nickel Chromium

0.45 | 0.45 | 0.46 | 0.46 |

The average diameter of the nickel chromium found by using a micrometer is 0.455 or 0.46 mm to two decimal places. I will use 0.46 mm in the equation Area = π (D x 10 ³)² 2

Conclusion/calculations

Resistivity formula R=PL

A

Formula found from graph R= P L +0

A

Y= m x +c

Gradient = Y = 5.8 = 6.9 Ω/m

X 0.85

Area = π (0.46 x 10 ³)² Area = 1.66 x 10

2

P = Gradient P= Gradient x Area

A P= 6.9 x 1.66 x 10

P= 1.14 x 10

P= 114 x 10 Ω m

From my graph on the previous page, I can see that the resistance of the wire is directly proportional to the length of the wire.

Conclusion

If I were to conduct the experiment again I wouldn’t change the way I performed it at all because my results were so accurate. If I were to perform the experiment again I would choose a different variable such as:

- Wire diameter :

I think that if the wire diameter 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. I would also test to see if diameter if also directly proportional to resistance.

- Material :

I think that the type of material of the wire will affect the amount of free electrons, which are able to flow through that wire. This is because 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 numbers 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.

Andrew Norman Physics AS level Coursework

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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