# Finding the resistance of a wire

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Introduction

Finding the resistance of a wire

Aim

For this experiment, I will be finding out the resistance of a wire in which its length is the variable. I will be investigating the process of how much the resistance increases due to the increase in the size of the resistor (nickel-chromium wire).

## Investigation

Resistance is the property of an electrical conductor, to work against the flow of the current and change some of the electrical energy into heat^{[1]}. The quantity of resistance in an electric circuit determines the amount of current flowing in the circuit for any given voltage applied to the circuit, according to Ohm's law. The unit of resistance is the ohm and the amount of resistance that limits the passage of current to one ampere when a voltage of one volt is applied to it happens. The standard abbreviation for electric resistance is R and the symbol for ohms in electric circuits is the Greek letter omega, Ω. For certain electrical calculations, it is convenient to employ the reciprocal of resistance, 1/R, which is termed conductance, G. The unit of conductance is the mho (ohm spelled backwards) and the symbol is an inverted omega, . To find the value of resistance, the equation

Resistance = Voltage / Current is used.

The resistance of an object is determined by a property of the substance of which it is made of, known as the resistivity and by the length and cross-sectional area of the object. Also, the temperature can determine the resistance of the resistor. At a given temperature, the resistance is proportional to the object's resistivity, length and inversely proportional to its cross-sectional area.

Middle

30 cm

3.88 V

0.63 A

6.15Ω

40 cm

4.04 V

0.50 A

8.08Ω

50 cm

4.05 V

0.41 A

9.87Ω

60 cm

4.05 V

0.34 A

11.91Ω

70 cm

4.06 V

0.29 A

14.00Ω

80 cm

4.09 V

0.26 A

15.73Ω

90 cm

4.17 V

0.23 A

18.13Ω

100 cm

4.19 V

0.20 A

20.95Ω

3rd set of results

Voltage | Current | Resistance | |

10 cm | 3.55 V | 1.51 A | 2.35Ω |

20 cm | 3.76 V | 0.88 A | 4.27Ω |

30 cm | 3.88 V | 0.63 A | 6.15Ω |

40 cm | 3.99 V | 0.49 A | 8.14Ω |

50 cm | 4.03 V | 0.40 A | 10.07Ω |

60 cm | 4.01 V | 0.34 A | 11.79Ω |

70 cm | 4.17 V | 0.30 A | 13.90Ω |

80 cm | 4.08 V | 0.25 A | 16.32Ω |

90 cm | 4.20 V | 0.23 A | 18.26Ω |

100 cm | 4.20 V | 0.23 A | 18.26Ω |

Average results

Resistance 1 (Ω) | Resistance 2 (Ω) | Resistance 3 (Ω) | Average resistance (Ω) ## R1+R2+R33 | |

10 cm | 2.45 Ω | 2.25 Ω | 2.35 Ω | 2.35 Ω |

20 cm | 4.19 Ω | 4.32 Ω | 4.27 Ω | 4.26 Ω |

30 cm | 6.0 Ω | 6.15 Ω | 6.15 Ω | 6.10 Ω |

40 cm | 7.98 Ω | 8.08 Ω | 8.14 Ω | 8.06 Ω |

50 cm | 9.83 Ω | 9.87 Ω | 10.07 Ω | 9.92 Ω |

60 cm | 12.26 Ω | 11.91 Ω | 11.79 Ω | 11.98 Ω |

70 cm | 13.96 Ω | 14.0 Ω | 13.9 Ω | 13.95 Ω |

80 cm | 16.23 Ω | 15.73 Ω | 16.32 Ω | 16.09 Ω |

90 cm | 17.58 Ω | 18.13 Ω | 18.26 Ω | 17.99 Ω |

100 cm | 18.3 Ω | 20.95 Ω | 18.26 Ω | 19.17 Ω |

### Analysis

With scientific knowledge, the graph has turned out like it should have and that my results are accurate. As the length of the nickel-chromium wire increases, the voltage increases but the current decreases. Using the equation;

Resistance = Voltage / Current I have worked out the resistance, according to Ohm’s Law.

From my graph, I have found the pattern that the higher the voltage, the higher the resistance becomes. The graph shows that as the length of the wire increases, so does the resistance of the wire. An example of this is when the experiment at 40 cm was taken place and the resistance was 8.14 Ω. When 10 cm more was added on, the amount of resistance at 50 cm was 10.07 Ω. The reason for this occurring is because the current has had to pass through more atoms in the wire so there is more resistance for the current.

There were 2 odd results that were received on my results. On the third set of results, at 90 cm and 100 cm, the results for the voltage and the current were the same. This meant that the resistance was the same.

Conclusion

- The power pack might have not been turned off during the change of the length of the nickel-chromium wire so heat would build up, leading to more resistance on the next experiment of the increased or decreased wire.

If I were to make improvements to the experiment, I would have tried to make the nickel-chromium wires length as accurate as can be, but in this experiment, there were no extremely odd results.

Another experiment that I could have done that would make the experiment fairer was to keep the resistor under a constant temperature. The circuit would be the same but the resistor would be in an atmosphere where the temperature wouldn’t affect the resistivity of the wire. An atmosphere where the wire would be under constant temperature is under water.

The reason why this way would make the experiment fairer is because there would be no slant at the end of the graph if the results were put into a line graph. Without the constant temperature, there is more resistance if the temperature rises, due to atoms with kinetic energy. With constant temperature, there is the right amount of resistivity there should be, making the experiment a very fair test. Although it won’t be perfect, it will still decrease the amount of atoms moving about when they are hot.

For my conclusion, I have found out that the resistance and the voltage are the same if the current is kept the same and that the resistance and the voltage are in proportion with the length of the wire.

Y:\svn\trunk\engine\docs\working\working\99692.doc

© Nick Wong

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[1]Oxford mini reference for science

[2] Taken from ‘physics matters’ text book

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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