# Investigating Resistance in an electrical circuit

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Introduction

Investigating Resistance in an electrical circuit

Planning

The aim of this experiment is to investigate the resistance in an electrical circuit. There are many different ways to investigate the resistance in a wire, however to do so there must be some background research and prior knowledge of electrical circuits and the components.

Through research I have learnt that George Simon Ohm was one of the forefathers of research into electrical resistance. And, thus accordingly resistance is measured in ohms (Ώ). Resistance is the “opposition of a body or substance to current passing through it, resulting in a change of electrical energy into heat or another form of energy.” (www.dictionary.com)

To calculate the resistance of a wire, you need to multiply together the current and voltage:

Resistance = Current x Voltage

R = I x V

The horizontal line is a divide sign. The calculation is started with whatever quantity that is looked for. "V=", "I=" or "R=" all possible formulae based on this particular Ohms law will be attained. Another useful method is if you place your finger on the calculation you are looking for you are left with the formula you are looking for, that is; V=IxR, I=V/R, R=V/I. It should be apparent that the formula works the other way to, that is; IxR=V, RxI=V, V/I=R and V/R=I. From this, we conclude that; Current equals Voltage divided by Resistance (I=V/R)

Middle

80

0.72

0.28

2.57

75

0.67

0.29

2.31

70

0.72

0.3

2.16

65

0.67

0.31

2.03

60

0.65

0.33

1.95

55

0.63

0.35

1.74

50

0.64

0.38

1.64

45

0.61

0.39

1.31

40

0.62

0.43

1.17

35

0.51

0.46

0.93

30

0.5

0.55

0.73

25

0.43

0.64

0.54

20

0.4

0.69

0.41

15

0.35

0.7

0.31

10

0.28

0.84

0.21

5

0.22

0.97

0.04

For the graph with all 3 tabled results for constantan 26swg see attached sheet 1.

Results for Constantan 28swg

Table 1

Length (cm) | Voltage (Volts) | Current (Amps) | Resistance (Ohms) |

100 | 1.75 | 0.39 | 4.49 |

95 | 1.73 | 0.38 | 4.55 |

90 | 1.66 | 0.4 | 4.15 |

85 | 1.65 | 0.42 | 3.93 |

80 | 1.63 | 0.44 | 3.7 |

75 | 1.6 | 0.46 | 3.48 |

70 | 1.56 | 0.48 | 3.25 |

65 | 1.5 | 0.5 | 3 |

60 | 1.44 | 0.52 | 2.77 |

55 | 1.4 | 0.55 | 2.55 |

50 | 1.34 | 0.58 | 2.31 |

45 | 1.27 | 0.61 | 2.09 |

40 | 1.2 | 0.65 | 1.85 |

35 | 1.14 | 0.68 | 1.68 |

30 | 1.04 | 0.74 | 1.41 |

25 | 0.95 | 0.8 | 1.19 |

20 | 0.82 | 0.86 | 0.95 |

15 | 0.66 | 0.93 | 0.71 |

10 | 0.54 | 1.06 | 0.51 |

5 | 0.36 | 1.22 | 0.3 |

Table 2

Length (cm) | Voltage (Volts) | Current (Amps) | Resistance (Ohms) |

100 | 1.7 | 0.38 | 4.47 |

95 | 1.7 | 0.39 | 4.36 |

90 | 1.66 | 0.4 | 4.15 |

85 | 1.66 | 0.42 | 3.95 |

80 | 1.62 | 0.44 | 3.68 |

75 | 1.58 | 0.46 | 3.43 |

70 | 1.55 | 0.48 | 3.23 |

65 | 1.5 | 0.5 | 3 |

60 | 1.46 | 0.52 | 2.81 |

55 | 1.4 | 0.55 | 2.55 |

50 | 1.35 | 0.58 | 2.33 |

45 | 1.2 | 0.59 | 2.03 |

40 | 1.18 | 0.66 | 1.79 |

35 | 1.12 | 0.68 | 1.65 |

30 | 1.03 | 0.74 | 1.39 |

25 | 0.92 | 0.79 | 1.16 |

20 | 0.82 | 0.86 | 0.95 |

15 | 0.68 | 0.94 | 0.72 |

10 | 0.54 | 1.06 | 0.51 |

5 | 0.36 | 1.25 | 0.29 |

Table 3

Length (cm) | Voltage (Volts) |

Conclusion

Analysis of thickness

In order to analyse the thickness of the wire I will first need to work out the area of the wire. I have got the thicknesses in British Standard Gauge and I have found a site (http://www.falcon-acoustics.co.uk/hintstipsgeneral.htm) which has a table with the thickness converted into millimetres. The conversions for the wires thickness’ are as follows:

Constantan 26swg = 0.457mm

Constantan 28swg = 0.376mm

Constantan 36swg = 0.193mm

This however is the diameter of each of the wires; and the formula for the area of a circle is π x r². The radius of a circle is half the diameter. To work out the area of the wire I must first halve the diameter then square it then multiply by pie. Pie (π) is 22 ÷ 7 the number has definite end.

Now I will work out the area for each of the wires.

Constantan 26swg:

0.457 ÷ 2 = 0.2285mm

0.2285² = 0.05221225mm

0.05221225 x π = 0.163946465 mm²

Constantan 28swg:

0.376 ÷ 2 = 0.188mm

0.188² = 0.035344mm

0.035344 x π = 0.11098016 mm²

Constantan 36swg:

0.193 ÷ 2 = 0.0965mm

0.0965² = 0.00931225mm

0.00931225 x π = 0.029240465 mm²

This shows that the Constantan 26swg is thicker than the Constantan 28swg and the Constantan 36swg and by how much in mm².

“I also believe that the thicker the wire is the less resistance will be present.”

This is correct. I have taken the resistance from all 9 tables and put them in a graph (sheet4). I have taken the resistance from 50cm for all of them. The graph clearly shows the huge difference in resistance. As you can see the Constantan 36swg is more resistant than the 26swg and 28swg Constantan wire. The area of the Constantan

Evaluation

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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