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# Investigating How The Length Of A Wire Affects Its Resistance.

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Introduction

Coursework        Physics GCSE        July 2003

Investigating How The Length Of A Wire Affects Its Resistance

Prediction:

I predict that as the length of a wire increases, the resistance too will increase. This is because the resistance is directly proportional to the length, meaning that as the length of a wire increases by a constant (k), the resistance too will increase by the same constant (k). For example, the length of the wire was 2 centimetres, and the resistance of the wire was 5 centimetres. If the length is now 4 centimetres, the resistance of the wire will be 10 centimetres, because 2 is the constant, and when the length is multiplied by the constant, so is the resistance. This can also be shown as r α l, or        r = kl, k being the constant. Because the length of the wire is directly proportional to the resistance, I predict that the graph will look like the Graph shown below:

Resistance of wire

(ohms)

Graph goes

through origin

(0,0)                                                Length of wire

(cms)

Because the length of the wire is directly proportional to the resistance, I predict that the graph will go through the origin (0,0), and will go up in a straight line. In addition to this, the gradient of the graph (change in y/change in x)  will equal the constant, i.e. in the equation R=kl, the gradient will b k.

Scientific Theory:

Metals are very good conductors due to their structural arrangement, which consists of ions and elections; each ion surrounded bout numerous electrons. When a current passes through a metal the ions appear to be in fixed positions and held together, but in reality vibrate, whilst the electrons are moving.

Middle

2.72

1.68

1.68

1.68

1.61

1.62

1.64

Thin

3.14

3.15

3.14

0.58

0.59

0.58

5.41

5.34

5.41

I chose a thin wire because the more thick that the wire is, the more collisions occur and therefore an increase in resistance as a result of the circuit heating up too quickly.

We additionally decided to use constantan wire instead of copper wire as the constantan wire heated up less, because of a lower current passing through it, and therefore a lower number of collisions. This was ideal because we wanted the temperature to remain constant, as explained in the ‘scientific theory’ section.

## Deciding the type of wire

 Type of wire Voltage (volts) Current (amps) Resistance (ohms) Constantan(30cm, thin) 3.143.143.15 0.580.590.59 5.415.325.34 Copper(30cm, thin) 0.390.380.38 1.301.291.32 0.300.290.29

The number of repeats for each individual measurement of resistance over a range of answers was decided to be as high as possible without being to time consuming.  In the end we decided to use 3 repeats per each individual measurement, because it was just about enough to avoid anonymous results and to get accurate results.

Digital voltmeters and ammeters was the decision I made regarding apparatus. This was because multimeters required continuous changes and we tended to receive over -  high results. Similarly, analogue ammeters and voltmeters proved to be difficult to read off (because of fluttering results) and inaccurate.

### Procedure

#### Method

Prepare apparatus for experiment, including digital ammeters and voltmeters, one cell, a thin constantan wire, crocodile clips (to secure the wire), sticky tape(to hold down the wire so it can be stretched from one end of the metre ruler to the other so that the wire is straight and ‘kinks’ are not present) and a meter ruler(with measurements of centimetres and millimetres, so that the results are recorded accurately).

Conclusion

Additionally if I chose a different metal, for example copper, then I would have obtained different results because each metal has a different ionic arrangement; and the number of ions and electrons affects the temperature and therefore the collisions, resulting in a change in resistance. Furthermore, I could have chosen to do the experiment with a non – metal, so see what kind of results I would obtain then.

As we go across the periodic table there are more electrons, therefore meaning that each of the metals are denser, because the nucleuses get larger. Therefore the metals would have a high atomic number, and resistance would become higher, because if the electrons and ions were larger there is more chance of collisions and the collisions become larger.

Ravi Dewji 10S

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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