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# What factors affect the resistance of a wire?

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Introduction

An Investigation into the Electrical Resistance of Wires

Introduction

My Physics coursework is about the electrical resistance of wires and to see what affects the resistance. Electrical resistance is the measure of the degree to which an object opposes the passage of electrical current. Ohm’s Law states that at a constant temperature, the resistance is the amount if current flowing for any given voltage.  This can be written by the formula:

R is the resistance in Ohms

V is the voltage in Volts

I is the current in Amperes

Scientific Background

A metal consists of a grid of atoms, each with a shell of electrons. The outer electrons are free to separate from their own atoms and travel through the grid, making the metal a conductor. When an electrical potential (a voltage) is applied across the metal, the electrons drift from one end of the conductor to the other under the influence of the electric field causing electrical conduction. These electrons can collide into impurities, the lattice and other free electrons and so cause resistance. A rise in temperature causes the atoms to vibrate more strongly, creating even more collisions, making it more difficult for the electrons to get through and so increasing resistance.

Variables

The possible independent variables for the investigation are:

• Thickness (Diameter, Circumference, Radius or Area) of wire: The cross sectional area of a piece of wire greatly affects the resistance. If the wire is very thick it will allow a high current through because there is more room for more electrons to transfer the current.  However as shown in the diagram, in a narrow wire (a) there is less room and therefore fewer electrons to carry the current, hence a higher resistance. This means that the thickness is inversely proportional to resistance so if you double the thickness, you cut the resistance in half.
• Temperature of wire: When current passes through a metal the electrons in the metal are trying to get past the protons. In a cold wire the protons are not vibrating much so the electrons can pass between them rather quickly. As the conductor heats up, the protons start vibrating and moving slightly out of location. As they begin to vibrate more and more they are more likely to get in the way and disrupt the flow of the electrons. This means that the higher the temperature, the higher the resistance. An example of this is when you turn on a light bulb. At first, the wire (filament) is cold and has a low resistance but as the wire heats up and gives off light it increases in resistance. As a result we can say that Ohm's law holds true unless temperature changes.
• Type of wire: Different types of wires are made from different metalsand therefore have different resistances. I am not going to use this as my independent variable as it is an internal and not an external factor affecting resistance.
• Length of Wire: If the wire is very long then it will have many atoms in it. This means that there is more material for the electrons to bump into as they move from one end to the other and so there is a greater resistance. If you double the length, you double the resistance of the wire. Therefore at a constant temperature the length will be directly proportional to the resistance.

The dependent variable for the investigation will be the resistance which will be calculated by recording the potential difference and current.

Fair Test

In order to make the investigation fair, it is important to change only one variable while I keep every other variable mentioned above constant. I will do this by:

• Keeping the thickness of the wire the same throughout the investigation.
• Keeping the room temperature constant throughout the investigation (around 22oC).
• Making sure that the type of wire used is kept the same throughout the investigation.

I will also make sure that my measurements of length are accurate by using a ruler and making sure that the wire is straight during experiments. I will also use the same ammeter and voltmeter for all the experiments.

Prediction

I predict that the longer the wire the more resistance it will have, and that the length of wire will be directly proportional to the resistance. For example when the length is doubled, the resistance will also be doubled.

The resistance (measured in ohms ‘Ω’) is opposition to the flow of an electric current: the greater the resistance in a circuit, the more energy is needed to push charged particles around the circuit.

As the electrons in an electrical current move around a circuit, they bump into the atoms in the wires through which they pass. In my case, the longer the wire of an electrical circuit, the greater collisions into atoms, therefore, there is higher resistance.

Here is a model illustrating resistance in a metal:

Ohm’s Law states that the current passing through a wire (or resistor) at constant temperature is proportional to the potential difference.

I expect my graph to look like this:

Safety

During the procedure of the experiments it is very important to be safe in the laboratory. I will ensure this by:

• Resisting form tampering with the power pack during the experiments.
• Using wires that have insulation (and are not bare).
• Making sure that there is no water anywhere around the equipment.

Middle

Material

Resistivity/m

Silver

Copper

Aluminium

Iron

Constantan

Mercury

Germanium

Alumina

Pyrex

Fused Quartz

The next decision I had to make was which thickness of wire to use.  The Imperial Standard Wire Gauge (SWG) is a measurement that it used for thickness (diameter and cross sectional area) and most wires are found in this unit of measurement. There is a wide range of wires I could have used as the table below shows:

 S.W.G 16 18 20 22 24 26 28 30 32 34 36 38 40 Diameter (mm) 1.62 1.25 0.91 0.71 0.56 0.46 0.38 0.32 0.27 0.23 0.19 0.15 0.12

The final thing I did in my preliminary work was to decide a suitable range of lengths to use in my main investigation.

I set up my equipment to make a circuit. At first I tried using a battery with 1.5V but found that my readings were too low so I decided to use 4.5V which worked a lot better.

Conclusion

Main Investigation

Apparatus

The equipment needed for the investigation are:

Ammeter

Voltmeter

Constantan Wire

Crocodile Clips

32SWG Constantan Wire

4.5V Battery

Meter Ruler

Method

1. I collected the apparatus I needed: a 4.5V battery, a voltmeter, an ammeter, 32 SWG constantan wires, a ruler and crocodile clips.
1. I set apparatus up as shown:

It was important that the voltmeter was set up in parallel and the ammeter in series.

1. I placed 3.0m of Constantan wire between two crocodile clips which were connected to the rest of the circuit as my ‘resistance’.
1. I took the voltmeter and ammeter reading.
1. I carried out the experiment three times for the 3.0m wire and recorded the ammeter and voltmeter reading each time.
1. I changed the length of wire by varying the position of the crocodile clips to the 5 lengths that were needed and took the ammeter and voltmeter readings for each three times.
1. I worked out the average ammeter and voltmeter reading for each length of wire.
1. I worked out the average resistance for each length of wire using Ohm’s law; R = V/I, suing the average voltmeter and ammeter reading.
1. I recorded my results in a table.

Results

 Length of Wire/m Voltmeter Reading/V Ammeter Reading/A Resistance/Ω 1 2 3 Average 1 2 3 Average Average 0.50 2.48 2.51 2.52 2.50 0.54 0.56 0.55 0.55 4.55 1.00 3.60 3.58 3.62 3.60 0.38 0.39 0.41 0.39 9.23 1.50 3.67 3.68 3.73 3.69 0.31 0.28 0.26 0.28 13.18 2.00 4.04 3.96 4.07 4.02 0.23 0.23 0.20 0.22 18.27 2.50 4.07 4.11 4.09 4.09 0.18 0.19 0.18 0.18 22.72 3.00 4.20 4.12 4.16 4.16 0.16 0.15 0.15 0.15 27.73

Sisan Sillo

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