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# How does the length and cross-sectional area of a wire affect resistance

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Introduction

PHYSICS COURSEWORK

How does the length and cross-sectional area of a wire affect resistance?

Introduction:

This investigation sets out to prove that resistance is affected if the length and cross sectional area of a wire is varied.

Theory:

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.  To calculate the resistance in a circuit this formula (Ohms Law Ώ) can be used.

Resistance (ohms Ώ) = Potential Difference (V)

Current (A)

Prediction:

I predict that if the length of the wire increases then the resistance will also increase in proportion to the length. If the length is doubled the resistance should also double. This is because if the length is doubled the number of atoms will also double resulting in twice the number of collisions slowing the electrons down and increasing the resistance. My graph should show that the length is proportional to the resistance.

I predict that if the cross-sectional area of the wire increases the resistance will decrease because it is inversely proportional.

Middle

To connect the above items and to complete the circuit.

Method:

1) The apparatus is collected.

2) The apparatus is set up as shown in figure 4 above.

3) Adjust the sliding contact in variable resistor 2 to the desired current (0.4 A)

3a) Adjust the sliding contact in variable resistor 2 to the desired current (0.5 A)

4) Change the length of the wire by adjusting the sliding wire connectors (crocodile clips)

4a) Change the cross sectional area of the wire.

1. Record results during observation period.

Fairtest:  to make it a fair test I must consider all these variables and make sure they remain constant.

• Temperature: If the wire is heated up the atoms in the wire will start to vibrate because of their increase in energy. This causes more collisions between the electrons and the atoms as the atoms are moving into the path of the electrons. This increase in collisions means that there will be an increase in resistance.
• Material: The type of material will affect the amount of free electrons, which are able to flow through the wire. 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 number 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.
• Wirelength: If the length of the wire is increased then the resistance will also increase as the electrons will have a longer distance to travel and so more collisions will occur. Due to this the length increase should be proportional to the resistance increase.
• Wirecross-sectionalarea: If the wires width 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 must ensure that I control all these variables so that my results are consistent with my prediction and I’m only testing one variable at a time.

In order to plot a good graph I need to ensure I have at least 5 sets of results for each experiment and for each trial I will test the wire with two corresponding currents so that I can calculate an average resistance.

Risk Assessment:

• I will handle the power supply carefully.
• I am going to only use a low current and voltage.
• I will be careful when handling live wires.

Conclusion

As temperature is such a huge variable and not constant it would be hard to measure this factor or test it as it can become quite dangerous so I have chosen not to further investigate this factor. Through my research, however I have found that temperature does indeed affects the resistance in a wire and so to that extent does the materials.  My research shows that the temperature of a wire heats up the atoms in the wire, which start to vibrate because of their increase in energy. This causes more collisions between the electrons and the atoms as the atoms are moving into the path of the electrons. This increase in collisions means that there will be an increase in resistance.

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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