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

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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.  If the cross-sectional area is doubled the resistance will halve.  This is because if the cross-sectional area is doubled there is an increase of space between atoms for the electrons to travel through. Due to this increased space between the atoms there should be less collisions.  My graph should show that the cross-sectional area is inversely proportional to the resistance.

The diagrams below show my prediction and should explain it more clearly:

Diagrams:

Figure 1

These diagrams show how the theory of resistance is affected by the alteration of the length of a wire. As you can see from the 1st diagram there is less collisions.  When 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.

                                                                                                                                                                                          Figure 2 The wire above is half the length of the wire in figure 2 and so there should be half the number of collisions between the electrons and the atoms. The length of the wire in figure 2 is double the length of the wire above resulting in twice as many collisions and a predicted doubling of the resistance.

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Figure 3

This diagram compared to figure 1 shows how the theory of resistance is affected by the alteration of the cross-sectional area of a wire. When the cross-sectional area of a wire is increased then the resistance will halve because the electrons have more space to move freely and less collisions will occur.  The width in figure 3 is double the width in figure 1 resulting in half the number of collisions and a predicted halve of resistance.  

Figure 4                Figure 4a 

                

RESISTOR 1 - is a rheostat.  I am using this ...

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