An investigation into the relationship between the length of a wire and its resistance.

Method

     To find the resistance of a wire two measurements must be taken, the current (I) and the potential difference (V). There will be a voltmeter in parallel with the wire to measure the potential difference and an ammeter in series to measure the current, the variable. I will first get the readings using a digital ammeter and voltmeter and then an analogue ammeter and voltmeter. This will tell me which one is more accurate. The circuit diagram shown below shows how I will set up the circuit: -

     The zigzag line above shows the wire, which I am testing. It will be between two contacts on a wooden board with a ruler on so I will know where to connect the crocodile clip. I will connect the crocodile clip in eight different places along the wire, starting at 5cm and ending at 40cm. At each point the rheostat will be moved up or down to keep the potential difference the same so it is a fair test. The resistance of the wire can be found by using ohms law.

     The current is directly proportional to the potential difference applied, if the temperature and other variables are kept the same. The actual formula to calculate the resistance is:

Resistance  =            Current (I)                                    

                       Potential difference (V)

     This formula can be applied to the data I have collected to work out the resistance per unit length, the resistivity. If you know the resistivity there is also another formula for working out the resistance. By using the idea that the resistance of a wire is directly proportional to its length but inversely proportional to it’s cross sectional area we can come up with the following formula:

R =  p L

     

p = resistivity

Resistivity is measured in Ω/M

The ruler on the wooden board that the wire is on will be used to calculate where the crocodile clip is connected. I will then use the micrometer to measure the diameter of the wire. I will measure the diameter in four different places and at four different angles along the wire. It is measured at four different angles to check that the wire is a cylindrical shape and not elliptical. From this I can work out the cross sectional area using the this formula:

A = πr2 I can then use all of my data to work out the resistance and resistivity of the wire.

Results

Digital Meters

     

Analogue Meters

Micrometer Readings

Average Micrometer Readings

Average current, potential difference and

Resistance using the digital meters

Resistivity

R =  p L  

p =      x A

5cm                                                                                  10cm

p =         x 0.1                            p =            x 0.1

   = 0.0048 Ω/M                                                              = 0.0046 Ω/M

15cm                                                                                20cm

p =               x 0.1                                                        p =              x 0.1

    = 0.0045 Ω/M                                                               = 0.0046 Ω/M

25cm                                                                                30cm

p =              x 0.1                                                         p =             x 0.1

    = 0.00448 Ω/M                                                            = 0.00443 Ω/M

35cm                                                                                40cm            

p =            x 0.1                                                           p =             x 0.1

    = 0.00442 Ω/M                                                            = 0.00465 Ω/M

Average Resistivity

  p = 0.00456 Ω/M

Conclusion        

     I conclude that the length of the wire does increase because the electrons in metals are free to move about from atom to atom. This is called a ‘sea’ of electrons. As soon as a potential difference is passed through the metal these electrons move faster causing harder collisions against the atom walls, though they can still pass through the atoms. This causes friction, which converts the potential difference into heat energy, which gives the wire its resistance. The longer the wire is the more collisions there are so there is more resistance. The cross-sectional area of the wire also will affect its resistance; this is why I have used a micrometer to determine the area. The area was found at four different places along the wire and at four different angles. This was done twice and then the average diameter and cross-sectional area was found. I found the wire to be cylindrical in shape. After the area, length and resistance data was collected the resistivity could then be found. The average resistivity of the wire is 0.00456 Ω/M which is quite a high resistance compared to things like copper which has a resistivity of 0.0000000156 and gold which has a resistivity of 0.0000000235 Ω/M. But a low resistance compared to silicon which has a resistivity of 640 Ω/M which is why it is used in electrical components like transistors and computer ‘silicon’ chips. The gradient on the resistance – length graph shows the resistivity in Ω/M. The gradient is 4.57 but as the length was dome in meters it has to be altered to 0.00457. This is only 1/100000 higher than the resistivity I got using my results so I think my graph is quite accurate. Also there are no anomalous results on this graph.

Evaluation

     I think this experiment could have been improved because as you were measuring the resistance of the wire the wire was getting hotter as the current was passing through it, which increased its resistance. If you keep the crocodile clip on the wire for a shorter amount of time you get a truer measurement of the resistance of the wire at room temperature. The experiment could also have been improved by adding new variables e.g. the cross sectional area of the wire could be altered. If this were altered I would expect the resistance to decrease as the friction caused would decrease. I could also change the material of the wire. If it was a more dense material it would have a higher resistance but if it was less dense it would have a lower resistance as there is less friction so less heat. I could also change the temperature of the wire. I would expect the wire to have a higher resistance as it got hotter.