Identification of an unknown test wire through the experimental determination of it's resistivity.

                                                 2                                                                                                                                

8. Then plot a graph of resistance against l because this will give you the gradient which will be ρ, as the rough sketch shows below: -

                            A

Using: y=mx+c

                                                        R=ρ X l

                                                             A                                                                                        

                                          Therefore the gradient is ρ and to get the

                                                                      A

           

Resistivity value we multiply the gradient by the cross-sectional area.

I will get the value straight in ohmmeters because I have converted everything into meters.                                                                                 

Diagram of the circuit:

Safety

• Don’t put your note pads or any kind of paper in contact with the wire because it might catch fire when the wire really hot up in the preliminary results.
• The taps must be turned off from the classroom mains because the experiment is about electricity. Therefore the reaction of electricity in water is very vigorous.
• Make sure that no one touches the wire when the current is switched on because at shorter lengths the wire might hot up and someone might burn their finger.
• Make sure that everyone dries their hands thoroughly so their hands are not wet.

Variables

1. The cross-sectional area of the metal have to be the same because then there will be the same amount of free electrons and the structure of the ions will be the same. If you increase the cross-sectional area there will be more free electrons and the structure and number of the ions will be different.
2. I am changing the length every 5cm up, starting from 60cm. This means when the length measured is greater the resistance will be greater because as the electrons have to travel longer they will collide with the ions more often therefore the current will decrease. So if the length being measured at gets smaller the resistance gets lower hence the current rises, because electrons shorter distance to travel therefore it will hit the ions less often.
3. The lower the resistance the hotter the wire gets, because there are less collisions between ions and electrons. Resulting in electrons going through the wire more quickly, therefore the wire gets hotter.
4. Different types of materials have different resistance. This is because different wires made out of different materials have different resistance. So I will have to do this experiment using the same piece of wire.

Diameter of the wire:

                                

From the total diameter I can work out the mean diameter and convert the diameter from mm² into m². As shown below: -

Mean Diameter=2.32=0.464

                             5

A=π x (0.464) ² = 0.17mm²

                                                          2            
√0.17=4.123105626x10־⁴ X 4.123105626x10־⁴= 1.7X10־⁷m²

  1000

The answer above is my cross-sectional area in m² so now my graph will be in meters and ohms.

Results Table

From the results above I will plot a graph of resistance against length, (R against l). From that graph I will get the gradient, which will be resistivity divided by area. I will then find the resistivity value as shown below: -

ρ = Gradient

A

ρ = GradientXA

Then I would be able to tell what material my wire is made out of, by looking up the resistivity value in the table. The table is in the book that shows the resistivity value of all the materials. Then I will do my conclusion and evaluation from that.

Errors

There are two types of errors: -

1. Systematic error
2. Random error

Systematic error could be caused by incorrectly calibrated scales e.g. cheap ammeters and voltmeters with low accuracy could have error when reading the values of them. If the equipments are accurate and the systematic error is small we say the measurements are accurate.

Random error, is the error made during measurements, e.g. experimenter doesn’t take the readings properly. Thickness of the wire could not be measured by a meter ruler hence equipment not sensitive enough. The crocodile clips have a poor connection with the wire. If random error is very small we say the measurements are precise. Repeating the experiment 3 or more times and taking averages can decrease the random error.

For every equipment I have used for this experiment had a range and an error which are written in the apparatus list.

My error in the resistance is the error in the voltmeter and the ammeter. From the table on pages 1 and 2 I can see that the error in the voltmeter is + 0.5% and the error in the ammeter is + 1%. Therefore the total error in the resistance is + 1.5%.

Resistance (Ω)                    Error in resistance (Ω)

      1.75                        1.5X1.75 = + 0.026         

                                               100

      1.87                               1.5X1.87 = + 0.028  

                                          100

      2.03                                1.5X2.03 = + 0.030

                                           100

      2.15                         1.5X2.15 = + 0.032 

                                        100

       

      2.31                          1.5X2.31 = + 0.035                                

                                 100                        

      2.45                         1.5X2.45 = + 0.037

                                                 100

      2.59                         1.5X2.59 = + 0.039

                                             100

      2.73                           1.5X2.73 = + 0.041

                                            100

   

88.                                1.5X2.88 = + 0.043

                                                 100

My error in length is the error in the meter ruler. From the table on pages 1 and 2 error in the meter ruler is + 1mm. After plotting my error bars for the resistance I will have an estimate maximum and minimum gradient. It will not be very accurate because the error in my length is very small as shown below and this will not allow me to put the horizontal error bars.

Length (m)         Error in length (m)

     0.6                           + 0.001

    0.65                               + 0.001

     0.7                           + 0.001

    0.75                           + 0.001

     0.8                           + 0.001

    0.85                           + 0.001

     0.9                       + 0.001

    0.95                      + 0.001

1. + 0.001

The error in my cross-sectional area is the error in the micrometer saw gauge which is + 0.01mm as shown in the table on pages 1 and 2. Therefore the error in the cross-sectional area is 1.7x10¯⁷m² + 0.00001m. This means that the error is very small and therefore does not needed to be taken into account.

Conclusion

I have drawn the graph for resistance against length. It showed me that the gradient  dy is ρ, this shows that the resistivity value can be determined by

dx    A

multiplying the cross-sectional area with the gradient. As I am going to do it later in this section.

dy stands for Difference in y co-ordinate = Gradient

dx                  Difference in x co-ordinate

On my graph I have plotted the error bars for resistance, I haven’t plotted the error bars for the length because the error in length is too small and would not fit on to my graph.

I am going to find the dy for three of my lines. The top one is the maximum, middle

                                   dx

one is the original and the bottom one is the minimum. To find the gradient of the minimum and the maximum I will have to find the minimum and maximum points from which I am going to get the gradient. To find the maximum point you add the error and to find the minimum point you subtract the error.

Maximum Gradient: -

Maximum point  = 2.88+0.043 = 2.923

Minimum point = 1.73-0.026 = 1.704

dy = 2.923-1.704 = 1.219

dx = 1-0.6 = 0.4

Therefore dy = 1.219 = 3.05  

                dx       0.4

ρ = dy

A    dx

ρ = Axdy

            dx

ρ = 1.7 X 10־⁷ X 3.05

ρ = 52 X 10־⁸

Minimum Gradient: -

Maximum point = 2.88-0.043 = 2.837

Minimum point = 1.73+0.026 = 1.756

dy = 2.837-1.756 = 1.081

dx = 1-0.6 = 0.4

Therefore dy = 1.081 = 2.7025

                dx      0.4

ρ = dy

A    dx

ρ = Axdy

            dx

ρ = 1.7 X 10־⁷ X 2.7025

ρ =  46 X 10־⁸

Original Gradient: -

Maximum point = 2.88

Minimum point = 1.73

dy = 2.88-1.73 = 1.15

dx = 1-0.6 = 0.4

Therefore dy = 1.15 = 2.875

                dx      0.4

ρ = dy

A    dx

ρ = Axdy

            dx

ρ = 1.7 X 10־⁷ X 2.875

ρ = 49 X 10־⁸ 

               

My resistivity value is 49 X 10־⁸. According to the resistivity value table, it shows me that it is constantn. I have got an error in my resistivity, which I have calculated below: -

Maximum error = 52 X 10־⁸-49 X 10־⁸

                     = 3X 10־⁸

Minimum error = 46 X 10־⁸-49 X 10־⁸

                          = - 3X 10־⁸

Therefore the error in the resistivity is + 3X 10־⁸ which will give me constantn. This                   also shows that my experiment was quite accurate.

Evaluation

Now I am going to evaluate my experiment. Overall my experiment was quite good, as it can be seen from the graph. There were a few errors in the equipment that I had to take into account. These errors are the systematic errors. My systematic errors were very small so this means that my measurements were accurate. I could have a high random error, as when I carried out this experiment there were a lot of people in the laboratory. If I had to this experiment again I would try to improve the following things as I think these things can make this experiment more accurate: -    

• The wire was not perfectly straight, there were a few twist in the wire. This increased the error in the length. To improve it I will hold the ruler in the right place by using a G-clamp, and then hang some weights made out of wood on the wire to make sure it is straight.
• The ammeter and the voltmeter were not sensitive enough. The error they carried was quite high for being precise. To improve it I will use an ammeter and a voltmeter with less error. Therefore they will have more significant figures.
• The temperature could destroy the structure of the atoms in the wire during the preliminary results. Therefore the damaged wire might not give accurate results. I think we should be given 2-meters of wire, 1 meter for preliminary experiment and 1meter for the real experiment. We should be allowed to use a thermistor to control the resistance which will control the temperature
• I should repeat the experiment 5 times to get more accurate average. I would also like to take more readings on the wire to find an accurate average of the diameter.
• The crocodile clips must be tested before being used, because some of them might have a poor contact with the wire and not allow current flow through the wire.
• I would try to use a bigger range on my graph so I could plot error bars more accurately.
• I can also try to let the wire cool down for 50 seconds between every length.
• From my preliminary results I have found out that the wire starts hotting up at 0.5m. This means the wire could start warming up before 0.5m from inside. Therefore even that would affect my results. So I would have to find a way to overcome the internal heat of the wire.
• I could use mass spectrometer to determine what the wire is made out of.