Ivestigation to show if constantan is a suitable replacement to copper wire

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aceInvestigation to show if constantan is a suitable replacement for copper wire


Electricity is the flow of electrons within a circuit. In current electricity negative charges are made. Resistance is anything, which hinders the movement of these electrons. The definition of resistivity is the ability, measured in ohm metres, of a cubic metre of material to oppose the flow of an electric current. (Symbol rho-r).


Resistance occurs because of the particles in the material of the wire/conductor and how the material moves around them.


E.g.


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Low resistance


In thicker wire the particles are a lot more spaced out so it is easier for the electric current to move around the particles-if the particles collided Ek is transferred to the particles causing an increases in heat.


High resistance


In thinner wire the particles are a lot closer together so that the movement of the current is hindered.


Other factors that may affect the resistance are;


· The physical dimensions of the wire, long wires have more resistance than shorter wires, so the longer the sample of material, the greater the resistance.


· Doubling the Cross Sectional Area of the wire also doubles the number of charge carriers there are to carry the current halving the resistance.


· He other factor that determines the resistance is the material that the resistor is made of. Any resistive properties are measured by its r. r is measured in Wm.


By considering all of these factors I will vary the length of my wire. I will keep the current, temperature and diameter constant.


Safety


When conducting any experiment using electricity, be careful that equipment does not come into contact with water. This will minimise the possibility of electric shocks, as water is a very good conductor. Check that any wires that you used have a plastic surrounding, as this is important to insulate the wire. Be careful when handling the wire as it could be come hot during the experiment.


Apparatus


· Micrometer (accurate to 0.01 of a mm)


· Power Pack


· Circuit wire with crocodile clips


· 100cm (1m) of constantan wire


· Digital Ammeter (reads to 1 mA)


· Digital Voltmeter (reads to 1 mV)


· Ruler (accurate to 0.1 of a mm)


· Sellotape to tape the constantan wire to the ruler.





How to set the apparatus up


Method


I will look up the resistivity of copper wire in order to compare it with that of the constantan. I will measure out 100 cm of constantan wire. I will measure the diameter of the wire using a micrometer. I will repeat this three times so I can calculate the average diameter and calculate the average percentage error of the micrometer. I will take the wire and tape it to a meter rule; this will avoid bends and twists in the wire.


I will then set up a circuit, as shown above ensuring that the ammeter is connected in series to the circuit. I will connect the wire, taped on to the meter rule to the circuit using crocodile clips. Next I will connect the voltmeter in parallel to the circuit.


I will then record the values of potential difference displayed on the voltmeter and the value displayed on the ammeter for this length. I will record these values in a table.


I will move the voltmeter 10cm along the wire within the range of 100 cm (1m) to 10 cm (0.1m). I will record the potential difference and current for each length. Again, the results recorded will be put into a table. I will repeat the experiment three times in order to average my results so I can eliminate any anomalous results and can then calculate my average percentage error.


I will calculate the resistance of wire for each recorded length using the following equation;


I will measure the diameter of the wire using a micrometer so that I can find a value for a mean diameter. I will then use this mean diameter to calculate the cross sectional area of the wire using the following formula;


I will then draw a graph and plot the resistance (on the y axis) against the length (the x axis). I will draw a line of best fit and highlight any anomalous results that I come across. I will use this graph to calculate the gradient (gdt = R/l) and I will then use this gradient to calculate r using the following equation.





To be certain that this investigation will consist of fair tests, I will measure the lengths of constantan with precision. I will keep the current at 0. A, I will keep this the same as if the current is too high, changed it will cause the wire to heat and will affect the resistance of the wire. To keep my errors to a minimum I will use digital ammeters and voltmeters as opposed to analogue meters as digital ammeters are a lot more accurate and are a lot less likely to be effected by human error.


Prediction


I predict that the longer the piece of constantan wire the higher the resistance and he higher the voltage. I think this will happen long wires have more resistance than shorter wires. I think that constantan will have a higher resistivity than copper and so might not make a suitable replacement as telephone wires need to have a low resistance.


Results


Measurement Number Diameter of wire (mm)


1 0.5


0.5


0.5


Average Diameter 0.5


Length of wire (cm) Voltage (x 10G)V Voltage (x 10G)V Voltage (x 10G)V Average Voltage (x 10G)V


10 084 08 08 08


0 16 176 176 174


0 57 6 6 60


40 48 50 50 4


50 47 44 47 4


60 58 58 5 58


70 64 617 64 6


80 71 704 71 710


0 78 74 78 77


100 886 881 881 88


Resistance  I will now calculate the resistance using the formula R=V/I


Length (cm) Formula Resistance 


10 R=8 x 10G/0. R=0.41


0 R=174 x 10G/0. R=0.87


0 R=60 x 10G/0. R=1.0


40 R=4 x 10G/0. R=1.74


50 R=4 x 10G/0. R=.1


60 R=58 x 10G/0. R=.64


70 R=6 x 10G/0. R=.11


80 R=710 x 10G/0. R=.55


0 R=77 x 10G/0. R=.8


100 R=88 x 10G/0. R=4.41


Average Resistance () .


I expect my graph to look something like this;


Graph


I will now draw graph on a separate piece of graph paper and I will use the gradient of my graph to determine whether the resistance that I have calculated above of correct.


Calculations


Using the results that I have recorded I will find the area of my piece of wire and will use the resistivity equation to work out the resistivity of my piece of wire.


A= pr²


= p x (0.18 x 10G) ²


= 1.0 x 10G 7 m²


So


r = (4.4) x (1.0 x 10G 7)


= 4.5 x 10G 7  m


Analysis of Graph


By looking at my graph I can see that as the length increases the resistance increases.


It seems that the length is somewhat proportional to the resistivity ℓ µ .


I have two anomalous results on my graph- these could be explained by errors that may have been made during the experiment e.g. there may have been a temperature change. The wire may not be exactly 1 meter long as not all meter rules measure the same and it is possible that there could be some error of observation of the micrometer both of the actual diameter and the zero reading.


Percentage Errors


I will now calculate my Average percentage errors to see how accurately I have conducted my experiment and to see how I could have improved my experiment


Percentage Errors


Voltage


Voltage (V) (x 10G) Percentage Error


08 1.0/08 x 100= 1.%


174 5.0/174 x 100= .87%


60 .0/60 x 100 = 1.15%


4 1.0/4 x 100 = 0.8%


4 .0/4 x 100 = 0.45%


58 1.0/58 x 100 = 0.18%


6 5.0/6 x 100 = 0.80%


710 6.0/710 x 100 = 0.84%


77 .0/77 x 100 = 0.7%


88 .0/88 x 100 = 0.%


Average Percentage Error 0.84%


Length


Length (cm) Percentage Error


10 0.1/10 x 100 = 1.00%


0 0.1/0 x 100 = 0.50 %


0 0.1/0 x 100 = 0.%


40 0.1/40 x 100 = 0.5%


50 0.1/50 x 100 = 0.0%


60 0.1/60 x 100 = 0.16%


70 0.1/70 x 100 = 0.14%


80 0.1/80 x 100 = 0.1%


0 0.1/0 x 100 = 0.11%


100 0.1/100 x 100 = 0.10%


Average Percentage Error 0.%


By looking at the average percentage errors for length I have noticed that as the length of the wire doubles the percentage error decreases by approximately half.


By taking three readings for voltage and diameter and finding the average I have reduced the percentage error. The use of digital voltmeters and precise equipment such as micrometers I have also reduced the probability of a high percentage error.


Any errors that have been made could be a result of human error e.g. I may not have taken readings from the ruler accurately. They could also be a result of environmental factors for; example there may have been a change in temperature in the room that I was working in, resulting in a difference in the resistance of my wire or even possible expansion or contraction of the ruler. The placement of crocodile clips may also have made a difference to the percentage errors as they were thick and touched more that 0.01 of a mm. I could have reduced the percentage error caused by this by using a jockey, which would have allowed a higher degree of precision. There may also have been some error when observing the measurements on the micrometer, this may have occurred from both the actual diameter and the reading from the zero mark.


Conclusion


I have researched the resistivity of copper in order to compare it with that of constantan and have found it to be 1.6 x 10-6  m. I have worked out the resistivity of constantan out to be approximately 4.5 x 10-7  m, and its actual resistivity is 4.8 x 10-7  m. Therefore constantan has a much higher resistivity than copper. This would not make it a suitable replacement for copper, as it would not be as conductive. Telephone wire needs to have a low resistivity in order for telephone signals to be efficiently carried. Due to its high resistivity, constantan would hinder the flow of these telephone signals and would not be effective or efficient as a carrier of telecommunication signals.





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