Investigating how thickness and length affect the resistance of particular wires

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Essay, Pages 8 (1849 words)

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The equipment that I will need to perform this experiment will be:-

* Battery pack

* 5 Wires

* A volt meter

* An ammeter ( 0-15)

* Crocodile clips

* Ruler

* Nickel chrome wire

Method

The first thing that needs priority when setting up a circuit is safety. I will handle everything with dry hands and take extra care so that I don't short circuit the experiment. The experiments will be investigating the relationship between the thickness of the wire and the length of the wire.

I will connect up a circuit like shown above, the power supply coming from a power pack.

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A volt meter and an ammeter will be placed in series and the wire which I will be investigating, so will be changing, will run in parallel to the ammeter. The set up of the circuit will tell me exactly how much current is going through the circuit. With this information I can put the figures into an equation that will work out how much resistance that particular wire has.

I chose to investigate length and thickness as they are both continuous as opposed to the type of wire which is -----. Once I have got the readings from the ammeter and voltmeter I can put the data into this equation.

Resistance (r) = voltage (v)

Current (i)

I am going to measure the amount of current which passes through six different thicknesses of nickel chrome. The range in thickness which I will use will be based on the standard wire gage (SWG) although the increase of SWG equals a decrease in the actual diameter of the wire. I will use 20, 22, 24, 26, 28 and 30 SWG which is the equivalent of 0.90, 0.71, 0.56, 0.45, 0.37 and 0.31mm in diameter. When coming to plotting a graph I will use the actually diameter as this is exactly how thick the wire is, which is what I'm investigating. For the length I will test ten different lengths of wire, increasing by a set amount each time to make it easier to plot a graph. The range of which I will investigate will be between 10cm and 100cm, the readings I'm going to take will as following. 10cm, 20cm, 30cm, 40cm, 50cm, 60cm, 70cm, 80cm, 90cm and 100cm. I have chosen these readings as they will give me a definate pattern if there is one. Once I have got my results I will retest all of the thicknesses and lengths a further two or three times and then take an average current which passes through each wire. By doing this the results will be a lot more accurate and it may help to identify anomalies in my readings. There are a few things that need to be taken into mind in order for my results to be accurate. The experiment has to be fair so that it is only length or thickness being altered and everything thing else which may affect the experiment is kept constant. These are the procedures I will take in order to make the investigation fair. Read also does length of wire affect current essay

* I will make sure that the same equipment is used in all the experiments so that if there is any different pieces of equipment it will affect all the experiments rather than only some or one.

* In both thickness and length experiments I will use the same type of wire. Other wires will act differently in the same situation.

* The temperature has to be constant as if the experiment gets to hot it will become a limiting factor and not produce true results. To keep the temperature down I will run a reasonably small voltage through the circuit.

* The voltage which will pass through the circuit will be kept constant at 3 volts but might change it for retesting and will be recorded and put into the equation.

* When it comes to changing the length of wire I will simply slid the crocodile clips to the right position so it saves time and allows more things to be constant.

* When experimenting thickness I will keep the length constant at 15cm.

* When experimenting length I will keep the thickness constant at 0.31mm.

* When I retest I will use the same piece of wire which I originally tested.

Preliminary

For my preliminary I chose to investigate the relationship between the three different types of wire. The three wires which I could test were copper, contantane and nickel chrome. I set up a circuit like show on the previous page and tested the wires fairly. I took 15cm of each wire at 0.37mm thick. I took down the ammeter reading=s and put them into the resistance equation. I found from the results that nickel chrome had a resistance of 2 ohms, constantan had a resistance of 1.71 ohms and copper had a resistance so low that it was off the scale. From this I can build a picture in my head of what's happening in the wire. As I illustrated previously the electrons collide with the ions in the wire that the resistance of a wire is about. The copper obviously has either smaller ions or just fewer ions than the other two wires. Constantan is the nest wire up with either small ions or fewer than nickel chrome. I will need to use the nickel chrome wire as it will be easier to record the larger results rather than the small results.

Prediction

I'm going to predict that as the thickness of the wire increases the resistance will decrease. I think this will be the case as the thicker the wire is the larger the diameter is and there fore the room between the ions will be more spread out. This will allow more room for the electrons to pass by. For the length experiment I predict that as the length increases the resistance will also increase. I think this as there are a lot more irons in a longer piece of wire so more electrons will be stopped.

Results

Thickness

Thickness (SWG)

Thickness

(mm)

Results 1

(A)

Results 2

(A)

Results 3

(A)

0.90

1.8

1.85

1.9

0.71

1.45

1.5

0.56

0.15

0.2

0.45

0.85

0.9

0.37

0.65

0.31

0.4

Average

Thickness

(SWG)

Thickness

(mm)

calculation

Average

(A)

0.90

(1.8 + 1.85 + 1.9) ï¿½ 3

1.85

0.71

(1.45 + 1.5 + 1.5) ï¿½ 3

1.48

0.56

(0.15 + 0.15 + 0.2) ï¿½ 3

1.17

0.45

(0.85 + 0.9 + 0.9) ï¿½ 3

0.88

0.37

(0.65 + 0.65 + 0.65) ï¿½ 3

0.65

0.31

(0.4 + 0.4 + 0.4) ï¿½ 3

0.4

To work out the resistance of each wire I am going to put in the average readings into the equation. The voltage was kept constant at 3volts so I'm going to divide 3 by each of the average readings.

Thickness

(SWG)

Thickness

(mm)

Calculation

Resistance

( ) 1dp

0.90

3 ï¿½ 1.85

1.6

0.71

3 ï¿½ 1.48

0.56

3 ï¿½ 1.17

2.6

0.45

3 ï¿½ 0.88

3.4

0.37

3 ï¿½ 0.65

4.6

0.31

3 ï¿½ 0.4

7.5

I have plotted a scatter graph of the results to see if there is a pattern. I am hoping that it will be inversely proportional where as the thickness in mm increases the resistance will decreases.

Length

Length (cm)

Result 1, amps (A)

Result 2,amps (A)

Result 3,amps (A)

1.5

0.85

0.6

0.45

0.4

0.3

0.25

0.225

0.2

100

0.15

Average

Length (cm)

calculation

Average, amps (A)

1.5 x 3 ï¿½ 3

1.5

0.85 x 3 ï¿½ 3

0.85

0.6 x 3 ï¿½ 3

0.6

0.45 x 3 ï¿½ 3

0.45

0.4 x 3 ï¿½ 3

0.4

0.3 x 3 ï¿½ 3

0.3

0.25 x 3 ï¿½ 3

0.25

0.225 x 3 ï¿½ 3

0.225

0.2 x 3 ï¿½ 3

0.2

100

0.15 x 3 ï¿½ 3

0.15

Resistance

Length cm (cm)

Calculation

Resistance ohms ( )

3 ï¿½ 1.5

3 ï¿½ 0.85

3.5

3 ï¿½ 0.6

3 ï¿½ 0.45

6.6

3 ï¿½ 0.4

7.5

3 ï¿½ 0. 3

3 ï¿½ 0.25

3 ï¿½ 0.225

13.3

3 ï¿½ 0.2

100

3 ï¿½ 0.15

17.2

Conclusion

Thickness

Looking at my graph I can say that the resistance of the wire decreased as the wire thickness increased. The graph also shows that the data was not proportion but disproportional as the trend line is a curve rather than a straight line. This tells me that as the wire thickness increased the resistance decreased more and more each time. This is what is called an exponential decrease. Eventually if I made the wire thicker and thicker then there would be an optimum where the thickness wouldn't have any affect on the wire. I think that the reason for the thinner wire having such a high resistance is based on the make up of the wire. The ions in the wire are a lot more tightly packed so there for it is harder for a larger flow of electrons to pass through the wire. When the electrons collide with the ions in the wire energy in the form of resistance and heat is released. When the resistance becomes too great then the heat energy produced from the colliding electrons would eventually melt the wire. This would be the other way round for the thicker wires. The gaps between the ions are a lot bigger so therefore a lot more electrons can pass through the wire with out colliding with any of the ions in the wire. Eventually there will be a thickness where by all the electrons will be able to pass through the wire with out colliding.

Length

I found by looking at my graph that as the length of the wire increased the resistance also increased. The line of best fit tells me that the relationship between the length and resistance is proportional. A few of the shorter readings are slightly out of place being above the line of best fit. I believe that the reason for this is because temperature effected them. In the shorter wires the current goes through the wire more times as it is shorter. This would mean that there would be more collisions between the ions and electrons more frequently. The result of this would be that the wire would get very hot which like I stated in the beginning does affect the resistance.

My graph shows that there is an anomaly; I believe this came from miss reading the ammeter. I was rushing to get results down which sacrificed accuracy. I can see where the result should have been, it is not too far out but it is still wrong. If I could extend this investigation I would have chosen more lengths between 10cm and 100cm as the wires wouldn't be able to stretch much further than a meter. I predict that the resistance would continue increasing as the length increased.

The reason for the resistance to increases as the length increased is because the electrons have to travel further meaning there will be a lot more points where the electrons will be colliding with the ions. I can see that there the results increase at a curtain rate. I have worked out that the average resistance increase is about 1.8 ohms. When working out this calculation I dismissed the reading for 50cm as it was an anomaly.

Evaluation

I personally think that the experiment went very well. The experiment proved what I originally thought would happen. The resistance increased as the thickness of the wire decreased. My results were very good as I seem not to have any anomilious data and they all support my prediction. I think that my results are quite accurate; the only thing that could have been inaccurate was the length of the wire as we had to keep changing the wires over. Even though I made sure I was as accurate as possible the results could have been 6.6% inaccurate due to the plus or minus 1 factor in the measuring.

If I had more time to do the experiment I would have done some more repeat readings as there wasn't enough time to do more than that three sets of results for each thickness of wire. I probably would change the length of wire is I got the chance to redo the experiment. I would make the wire longer, about 50cm or even 100cm. This will reduce the amount of possible inaccuracy as it would go down to 1% or 2%.