How I will make the experiment a fair test:
First of all I will have to control all the other variables and ensure that they remain constant. I will be keeping the current flowing through the circuit constant by monitoring the ammeter which will be used and making sure that the needle is focused on one set unit of current for all three repeats and for all the lengths that will be measured. Material of wire will be kept constant as we will be using the same type of wire for all the lengths that we will be using (we don’t have to worry much about this), this also applies to the cross sectional area of the wire, because we are using the same type of wire for all the experiments. The temperature inside the wire can only be controlled by controlling the current flowing through the circuit; even a decrease in current can cause an increase in resistance and vice versa and so temperatures is kept constant by keeping current constant (mentioned before).
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Prediction – what I expect to happen:
I expect to see an increase in resistance with an increase in voltage as I increase the length of the wire, and similarly a decrease in resistance with a decrease in voltage as the length of wire decreases. I can say quantitatively, that if voltage doubles, resistance will also double. So I expect to see the results being directly proportional between length and resistance.
I can explain this by using the collision theory. When a power supply is connected in a circuit an electric field is set up in the wires. Potential difference (PD) is a property of this electric field. The free negative electrons in the wires experience a force in the electric field and therefore flow down the wire. The stronger the electric field the greater the PD and the greater the force on the electrons causing them to move faster down the wire. If the length of the wire increases, there is a greater distance for the fast flowing electrons to travel. As they move faster through the wire, there are collisions between the electrons and the positively charged ions of the wire and when the fast flowing electrons collide with the ions, it causes resistance.
We can also predict this in a microscopic view. We can say as length increases, then energy converted to heat per unit charge (W) increases as well. And so voltage must also increase as V = W/Q (Q = electric charge), and so if the length of wire is being increased then the voltage is being determined by a higher W and will also increase. And so as V increases, then using the formula; R = V/I, we can say resistance will also increase (by using the collision theory). So I am also predicting a directly proportional relationship between R and length and also predicting that if we double length then V and R will also double.
Apparatus:
* Acknowledgments for the above definitions go to; Wikipedia (encyclopedia).
Method:
I am aiming to take 5 readings for the preliminary results, these are; 20cm, 40cm, 60cm, 80cm and 100cm. I will then be taking three repeats for each length for the voltage for each length. Firstly collect and set up the above apparatus as shown in the diagram:
Start off the experiment by setting the crocodile clips apart by the start length. Length is measured accurately by measuring to the nearest centimeter (cm). Turn on the power supply and control it to make sure that the ammeter displays 0.8A, record the voltage shown by voltmeter. Turn off power supply, remove crocodile clips and replace on same length and repeat the previous steps three times. Do this for the rest of the measurements.
Preliminary results:
Safety:
- When setting up apparatus make sure that the power supply is fully switched off.
- Do not touch the Nichrome wire while the experiment is undergo as it may burn skin.
- Do not turn the power supply too high, otherwise it could result in the fuse blowing.
- While the experiment has commenced do not touch the crocodile clips as you could get a shock.
- Make sure that the Nichrome wire is not so long that it makes contact with another object (e.g. a metallic pen).
Comments on preliminary results:
The results have helped me decide that 0.8A is a good current measurement to use in the real experiment because I get very little voltage variation. This will later ensure accuracy and precision. Also 0.8A is a good measurement because it is not too high current and so will not result in the wire increasing in temperature (due to more resistance).
B. OBTAINING EVIDENCE
These are the results obtained from the experiment.
Please find enclosed on the following page, the graph to represent this data.
C. ANALYSIS
For the results I have recorded three repeats of voltage for each of the lengths and have rounded each numerical value to three significant figures. This I thought was sensible enough to ensure a good degree of precision and reliability (1000th to an ohm).
Fortunately, I managed to steer away from any anomalous results while I conducted the experiment. This has ensured that I have done the experiment with care and responsibility and has also shown that I have used the preliminary results to decide how many lengths and readings to take in a way in which I achieved the above results.
Conclusion:
By forming a graph using my results we can instantly see the relationship between the length of wire and the resistance. It is a positive directly proportional relationship and this is illustrated with the straight red line of best fit that has passed through the origin. It also shows a positive gradient of moderate elasticity (medium steepness) and is also close to 45 degrees (meaning it suggests an almost perfect directly proportional relationship between resistance and length). All the points seem to immensely close to the line of best fit.
Original prediction:
I expect to see an increase in resistance with an increase in voltage as I increase the length of the wire, and similarly a decrease in resistance with a decrease in voltage as the length of wire decreases. I can say quantitatively, that if voltage doubles, resistance will also double. So I expect to see the results being directly proportional between length and resistance.
I can explain this by using the collision theory. When a power supply is connected in a circuit an electric field is set up in the wires. Potential difference (PD) is a property of this electric field. The free negative electrons in the wires experience a force in the electric field and therefore flow down the wire. The stronger the electric field the greater the PD and the greater the force on the electrons causing them to move faster down the wire. If the length of the wire increases, there is a greater distance for the fast flowing electrons to travel. As they move faster through the wire, there are collisions between the electrons and the positively charged ions of the wire and when the fast flowing electrons collide with the ions, it causes resistance.
We can also predict this in a microscopic view. We can say as length increases, then energy converted to heat per unit charge (W) increases as well. And so voltage must also increase as V = W/Q (Q = electric charge), and so if the length of wire is being increased then the voltage is being determined by a higher W and will also increase. And so as V increases, then using the formula; R = V/I, we can say resistance will also increase (by using the collision theory). So I am also predicting a directly proportional relationship between R and length and also predicting that if we double length then V and R will also double.
Now I can compare my prediction to my results. In my prediction it states that resistance will increase as length increases, which are precisely what has happened in my results. I can conclude that if length increases, resistance shall also increase. And we can now take figures from the graph to prove this; 20cm length gives us 0.965Ω but 60cm length gives us 2.601Ω. We also have another trend. If we double length from 20cm to 40cm we get 1.791Ω. This is almost double the 20cm resistance, so the proportionality is very direct that it proves my results only show a very small margin of error. I also stated that even voltage increases with resistance and this too has been proven; 0.772 average voltages for 20cm length and 0.965Ω, to 1.433 average V for 40cm length and 1.791Ω, we also see that the average voltage has also doubled as the length has doubled. This proves my point about voltage and resistance doubling as length doubles.
Collision theory; The reason why if we double the length we get a doubled resistance is because the negative electrons must travel double the length and so there is double the chances of a collision and so increases the resistance by twice as much.
D. EVALUATION
Quality of observations:
Generally, the accuracy for all the observations seem very consistant and reliable. This is because all my results have shown very little percentage error:
We see there is only such a slight % error from the results, with the highest being at 2.4%. I also get the feeling that as length increases; the variation in results also increases. This may be due to the fact that as the wire is longer, then electrons have different possibilities of successfully colliding rather than in a short wire where the length is not so great, and then the electrons are in a much more squashed area and so there is a lower possibility for the number of collisions each one will have. However, due to this I acquired no anomalous results.
Improvements:
There were several flaws in accuracy due to limitations in the apparatus. Firstly, the Nichrome wire which we used was not perfectly straight and so we would have made measuring errors while conducting the experiment for each length, which gave us systematic errors (even though we estimated it was straight, we cannot guarantee perfect accuracy). But also when we re-positioned our crocodile clips to measure the other runs. It is almost impossible to position them in the exact same place as we did the first time, so we would get a slightly different length for each run of that particular measurement value which gave us random errors. Also with the ammeter, I am sure that I didn’t always look at it directly from the top so that the position of the needle so we couldn’t make sure it remained constant at 0.8A for all the experiments, which provided us with parallax errors.
So next time, I am thinking of using an additional partner just to make sure the current on the ammeter is being kept constant, as for us we rushed the procedure of keeping the current constant so the quality of how the experiment was conducted was not so great. Also instead of using Nichrome wire which we had to use from our preliminary experiments, I will take a fresh wire sample and use that for the main experiment, so we can eliminate systematic errors. Also next time we can mark on the wire exactly where the crocodile clips have been positioned the first time, so we can get a much better degree of accuracy when positioning the second time in hope to not get random errors. But my results were still very good even if we take this into account so there is really not much I can do to make it better next time.
Reliability of conclusion:
The evidence which has been acquired is satisfying enough to support a firm conclusion. This is because the graph clearly showed a line which was directly proportional (as I predicted as well) and there were no anomalies to be found in any of the results. Even though I did get very minor errors before this has obviously shown very little. The graph has shown very little scatter and also I explained earlier how there is very little change in variation. However we cannot safely say that however, we do not have enough evidence to say whether length is directly proportional to length as this is just one experiment, so we need to do other experiments to confirm this theory.
We can do further work and justify the experiment further by using more sophisticated equipment to ensure more accuracy for more reliable results. We could do other investigations such as; using a different thickness of wire and a different material of wire (to see if the same results apply to copper wire). We can also use a different current instead of 0.8A or actually use a larger wire with different measurements.
