Charge (Q), flow (V) and resistance (R) are all linked, which is demonstrated by the fact that when current is decreased, resistance increases. We know the following formulae:
I=Q/T and R=V/I
This shows me that if the charge changes then the current will change. Therefore the resistance will change because to calculate resistance I use the current (i.e. if the current decreases than the resistance will increase).
There are many factors which affect the amount of resistance:
Length: If I increase the length of the wire, the resistance increases: the longer the wire the more resistance. This is because it takes longer for the electrons to flow through the wire… as explained earlier the more atoms there are in the electrons’ way, the harder it is to get through which increases the resistance of the wire.
Temperature: The higher the temperature, the higher the resistance. As with all metals, when their temperature increases they begin to vibrate more side to side. As a result, they get in the way of the electrons which makes it harder for them to get through which consequently increases the resistance of the wire.
Cross sectional area (thickness): The cross sectional area of a length of wire is inversely proportional to its resistance – when the cross sectional area is doubled, the resistance is halved. This is because there are more electrons to carry the current. It works like a hose – the wider the hose is, the easier and faster water passes through it.
If one was looking to use a piece of wire with the optimum (least) amount of resistance the wire would be thick, as short as possible and as cold as possible.
For this investigation, as mentioned in the aim, I have chosen to investigate what effect the length of the wire has on the resistance thereof. I chose this as my variable because it is by far the easiest to measure – all the other factors are relatively difficult to work with, harder to control and may produce inaccurate results.
Hypothesis: Because I am using copper wire as a resistor, when I increase the length of the wire the resistance should work how resistors in series work. This means that when I increase the length of wire (or add a piece in a series circuit) the resistance should increase too. Due to the increase in the number of atoms and ions between the two terminals it takes the electrons longer to get from one side to the other. For example if I double the length of the wire the resistance will double and the current will halve. My graph at the end should look something like this:
The length of wire and resistance should be directly proportional to each other.
Equipment:
-2 1.5V cells
-Metre ruler
-Copper wire
-Voltmeter
-Ammeter
-Wiring
-Crocodile clips
Method:
First I decided upon the type of wire I was going to use (copper), I made sure it was the same thickness each time I took readings because as aforementioned, if the cross sectional area is not kept constant, it will definitely affect the resistance and thus make my results inaccurate. Then I measured it to 100cm by laying it across a metre ruler, because this way I can be accurate to the millimetre.
I then hooked the 2 cells up to the copper wire stretched across the metre ruler using my wires and crocodile clips. I connected the two terminals on the metre ruler 40cm apart. For this experiment I will take readings for p.d (potential difference) and the resistance using an ammeter and a voltmeter at distances ranging from 40cm to 100cm – I will take measurements in 5cm intervals (i.e. take measurements from 40cm, 45 cm and so on so forth). I made sure that the voltmeter and ammeter were set up in PARALLEL not series as this would damage them. Below is a diagram of my apparatus and how I set it up:
And the (simple) schematic of the circuit:
In this experiment I will keep all things constant (apart from the length of wire). I will keep do all my measurements in one day in a short space of time in the same room away from the windows (out of the sun) so the temperature does not change noticeably while I am carrying out the experiment, as this would affect my results and make them inaccurate. Also, when charge flows through the wire and there is resistance, it generates heat in the wire. I will keep the power on the wire for the least amount of time and take my readings quickly so the temperature does not affect my results. In addition to this I will also wait a minute after each reading so that the wire cools to room temperature again and my results are accurate. In theory the graph-line should be straight – if it isn’t then it indicates that there is another variable.
The other constant is the cross sectional area of my wire – this is fairly easy to keep constant – just use the same piece of wire. I have to keep this the same because cross sectional area of wire is proportional to the resistance – if I do not keep it the same it will also make my results inaccurate. I will take readings from each distance 3 times and take the average of those, so I can greatly decrease the chances of getting an anomalous result.
Results: Here is the results table followed by a graph representing each of the 3 – p.d, Current and then resistance.
And finally, to calculate the resistance I used the ohm’s law formula of R=V/I.
Analysis:
My experiment was very successful and the results I got proved to be quite accurate and precise. Therefore my graphs and result tables provide me with a base to understand just why length affects the resistance. My prediction was that “when I increase the length of wire the resistance should increase too”; my prediction is supported by my results - and appears to be correct. The graphs and tables prove that the longer the copper wire, the higher the resistance. Resistance is also linked to charge flow, if I change the charge flow it will have an affect on the equation I = Q/t. If the current is changed then this will have an affect on the resistance. So with the help of the formulae I=Q/t and R=V/I, I now know that if I increase the charge flow, the current increases and the resistance decreases. Consequently if I double the length of wire the equation I = Q / t will be halved (due to the time increasing) causing the current to be halved and the resistance to be doubled. I can see one anomalous result in the ‘Current’ graph, which is at a length of 80cm – it appears to be at a slightly lower current than it should be in relation to the others.
Evaluation:
Using my results and my graphs I can clearly tell that my experiment was successful, I can tell this because, generally, none of my results have any inconsistent results and my graphs show straight lines. Even after repeating my experiment many times my graphs still remained just as precise and the graph showing the average results of the experiment is a perfect straight line. The fact that I got the similar results each time I did the experiment suggests that is was successful and also reliable, thus I must have carried out the experiment well.
The way in which I conducted the experiment was good because I made sure that the voltage supplied to the wire was equal each time, the cross sectional area of the wire remained the same, and also that the wire cooled down between each result. The use of mm instead of cm made sure that the length was exact and not longer or shorter. Therefore my results were successful and reliable for us to work from. However this did not mean that the way in which I did the experiment couldn’t have been improved. Having to secure the wire so as to measure the length meant that it was difficult to attach the crocodile clips to exactly the end of the wire. I could not be sure that as I left the wire to cool it was not at a different temperature each time I begun again; this could have affected my results if it had been vastly different.
In my experiment, I could also have investigated a number of other things, such as the effect of cross sectional area or temperature on the resistance. If I had looked at the effect that the cross sectional area had on resistance I would probably discover that as the wire doubled in cross sectional area the resistance would halve. This would be due to there being twice as many electrons - the current would travel a lot quicker and thus decrease the resistance. If I looked at how temperature affected resistance I would probably find that as the temperature of the wire increases, the particles within begin to vibrate much more because they have some extra energy, therefore it is much harder for the electrons to move through and thus the resistance will rise. So instead of just investigating how length affected the resistance of a piece of wire I could also have investigated the affect of temperature or cross sectional area on the piece of wire.
