An Investigation Into the Resistance of a Wire - GCSE Physics Coursework
In this article I will investigate what affects the resistance of a wire.
Electricity flows in metals. Metal wires are made of millions of tiny metal crystals, and each crystal’s atoms are arranged in a regular pattern. The metal is full of "free" electrons that do not stick to any particular atom; rather, they fill the space between the atoms. When these electrons move, they create an electric current.
Conductors have resistance, but some are worse than others. The free electrons keep bumping into atoms. A wire's resistance depends on four main factors:
- Length of the wire
- Cross-sectional area
- Temperature of the wire
I will investigate how the length of the wire affects the resistance. I have done a preliminary experiment to help me decide the best way to do my investigation. The results will help me make predictions, as well.
Below are my results from the preliminary experiment (see Table 1). To ensure accuracy, I have taken three readings each of volts and current.
Table 1: Preliminary Results
These results show that as the length of the wire increases, the resistance increases, as well. Furthermore, if you double the length of the wire, the resistance is roughly doubled. For example, when the length of the wire is 20cm the resistance is 3.14 ohms; when the length of the wire is 40cm the resistance is 6.18 ohms, which is roughly double. In my main investigation I will see if this observation applies to my results.
I found that the apparatus I used was suitable, but I think that I could possibly increase the number of data points to generate more reliable results, perhaps by increasing the length of the wire by 5cm each time, instead of by 10cm.
Investigating the Resistance of a Wire
I will investigate the resistance of a wire in relation to its length.
I predict that the longer the wire, the larger the resistance. This is because the free electrons in the wire bump into more atoms, thereby making it harder for electricity to flow. Similarly, the shorter the wire, the smaller the resistance because there will be fewer atoms for the electrons to bump into, thereby easing the flow of electricity. Furthermore, the resistance of a wire is directly proportional to the length and inversely proportional to the area, so doubling the length of a wire should increase the resistance by a factor of two. This is because if the length of the wire is doubled, the electrons bump into twice as many atoms, so there will be twice as much resistance. If this is correct, the graph should show a positive correlation.
The apparatus I will use in this experiment is as follows:
- 1 ammeter (to measure current)
- 1 voltmeter (to measure voltage)
- 5 x wires
- 2 crocodile clips
- Power pack
- 100cm nichrome wire
First, I will collect the apparatus I need and set it up as shown in Diagram 1, below. Next, I will set the power pack on the lowest voltage possible to ensure that the current passing through the circuit isn't too high (which could potentially affect the results because the wire would get too hot).
I will place one crocodile clip at 0cm on the wire and the other at 5cm to complete the circuit. I will then turn the power pack on and record what voltmeter and ammeter readings. I will switch off the power pack, move the crocodile clip that was at 5cm up to 10cm, and switch on the power pack. Again, I will record the voltmeter and ammeter readings and turn off the power pack. I will repeat this method every 5cm until I get up to 100cm, taking three readings from both the voltmeter and ammeter each time to ensure accuracy. In addition, after each reading I will switch the power pack off to ensure that the wire doesn’t get too hot and affect my results.
Diagram 1: Apparatus
To ensure accuracy I will record the voltage and the current three times every 5cm and take the average reading. This will reduce the chance of false readings and will cancel out any anomalous results. I will also ensure that the wire does not heat up too much by confirming that I do not set the voltage too high on the power pack and by maintaining the same the voltage for every reading. In addition, I will make sure I turn the power pack off after each reading. I will try to make this investigation as accurate as possible.
There are different variables that can be changed in this experiment; these are the independent variable. However, due to my line of enquiry, I will only change the length of the wire. The variables I will control will be the type of wire (resistivity) and the cross-sectional area of the wire. I will also control, using the power pack, how many volts pass through the wire. Below is a table illustrating the effect of changing the variables (see Table 2):
Table 2: Variables
I will ensure experimental safety by confirming that all the wires are connected properly and that none of the insulation on the wires is worn. I will also ensure that there is a clear indication that the power is isolated by means of a switch and an L.E.D. I will stand up during the investigation to ensure that I do not injure myself if something breaks.
Below is a table of my results (Table 3). I have taken three reading and have worked out the average, shown in red.
Table 3: Results
Table 4: Length & Resistance
Table 3 shows that as the length of the wire increases, the resistance increases, as well. This confirms the first part of my prediction: that the longer the wire the larger the resistance.
In addition, my prediction that doubling the length of the wire increases the resistance by a factor of two is correct (see Table 4).
Graphing these results shows a nearly straight line, illustrating a strong positive correlation between length and resistance, which is consistent with my prediction.
Overall, my results are very consistent with my predictions. Most of the data points were on, or very close to, the line of best fit. There are a few data points that are farther away from the line of best fit than the others, but they are still consistent with the general trend. There are no anomalous results that I would consider to be far away from the line of best fit.
There are possible sources of error that might have led to inconsistent results, such as a kink in the wire. This would have prevented the area of the wire from remaining constant and would have affected my results. However, I made sure that the wire remained straight throughout the experiment.
I think that the range of my results was sufficient enough for me to draw a valid conclusion about how the length of the wire affected the resistance. This was because I could plot a graph and show the general trend.
I think that the pattern/general trend would continue beyond the range of values I used. However, I think that unless I had specialist equipment the results would be distorted because the wire would eventually get very hot. Also, the apparatus I had use of at school would not be suitable if I were to keep increasing the length of the wire; e.g., in a classroom environment I could not increase the length to more than 150cm because of safety concerns as well as space constraints.
I think my method could have been improved to produce results that were even more consistent. I could have considered using a new piece of wire each time in order to regulate the temperature more stringently. Using the same piece of wire throughout the experiment meant its temperature rose slightly over time, which may have affected my results. However, using new pieces of wire each time would have been too impractical and time-consuming in the context of this lesson. Overall, I think my method was sufficient to obtain reliable results.
To support my prediction and conclusion, I could do further experiments. For example, I could use different types of wire instead of using only nichrome. I could also consider using different cross-sectional areas of wires or even change the temperature of the wires deliberately and see how manipulating these variables affect the resistance of the wire.