INTRODUCTION AND BACKGROUND THEORY
When electrons travel through wires or other external circuits, they travel in a zigzag pattern that results in a collision between the electrons and the ions in the conductor, and this is known as resistance. The resistance of a wire causes difficulty for the flow of the electrical current of a wire to move and is typically measured in Ohms (Ω).
George Ohm discovered that the potential difference of a circuit corresponds to the current flowing throughout a circuit and that a circuit sometimes resists the flow of electricity. The said scientist hence came up with a rule for working out resistance, shown on the image on the side:
Resistance is an important factor to pay attention to because, one, an overly-high resistance can cause a wire to overheat due to the friction that is caused when the electrons move against the opposition of resistance, which is potentially dangerous as it could melt or even set fire. It is therefore important to take note of the resistance when dealing with wires to supply power to a device or so.
A real life application would be a toaster where the wires are sized to get hot enough to toast bread but not enough to melt.
Secondly, resistance can also be used a very useful tool that enables you to control certain things. An example from the real-life world would be LED lights that require a resistor to control the flow of the electrical current to prevent getting damaged by high electrical current. Another example would be the volume control on a radio where a resistor is used to portion out the signal, which allows you to control the volume level.
It is clear now that resistance is an important attribute that has been applied to many forms of technology to perform a useful function, and this experiment aims to see how we can control it. The resistance of a wire varies according to the four factors of the wire; are temperature, material, diameter/thickness, and length of the wire.
This experiment will be focusing specifically on that last factor – length – and investigate just how much of a role a length of a wire would have on its electrical resistance by using a range of wire lengths to test with.
How does changing the length of a nichrome wire with a diameter of 0.315 mm – cut into measurements of 10cm, 20cm, 30cm, 40cm and 50cm — affect the electrical resistance generated within the nichrome wires that can be captured by an ohmmeter while keeping the temperature and the location of the experiment controlled?
If the length of nichrome wire is increased by an increment of 10cm starting from 10cm in length, then the graph measuring the electrical resistance of the wires will observe a positive slope with the mathematical function of y = mx that displays the increasing amount of resistance generated.
REASON FOR HYPOTHESIS
Doubling a length of a wire is just like having two of the shorter wires in series. If one short wire has a resistance of 1 ohm, then 2 shorts wires would have a resistance of 2 ohms when connected in series.
A longer wire also means that it would have more atoms, which means it will be more likely for moving electrons to collide with them; hence, higher resistance. For instance, a 10cm wire has 5 atoms, a 20cm wire has 10 atoms. If say 5 electrons try to pass through those two wires, the chances of them bumping into atoms are higher in the 20cm wire than the 10cm one. Therefore, the longer the wire, the higher the resistance.
Source: “Resistance” Physics Classroom. The Physics Classroom, n.d. Web. May 8. 2018. [http://www.physicsclassroom.com/class/circuits/Lesson-3/Resistance]
|Independent Variable||Dependent Variable|
|Length of the nichrome wire||Resistance of the nichrome wire|
|The experiment will work with 5 sets of nichrome||Each wire will be measured with an ohmmeter of|
|wires, starting from the length of 10 cm, added||a multimeter with an uncertainty of ±0.01Ω|
|with increments of 10cm. The lengths of each wire||accurately by clipping the probes of the ohmmeter|
|will be measured in cm with a 30 cm ruler with an||to the edges of the nichrome wires that are to be|
|uncertainty of ±0.05cm and will be as follows: 10,||tested.|
|20, 30, 40, 50.|
|Controlled Variables||Impact if not controlled||How to control|
|Material of wire||Different materials have different||The material of wire that will be|
|resistances; some are better conductors,||used throughout the entire|
|meaning they have more free electrons,||experiment will be kept exactly|
|thus having less resistance.||the same, that is nichrome wire.|
|Materials also have different heating|
|point. Some heat up easier than others|
|after use, which could potentially be|
|Diameter of wire||A diameter of a wire is one of the factors||The diameter of the wire that will|
|that could affect a wire’s resistance for||be used throughout the entire|
|there will be more room available for the||experiment will be kept exactly|
|electrons to flow through, which would||the same, that is 0.315 mm.|
|result in less resistance. Keeping the|
|diameter of the wires constant would|
|result in a fair experiment|
|Temperature||Working in different temperatures can||The temperature will be kept at|
|affect the resistance of the wire because||room temperature, which can|
|the higher the temperature, the higher||be done by simply doing the|
|the resistance of the wire since it causes||experiment in one room, within|
|the electrons will move faster due to an||the same period of time. The|
|increase in energy, resulting in more||experimenters should also avoid|
|collision with the atoms, thus more||using any light, such as a torch,|
|resistance.||for it can be a source of heat.|
|Power supply voltage||The power supply has to be kept the||The voltage will kept as 1.5 V,|
|same as the voltage and current sent||and the current would change|
|depends on it; the higher power supply||depending on the voltage.|
|voltage, the more voltage and current will|
|be sent to the wire, which would affect|
MATERIAL AND APPARATUS
|Positive and negative multimeter probes||–||2|
EXPERIMENT DESIGN SETUP WITH CLEAR LABELS
- Put on safety goggles, lab coats, gloves and masks for safety.
- Handle all materials carefully.
- Have a clear and clear working space for the experiment.
- Do not consume any of the materials used, and keep them away from the eyes.
- Complete all trials in the same area/room, at the same time of the day, using the same materials.
- Clean up the lab area after the experiment.
- Wash all materials thoroughly with warm water and soap after the experiment.
- Gather materials and set up the circuit as shown in the experiment diagram above.
- Set the multimeter into ohmmeter, and connect the red probe to the output that says COM and the black probe to the output that has the mAVΩ label.
- Get 150cm of nichrome wire and scrap or rub it with sandpaper in order to make it conductive.
- Cut the wire with scissors into 5 separate wires with measurements of 10, 20, 30, 40 and 50cm.
- Measure each wire by putting the points of both probes to the edges of the wires, and measure them four times/trials each.
- Record the resistance reading from the multimeter of each of the 5 wires.
Recorded Resistance for 5 Different Lengths of Nichrome Wire
|Length of||The amount of the resistance of wire of 5 different lengths|
|No.||unit: cm||unit: Ω|
|inst. uncertainty:||instrument uncertainty: ±0.01||Average|
|Trial 1||Trial 2||Trial 3||Trial 4||Average||(max-min)/2|
SAMPLE CALCULATION OF PROCESSED DATA
Average data no. 3: (6.50+7.00+6.50+7.90) ÷ 4 = 6.98 Average uncertainty data of no. 3: (7.90-6.50) ÷ 2 = 0.70
GRAPH (based on average data)
CONCLUSION & EVALUATION
The graph shows an increasing linear trend-line with the mathematical function of Y = 0.132X + 2.3, which displays a positive correlation as seen in the line that goes above and to the right, which indicates positive values, as well as the gradient that displays a positive value. The graph also has an identified slope or gradient of 0.132.
This unit for this gradient is ohm/cm, and the gradient represents the rate of the overall increase in the dependent variable as the independent variable progresses. The slope reveals that when the length of a wire is increased, the resistance would go up by an approximate measurement of 1.25 Ω, which could be proven by the calculation of the graph where all the average was calculated from the average increments of each wire — (0.7+0.78+2.42+1.1)÷4=1.25.
Another aspect from the mathematical function that can be identified is the Y intercept which was 2.3, and it represents the average resistance (dv) of the first data of the independent variable, which was 3.48 Ω.
The data for the length of wires (independent variable) was 10cm to 50cm with an increment of 10cm between each wire, while the resistance (dependent variable) seemed to display the lowest data of 3.48 Ω and the highest data of 8.48 Ω, which seems to fit well with modeled best fit line graph, which is visibly supported by the coefficient determination (R2) which states that the best-fit line fits the scattered data by 94.98%
The data does not perfectly fit the modeled best fit line as errors did occur along with the experiment, as displayed by the rather large error bars over the data. The maximum error bar that can be identified there is the 4th independent variable, which was the 40cm wire, and the minimum error bar was located in the 1st data, which was the 10cm wire.
Two data of the largest errors went way above the predicted line, which from it we can infer that the collected data is considered to have an inconsistent precision. When coming to measure those two data, the data gained from each trial were very inconsistent, which was presumably caused by the inconsistent rubbing with sandpaper, which will be further elaborated in the suggestions for improvements.
The pattern on the graph supports the hypothesis of the experiment which predicted that if the length of the wire increased, the resistance measured would increase as well, the graph will observe a positive gradient with the mathematical function of y = mx + c which is supposed to display the increasing amount of resistance.
This was proven and supported by the trend-line in the graph which basically shows a positive correlation in the increase in resistance at the same rate as the independent variable increases, which is just as the hypothesis predicted. The graph also manifested a positive mathematical function of y = 0.132x + 2.3 with a positive gradient (0.132x) as well.
There is, however, a scientific explanation behind all this. It has been a known fact that the length of a wire is one of the four factors that have a role in the resistance of the wire, and this experiment has simply confirmed it.
The logical explanation would be that a longer wire also means that it would have more atoms, which means it will be more likely for moving electrons to collide with them; hence, higher resistance. For instance, a 10cm wire has 5 atoms, a 20cm wire has 10 atoms. If say 5 electrons try to pass through those two wires, the chances of them bumping into atoms are higher in the 20cm wire than the 10cm one. Therefore, the longer the wire, the higher the resistance.
In conclusion, the experiment was a successful investigation that successfully answers the research question of how basically changing the length of a wire (especially a nichrome wire with a diameter of 0.315 cut into measurements of 10cm, 20cm, 30cm, 40cm and 50cm) could affect the electrical resistance generated within the wires.
The investigation has concluded that there is a clear relationship between the length and the resistance of a wire and that the former does in fact affect the latter.
EVALUATION AND SUGGESTIONS
|Random Error||Description (Significance of Error)||Suggestion of Improvement|
|The inconsistent||The wires that were used for the||After looking at jewellery crafting|
|form of the wire||experiment were all cut from a long roll||tutorials, I have discovered a method|
|of nichrome wire, and because they||of straightening wires, which was to|
|have been rolled for a significant||hold them on the other edge while|
|amount of time and due to their stiff||the other hand that is pulling the wire|
|form, it was hardly possible to||out from the roll/coil straightens it|
|completely straighten the wires. So||with heat and a strong pinch, which|
|because the wires were still rather||would require gloves, and that was|
|coiled up, the experimenters were not||something we did not do. Therefore,|
|able to get the precise measurements||the next time we work with wires, it|
|of the wires.||would be a good idea to ensure that|
|they are straight when they are still|
|fresh from the roll with the aid of|
|tutorials from the internet to know|
|how to straighten them properly|
|Systematic Error||Description (Significance of Error)||Suggestion of Improvement|
|Inaccuracy of||The wires were measured and cut||It would have been much easier if|
|measurements of||manually, with a ruler and scissor, and||we straightened the wires|
|wire lengths||because it was done manually by||beforehand so we could simply tape|
|humans, human errors were inevitable,||the wires unto the ruler, and carefully|
|causing us to not being able to||observe the measurements then.|
|measure the wire exactly using the wire||However, because the wires were|
|since the wire kept moving, and the||wiggly and curvy, we had to|
|measurements depended on our view||estimate the measurements. The|
|of the ruler, which would make the||cuttings were also not precise since|
|measurements even more unstable.||we couldn’t mark the wires on|
|where exactly to cut.|
|Systematic Error||Description (Significance of Error)||Suggestion of Improvement|
|Inconsistency of||There was an inconsistent use of||Next time, the experiments should|
|making the wires||materials throughout the experiment,||think the steps through and cut|
|conductive||one of which was the rubbing of the||them into one whole 150cm wire,|
|wires with the sandpaper, which was a||and rub the entire thing with the|
|crucial step as it would result in better||same sandpaper in the same time,|
|and consistent reading. However,||but the same person, all at once, so|
|because the experimenters did not||the wires have the same amount of|
|think this through, we cut the wire from||conductivity even when they are|
|the rolled coil one by one and rubbed||later cut into smaller pieces of|
|them separately, which means some of||different lengths.|
|the wires were rubbed in more areas|
|than others, or rubbed more evenly|
|than others, or the other many possible|
|errors. This was what resulted in the|
|large error bars of those 2 datas|
- “Potential Difference” BBC – GCSE Bitesize. BBC, Sep 15. 2006. Web. May 8. 2018. [http:// bbc.co.uk/schools/gcsebitesize/design/electronics/calculationsrev1.shtml]
- “Resistance” Physics Classroom. The Physics Classroom, n.d. Web. May 8. 2018. [http:// physicsclassroom.com/class/circuits/Lesson-3/Resistance]
- “Resistance and Resistivity” N.p., n.d. Web. May 8. 2018. [http://resources.schoolscience.co.uk/CDA/16plus/copelech2pg1.html]
- “Resistance: Chapter 1 – Basic Concepts of Electricity” All About Circuits. EETech Media, LLC, n.d. Web. May 8. 2018. [https://www.allaboutcircuits.com/textbook/direct-current/chpt-1/resistance/]