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 different 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 requires 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 of it 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; they are the 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.

RESEARCH QUESTION

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?

HYPOTHESIS

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]

VARIABLES

Independent Variable

Dependent Variable

  
Length of the nichrome wireResistance of the nichrome wire
  
The experiment will work with 5 sets of nichromeEach wire will be measured with an ohmmeter of
wires, starting from the length of 10 cm, addeda multimeter with an uncertainty of ±0.01Ω
with increments of 10cm. The lengths of each wireaccurately by clipping the probes of the ohmmeter
will be measured in cm with a 30 cm ruler with anto 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 wireDifferent materials have differentThe 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 
 dangerous. 
   
Diameter of wireA diameter of a wire is one of the factorsThe diameter of the wire that will
 that could affect a wire’s resistance forbe used throughout the entire
 there will be more room available for theexperiment will be kept exactly
 electrons to flow through, which wouldthe same, that is 0.315 mm.
 result in less resistance. Keeping the 
 diameter of the wires constant would 
 result in a fair experiment 
   
TemperatureWorking in different temperatures canThe temperature will be kept at
 affect the resistance of the wire becauseroom temperature, which can
 the higher the temperature, the higherbe done by simply doing the
 the resistance of the wire since it causesexperiment in one room, within
 the electrons will move faster due to anthe same period of time. The
 increase in energy, resulting in moreexperimenters should also avoid
 collision with the atoms, thus moreusing any light, such as a torch,
 resistance.for it can be a source of heat.
   
Power supply voltageThe power supply has to be kept theThe voltage will kept as 1.5 V,
 same as the voltage and current sentand the current would change
 depends on it; the higher power supplydepending on the voltage.
 voltage, the more voltage and current will 
 be sent to the wire, which would affect 
 the resistance. 
   

 

MATERIAL AND APPARATUS

Materials

Size

Quantity

Uncertainty

    
Nichrome wire150cm1 
    
Scissors1 
    
Digital multimeter1±0.01cm
    
Positive and negative multimeter probes2 
    
Ruler30cm1±0.05cm
    
Sandpaper 1 
    

EXPERIMENT DESIGN SETUP WITH CLEAR LABELS

  1. Put on safety goggles, lab coat, gloves and masks for safety.
  2. Handle all materials carefully.
  3. Have a clear and clear working space for the experiment.
  4. Do not consume any of the materials used, and keep them away from eyes.
  5. Complete all trials in the same area/room, in the same time of the day, using the same materials.
  6. Clean up lab area after experiment.
  7. Wash all materials thoroughly with warm water and soap after experiment.

EXPERIMENT METHOD/PROCEDURE

  1. Gather materials and set up the circuit as shown in the experiment diagram above.
  2. 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.
  3. Get 150cm of nichrome wire and scrap or rub it with sandpaper in order to make it conductive.
  4. Cut the wire with scissors into 5 separate wires with measurements of 10, 20, 30, 40 and 50cm.
  5. Measure each wire by putting the points of both probes to the edges of the wires, and measure them four times/trials each.
  6. Record the resistance reading from the multimeter of each of the 5 wires.

RESULTS

Recorded Resistance for 5 Different Lengths of Nichrome Wire

 Independent   Dependent          
 Length ofThe amount of the resistance of wire of 5 different lengths      
 nichrome wire      
               
No.unit: cm   unit: Ω          
 inst. uncertainty: instrument uncertainty: ±0.01 Average      
         
   uncertainty      
 ±0.05cm           
 Trial 1Trial 2Trial 3Trial 4Average(max-min)/2      
       
        
           lowest  
110.003.503.503.503.403.48    
 0.05  average  
            error  
220.004.404.504.704.704.580.2  
       
                
330.006.507.006.607.907.000.7       
  highest 
            
440.007.807.007.507.787.78    
 0.9  average 
            error   
550.008.407.008.608.488.480.6  
       
                

 

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 increase, 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 datas for the length of wires (independent variable) were 10cm to 50cm with an increment of 10cm between each wire, while the resistance (dependent variable) seemed to display a lowest data of 3.48 Ω and a highest data of 8.48 Ω, which seems to fit well with modelled 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 modelled best fit line as errors did occur along the experiment, as displayed by the rather large error bars over the datas. 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 datas, the datas 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 an positive correlation in the increase in resistance in 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 has 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 (specially 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 inconsistentThe wires that were used for theAfter looking at jewellery crafting
form of the wireexperiment were all cut from a long rolltutorials, I have discovered a method
 of nichrome wire, and because theyof straightening wires, which was to
 have been rolled for a significanthold them on the other edge while
 amount of time and due to their stiffthe other hand that is pulling the wire
 form, it was hardly possible toout from the roll/coil straightens it
 completely straighten the wires. Sowith heat and a strong pinch, which
 because the wires were still ratherwould require gloves, and that was
 coiled up, the experimenters were notsomething we did not do. Therefore,
 able to get the precise measurementsthe 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 ofThe wires were measured and cutIt would have been much easier if
measurements ofmanually, with a ruler and scissor, andwe straightened the wires
wire lengthsbecause it was done manually bybeforehand so we could simply tape
 humans, human errors were inevitable,the wires unto the ruler, and carefully
 causing us to not being able toobserve the measurements then.
 measure the wire exactly using the wireHowever, because the wires were
 since the wire kept moving, and thewiggly and curvy, we had to
 measurements depended on our viewestimate the measurements. The
 of the ruler, which would make thecuttings 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 ofThere was an inconsistent use ofNext time, the experiments should 
making the wiresmaterials throughout the experiment,think the steps through and cut 
conductiveone of which was the rubbing of thethem into one whole 150cm wire, 
 wires with the sandpaper, which was aand rub the entire thing with the 
 crucial step as it would result in bettersame sandpaper in the same time, 
 and consistent reading. However,but the same person, all at once, so 
 because the experimenters did notthe wires have the same amount of 
 think this through, we cut the wire fromconductivity even when they are 
 the rolled coil one by one and rubbedlater cut into smaller pieces of 
 them separately, which means some ofdifferent 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  
 mentioned previously.  
    

 

BIBLIOGRAPHY

  • “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/]

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