## 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.

## 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]

## EXPERIMENT DESIGN SETUP WITH CLEAR LABELS

1. Put on safety goggles, lab coats, 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 the eyes.
5. Complete all trials in the same area/room, at the same time of the day, using the same materials.
6. Clean up the lab area after the experiment.
7. Wash all materials thoroughly with warm water and soap after the 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

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

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/] Inline Feedbacks  