4. Measure the resistance of one slice of apple three times. Record the values.
5. Repeat step 4 with the remaining slices of apple.
Preliminary trials
For our preliminary trial we first cut the apples before the lesson started. Using the multimeter, we measured its resistance during class.
Data:
Modifications
The results we obtained were non-precise and irregular, so the graph plotted is not linear. From the graph before it is obvious that there is little correlation and the error uncertainty associated with the results is very large.
As mentioned before, we chopped up the apples into slices a long while before measuring its resistance, so the moisture in the slices of apples would have evaporated, making the amount of water in each slice of apple different and hence producing inaccurate results. To reduce this we will only cut the apples before measuring its resistance. This might improve the results by making sure that the apples are still fresh and full of moisture when it is being measured.
Also while we were conducting our preliminary trial, we discovered that the resistance for one slice of apple varied. To minimize this effect, we decided to measure the resistance of one slice of apple three times.
Improved method
1. Using the ruler and pencil, mark the places of the apple to cut.
2. Cut one 1 x 1 x 1 cm slice of apple with the fruit knife and immediately measure the resistance three times using the multimeter.
3. Cut another 1 x 1 x 1 cm slice of apple and immediately measure the resistance three times again.
4. Repeat step 2 until three slices of apple of the same length have been measure for its resistance three times each.
5. Record the values in a table.
6. Repeat steps 2 to 5, except with 2 x 1 x 1 cm, 3 x 1 x 1 cm, 4 x 1 x 1 cm, and 5 x 1 x 1 cm slices of apple.
Experiment data
Length of apple slice against its resistance
Outliers:
These two values are obviously outliers because all the results with the 3cm slice of apple are within the range of about 110.0 Ω to 120.0 Ω.
Calculations
A = 10-2 x 10-2
= 10-4 m2
Gradient =
= 1.80 x 106
Gradient =
ρ = 1.80 x 106 x 10-4
= 1.80 x 102 Ωm
Since
The % error = 4.82 + 0.1 + 0.05
= ± 4.97 %
resistivity of apples = 1.80 x 102 ± 4.97% Ωm
Error analysis
We tried to ascertain our data was accurate by reading the ruler right above the mark so that there will be no parallax error.
For the uncertainty associated with length, it is ± 0.05 x 10-2 m. The largest percentage error associated with this is .
The uncertainty for the resistance measured is ± 0.05 x 103 Ω. The largest percentage error associated with this is which is negligible compared to the human error when cutting the slices of apple.
Since area = l x l, and the percentage error for length =,
% error for area = (+ )
= ± 1.00 x 10-1 %
The uncertainty for the average resistance for each length of apple is:
Largest percentage error:
We are not quite confident with our results. We do not have a value to compare our results with, so we do not know if we are accurate. Also, from the second graph it can be seen that when the length is 0cm, the resistance is about 6.00 x 104 Ω, which is definitely not possible. This means that the data is not accurate, hence I am not extremely confident with my results.
Discussion
The main trend in the graph is that as length increases, the resistance increases linearly. There is a moderate positive linear relationship between the dependent and independent variable. This is because as length increases, the amount of distance the electrons have to travel increases, experiencing more collisions with the atoms of the apple, hence resistance increases. Although an apple contains a lot of water, when we measure its resistance we are also measuring the fibres. Since fibres are solids, when there is a greater length its resistance will increase.
Using the equation, we are able to derive that resistivity,. From this equation we know that resistivity is proportional to resistance (), so when resistance increases so will resistivity. This supports the hypothesis.
The calculate value for the resistivity of apples, 1.80 x 102 ± 4.97% Ωm, seems to be quite reasonable as apples are non-conductors of electricity, so their resistance will be quite high and hence their resistivity will be a larger value as well. Also the percentage error is quite small, so our data calculated are quite precise.
Sources of error
1. The main source of error is with cutting the apples. Since it is very difficult to cut straight, the length of the apples all vary a little bit so the resistance measured will be inaccurate.
2. Since the length of the apples cut is not very accurate, the cross-sectional area will also be slightly different.
3. There might be a different amount of time between cutting the apple and measuring its resistance, so some of the water in the apple could have evaporated.
4. For our slices of apple, we did not cut them all from one apple as it is not large enough. Although the apples are of the same type, there could still be something different with their content or water content, contributing to the resistance measured being different.
5. There is not a very large sample size (3 slices of apple for each length).
6. When we have to measure its resistance, we have to poke in the wires of the multimeter into the apple, and this is not extremely constant as we could have poked in very deeply into the apple or quite shallow. This may shorten the length measured so its resistance will decrease.
7. Measurement error associated with the ruler, such as not reading the markings on the ruler correctly.
8. As the different lengths of apple all have the same cross-sectional area, their surface area to volume ration will be different. This will allow evaporation to take place at a different rate so the slices of apples will not have the same amount of water content in them, which will obviously affect the resistance measured.
Improvements
1. Use a sharper knife so the apple will be sliced with greater precision.
2. When measuring the lengths to cut, make sure that it is being read correctly and is right above the mark to reduce parallax error.
3. Poke the multimeter about the same amount into the apple. This will hopefully ensure that the length being measured is kept quite constant.
4. Using a larger sample size, for example 5 slices per length, will increase the precision of the results.
5. Instead of just using 5 different lengths (1cm, 2cm, 3cm, 4cm, and 5cm), there could be more lengths used such as 0.5cm, 1cm, 1.5cm, 2cm… 6cm. This will ensure a greater accuracy as there are more different lengths measured.
6. Before the apples are not cut, place them in an isotonic solution so that the water content in them will remain the same.
7. To somewhat reduce the effect of evaporation, a timer can be used to measure the time in between cutting and measuring so that they can be kept constant.
Conclusion
In conclusion, I have learned that when the length of an apple increases, so does its resistance and resistivity. The outcome is not different from the hypothesis. Although the graph does not reach 0 Ω at 0cm, it clearly shows the positive liner relationship between resistance and length. Also from what we learned last year, when the length of a material increases, its resistance increases.
resistivity of apples = 1.80 x 102 ± 4.97% Ωm
