Investigation On The Resistivity Of Apples. Since we are measuring the resistance of an apple, when the length increases, resistance will increase. Although we are mostly measuring the water content in the apple, we are also measuring the resistance of th
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Introduction
RESISTIVITY OF APPLES
The aim of this investigation is to verify that there is a linear relationship between the length of a slice of apple and its length. We can then use this relationship to determine the resistivity of an apple.
Background
Since we are measuring the resistance of an apple, when the length increases, resistance will increase. Although we are mostly measuring the water content in the apple, we are also measuring the resistance of the apple fibres. When length increases, the electrons have to travel a greater distance and will also experience more collisions with the atoms in the apple.
Variables that may affect the resistance are the cross-sectional area of the slices and evaporation, which will cause the water content in the slices of apple to be different.
To find the resistivity of the apple, we will use the resistivity equation.
Equation: 
Where R = resistance of substance (apple) in Ω
ρ = resistivity of substance (apple) in Ωm
l = length in m
A = area in m2
The graph plotted will have the equation 
Gradient = 
Hypothesis
As the length of the apple increases, its resistivity will increase.
Variables
Independent: Length of apple
Dependent: Resistance of apple
Controlled: Type of knife
Type of apple
Same multimeter
Cross-sectional area
Person cutting the apple
Person measuring length of apple
Middle
3
176.0
190.0
178.2
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
Length (± 0.05 x 10-2 m) | Sample | Resistance (± 0.05 x 103 Ω) | |||
Trial 1 | Trial 2 | Trial 3 | Total Average | ||
1 | 1 | 66.0 | 65.0 | 64.0 | 66.4 ± 3.2 |
2 | 67.0 | 69.0 | 67.2 | ||
3 | 69.0 | 63.2 | 67.0 | ||
2 | 1 | 102.0 | 104.0 | 106.2 | 104.8 ± 3.0 |
2 | 102.6 | 104.0 | 106.2 | ||
3 | 107.4 | 107.8 | 106.8 | ||
3 | 1 | 115.3 | 116.0 | 113.6 | 114.3 ± 2.2 |
2 | 114.2 | 115.3 | 112.1 | ||
3 | 113.5 | 66.3 | 66.2 | ||
4 | 1 | 125.7 | 122.0 | 120.3 | 125.1 ± 4.8 |
2 | 126.3 | 127.5 | 126.3 | ||
3 | 124.3 | 126.3 | 127.0 | ||
5 | 1 | 162.9 | 168.4 | 170.4 | 165.8 ± 4.6 |
2 | 167.6 | 165.3 | 166.2 | ||
3 | 163.2 | 165.2 | 163.4 | ||
Outliers:
Resistance (± 0.05 x 103 Ω) | |
66.3 | 66.2 |
Conclusion
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
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