I predict that the internal resistance will decrease as the electrodes are moved closer. I also predict that the EMF of the potato will decrease as more and more of the chemicals inside of the potato are being used up over the duration of the experiment; by the time the 3rd set of readings have been taken the potato cell will have reacted with most of the acid and so the EMF produced by the potato will decrease.
In the data I have been given there is a column for the Load Resistance (kΩ). This was recorded by an ohmmeter checking the exact resistance of the variable resistor.
By having this bit of information it means I can calculate the maximum power of the potato. To see what the maximum power is I need to plot a graph of Power against Load Resistance, where the curve peaks will supposedly show the maximum power output possible for the potato cell.
Maximum Power Theorem: This is the popular theory claimed to have been discovered by Moritz Von Jacobi (1801-1871). The “Jacobi’s Law” as it is sometimes called states: “Maximum power is transferred when the internal resistance of the source equals the resistance of the load, when the external resistance can be varied, and the internal resistance is constant."
Or in my words, the Maximum Power output can be achieved from the potato cell to the load can be achieved when the internal resistance is equal to the load resistance.
By observing what values of resistance the peaks of the curves are I can then see if it matches or is close to the internal resistance calculated from the other graphs. With the amount of data I have been given I believe I cannot prove the Maximum Power Theorem but, if the peak does equal the internal resistance then the experiment will agree with the theory. I will also compare where the curves peak; at what distance does the curve peak (earliest/latest) in relation to the load resistance.
Method: The following method was used to gain the data I need to process. Knowing how the data was collected will help me ascertain where errors may have occurred and how they may have been prevented.
Knowing that the gradient is negative I am informed that all of the results were recorded in a way that if a result fell short of the expected reading it was tested again. This means there should not be too many anomalies on the graphs.
- The apparatus was set up as shown in the diagram. The circuit measures the p.d. (V) across the potato cell and the current (I) that is drawn from the cell.
- The copper and zinc electrodes were placed in the potato parallel to each other and at varying distances apart. The first set of reading came from 8cm apart.
- The load resistance was then altered so that different values of I and V could be taken and recorded in a table. The first readings were taken at 0.08mA and from then on the load resistance was altered by the variable resistor so that each subsequent current reading increased by 0.02mA.
- Whenever the current reached the required value of mA the variable resistor was taken out of the circuit and put into the ohmmeter to read the exact load resistance, this value was then put into a column on the data table.
- The variable resistor was then connected back into the circuit and the process repeated.
- Once all of the readings were recorded for the electrodes being 8cm apart the electrodes were moved closer, 4cm apart, and the whole experiment was repeated.
- The electrodes were finally placed so that they were only 2cm apart from each other and once again the values of V, I and Load Resistance were recorded.
The Data:
Graphs for Terminal p.d. (V) against current (I) to find EMF and internal resistance:
y = -4300x + 0.71
V = - rI + EMF
EMF: 0.71 Volts
Internal resistance: 4300Ω
y = -2425x + 0.60
V = - rI + EMF
EMF: 0.60 Volts
Internal resistance: 2425Ω
y = -2325x + 0.67
V = - rI + EMF
EMF: 0.67 Volts
Internal resistance: 2325 Ω
Terminal p.d. (V) against current (I) graph analysis.
I have put the values for EMF and internal resistance in the table above so that the data can be more easily compared. From the table I can see that, as I predicted, the internal resistance decreases as the electrodes are moved closer together. However, the EMF is not exactly what I expected as it increases somewhat from electrode distance 4cm – 2cm.
Internal Resistance: The internal resistance when the electrodes are 4cm apart is approximately half of what the internal resistance is at 8cm apart. However, the internal resistance does not decrease as much from when the electrodes are then moved to 2cm apart, therefore the distance between electrodes is not proportional to the internal resistance even though at first it looks like there could be a relationship. If I had more results I could further explore the relationship between distance and internal resistance.
Potatoes contain a huge amount of starch which is essentially why the internal resistances in general are all in the kΩ range. As the electrodes are moved closer together there is less starch for the particles to get through and so the internal resistance is decreased.
There are a few reasons I can think of for there not being such a large internal resistance decrease from 4cm-2cm. Zinc is a very soft mental which can be easily bent. The electrode may have been bent slightly on entering the potato which resulted in the zinc sheet not being exactly parallel to the copper electrode. The distance between electrodes on the surface would then be different to that inside the potato, see diagram below. The internal resistance would therefore be more than initially presumed by comparing it to the internal resistance when the electrodes are 8cm apart.
Aside from the error in inserting the electrodes there is the possibility that, because they are in the potato for some time during the experiment, a protective layer is formed on the electrodes from the contents of the potato which in turn acts as a barrier increasing the internal resistance. However, this is only a presumption and cannot rely on this as I do not know whether or not the electrodes were cleaned between readings taken at different distances.
EMF: Earlier on in the theory section of my coursework I predicted that the EMF would decrease as the electrodes were brought closer together. The potato cell will have been running for some time and so I would expect the power to decrease over time. However, the EMF calculated from the intercept of the graph decreased at first between 8cm and 4cm (0.71A – 0.60A) and then increased from 4cm – 2cm (0.60A – 0.67A).
If I take into account the errors explained above for the internal resistance it would make sense for the EMF of the potato to also be effected as:
Error Bars: From the data I was given I have the resolution of the ammeter, and voltmeter. Using the resolutions for each I was able to add error bars to the graphs.
Ammeter: 0.02mA
Voltmeter: 0.02V
I could have added to the error bars by taking into account the human error however, because I did not carry out the experiment myself I cannot judge how precisely the reading were taken. There are two points where the error bars only just touch the trend line; this suggests that they could be anomalies. These points are:
Curiously both anomalies occur when the terminal p.d. is 0.22V; this suggests there may have been a problem with the voltmeter.
Graph for Maximum Power analysis: I was not able to draw reliable curves with excel so instead I drew the curves by myself using a flexi-curve ruler. This allowed me to minimize but not eliminate my error in drawing the curves by hand. However, the Maximum Power Graph can never be as accurate as a straight line graphs.
According to the maximum power theorem, the maximum power (the peak) will be where the load resistance is equal to the internal resistance. Although the load resistance for the graph curves are close to the internal resistances they are not equal. The difference will be caused more by the maximum power graph than the p.d. against current graphs because of the error in drawing of the curves compared to straight lines.
*As the highest value of power was the last point on the graph I went into excel and found the exact value instead of estimating it from the graph as I did for the other two curves.
** From the graph the maximum power appears to cover a 500Ω range and so I took the midpoint which was 2250Ω.
From the graphs I can see that the power peaks higher at a lower load resistance when the electrodes are closer together. As the electrodes are moved further apart the power peaks lower at higher load resistances.
I have not added error bars to my maximum power curves because then resolution of the ohmmeter was so small that the bars took up the width of the point and made no difference to my estimation of the load resistance.
The closer the electrodes are the more power is exerted at a lower load resistance as R=r. Fewer volts are being lost inside the potato cell by pushing them through the system and therefore more volts can be turned into p.d which creates a greater power. The opposite applies when the electrodes are moved further apart from one another.
According to the data I have been given and processed the maximum power of the potato cell that can exert is reached when the electrodes are 2cm apart and load resistance is equal to internal resistance. I cannot say what the overall maximum power of the potato is as I do not have data for the potato when electrodes are any closer than 2cm apart. I presume from what I have found out that the maximum power will continue increase until the electrodes touch and a short circuit is created.
Conclusions:
I expected the EMF to stay the same throughout the experiment but it did not. I now understand that the EMF would decrease because the potato is being discharged like a normal cell. Like a normal cell the potato cell will eventually stop working all together. This however, does not explain why the EMF decreased from 8-4cm and then increased from 4-2cm. I do not know what order the results were recorded in but from my understanding it would make sense for the data to have been collected in the following order: 8cm, 2cm and then 4cm.
As the distance between the electrodes increase
- EMF stays more or less the same depending on how long the cell has been running. The EMF will eventually run out and the potato cell will be discharged.
- The internal resistance increases as there is more starch and actual potato for the electrons to get though which requires more energy.
-
The p.d. decreases because the internal resistance increases
- I can see how The Maximum Power Theorem could relate to my set of data however, because of the inaccuracy of the curve due to the lack of results and the difficulty in calculating the turning point I cannot assume that it is true.
Bibliography
Websites used:
Books used:
- Chemistry in Context
- Advanced Physics text book – Steve Adams & Jonathon Allday
- Advancing physics text book.
Other:
- Advancing Physics CD ROM (Chapter 2)
