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Aim To determine the internal resistance, EMF, and power dissipated in a series potato circuit. Variables Independant: The current (I) measured in amperes which passes through the circuit per second.
- Implemented by: The resistance of a variable resistor will be changed 5 times which will cause the current to change accordingly. The current is measured by an ammeter in series with the circuit.
- The five values of current for the 5 scenarios are: 0.000847, 0.000851, 0.000857, 0.000859, and
Dependant: The potential difference (V) measured in volts which passes through the circuit per second.
- The potential difference is measured by a voltmeter connected in parallel with the circuit. The potential difference will change in accordance to the current. Controlled variables: Controlled Variable Why must it be Controlled? How will it be Controlled? same electrolytes (galvanized metal and copper) The exact electrolytes used in this experiment must be consistent because:
- Internal resistance depends on surface area and the nature and concentration of electrolyte. This means a change in surface area or concentration of the electrolytes could skew the results.
- E.m.f. of a cell depends on the material of electrodes and electrolyte used in the cell (Toppr, n.d.) The strips of galvanized and copper metals will be set aside and marked uniquely to ensure the same ones are used in each scenario and each trial. Temperature of the copper and zinc metal The emf is dependent on the temperature of the electrolytes which are copper and zinc metal strips in this lab. Therefore the temperature of the electrolytes must be kept constant. The entire experiment will be conducted in the same room and the electrolytes will not be in contact with any heat sources. Wires and leads The internal resistance is dependent on the length, cross sectional area, and material (level of conductivity of the material) of the wires or leads. Therefore this must be controlled. The 9 wires and leads will be marked uniquely to ensure the same ones are used in each trial. The potato used as the cell If different potatoes were to be used, the different size, densities, and chemical properties would affect the EMF and internal resistance. In each trial, the same potato will be used. Apparatus Material Function Quantity Potato Act as a cell from which Potential Difference (Voltage) and current values can be taken from 1 Variable resistor Change the load resistance 1
Multimeter One set up to be used as a voltmeter to determine the P.D. (Voltages) of the potato. The other set up to be used as an ammeter to determine the current passing through the circuit. 2 strip of copper metal Act as the the positive electrolyte of the potato battery 1 strip of zinc metal/galvanized metal Act as the the negative electrolyte of the potato battery 1 alligator clips To connect different parts of the circuit and carry the flow of electrons 5 leads To connect different parts of the circuit and carry the flow of electrons 4 cloth To clean the surface of the experiment 1 plastic gloves To protect hands when handling zinc and copper materials as advised by the MSDS sheets. 2 Plastic wrap/newspaper Optional to protect delicate surfaces Method Diagram 1. the experimental set-up (annotated) Diagram 2. Circuit diagram Potato Battery Set-up
- Ensure you have a large clear workspace (approx 2 by 2 ft) that has been wiped down from any other residue and dried with a clean cloth
- If the workspace is easily damaged or delicate, it is covered with plastic wrap or newspaper.
- The potato is placed on the workspace and, with rubber gloves on hands, the strip of copper metal is pierced into the potato in the middle until the strip is halfway buried into the potato. This will be the potato cell’s positive terminal/cathode.Take caution that the strip of copper should not be inserted all the way through the potato. Juice of the potato will come out during this step - this is normal.
- About an inch from the strip of copper, the strip of zinc coated metal is inserted parallel into the potato in the same manner as the copper. This will be the potato cell’s negative
Current (A ± 0.000001A) Trial 1 Trial 2 Trial 3 0.000847 0.049119 0.049221 0. 0.000851 0.048765 0.048621 0. 0.000857 0.046509 0.046609 0. 0.000859 0.045459 0.049892 0. 0.000862 0.045631 0.044991 0. Data Processing Data processing for EMF
- Determining current’s uncertainty The current, as the independent variable, is simply just read off of the digital multimeter (which acted as an ammeter). To calculate the uncertainty we simply look at the last decimal place in which the ammeter accounts for, and we replace the number with all zeros except a number 1 is replaced in that last place value. For example:
- The ammeter is giving a steady reading of 0.000847A
- Therefore the uncertainty of the digital ammeter is ± 0.000001 A This means that the actual current could be between 0.000846A and 0.000848A, so the reading is 0.000847 ± 0.000001 A.
- Calculating the average potential difference Scenario 1: current = 0.000847 amperes Average = T₁ + T₂ + T₃ 3 = 0.049119 + 0.049221 + 0. 3 = 0. = 0.049197 volts ∴ the average potential difference through the circuit is 0.049197 volts in scenario 1
- Calculating the raw uncertainty for average potential difference Raw Uncertainty = ± 𝑙𝑎𝑟𝑔𝑒𝑠𝑡 𝑟𝑎𝑛𝑔𝑒 2 Calculate the range of potential difference across each trial Scenario 1: current = 0.000847 amperes
Range = highest value - lowest value = 0.04925 - 0. = 0.000131 volts ∴ the range of potential difference in scenario 1 is 0.000131 volts Selecting largest range to calculate the raw uncertainty ∴ Current (A) Potential Difference Range 0.000847 0. 0.000851 0. 0.000857 0. 0.000859 0.004433 (Largest range) 0.000862 0. Calculate raw uncertainty ∴ Raw Uncertainty = ± = ± = ± 0.002217 = ± 0. 𝑙𝑎𝑟𝑔𝑒𝑠𝑡 𝑟𝑎𝑛𝑔𝑒 2
2
- Processed data table for Current VS Average Potential Difference Calculation 2 is repeated for all scenarios to find the average potential difference for each Average Potential Difference (V ± 0.002V) Current (A ± 0.000001 A) 0.049 0. 0.049 0. 0.046 0. 0.047 0. 0.045 0.
- Processed data graph: Current VS Average Potential Difference
By substituting y = potential difference (V), x = current (I),as we defined before, into y = -239.29x
- 0.2521 we get: V = – 239.29I + 0. ∴ EMF = 0.2521, Internal Resistance = 239.29 Ω (r = -m/slope therefore the internal resistance (r) is positive) Data processing for Power DIssipated Current (A ± 0.000001 A) Potential Difference (V ± 0.002 V) Power (P ± 0.000002 W) 0.000847 0.049 0. 0.000851 (^) 0.049 0. 0.000857 0.046 0. 0.000859 (^) 0.047 0. 0.000862 0.045 0. Multiplying current times potential difference to calculate power (with Uncertainties) (I * V = P)
- Convert uncertainties of current and average potential difference into percentages for scenario 1 Current: (0.000001 / 0.000847) * 100% = 0.001181% Potential Difference: (0.002 / 0.049) * 100% = 4.506372%
- Multiply current * potential difference to calculate power I * V = P ∴ 0.000847 A * 0.049 V = 0.000042 W
- Add the percent uncertainties of current and potential difference together 0.001181% + 4.506372% = 4.507553% ∴ P = 0.000042 W ± 4.507553%
- Convert uncertainty of the trial back to raw uncertainty 4.507553% * 0.000042W = 0. ∴ P = 0.000042 W ± 0.000002W
** The following steps were repeated for each trial, it is a pure coincidence that the uncertainty of each trial rounds to the same value (± 0.000002W). Conclusion In this lab, a circuit was constructed to simulate the flow of electric current where a potato acted as the cell and powersource. In this circuit, a variable resistor is adjusted 5 times to alter the independent variable (current) and consequently alter the dependent variable (potential difference) in each scenario; this is because current and potential difference are indirectly and directly proportional to resistance respectively. This relationship is assumed to be general knowledge but is further validated through Ohm’s Law where R = V/I (Kognity, 2014). Through this procedure sufficient data was collected to achieve the aim of the lab to determine the electromotive force (EMF), power dissipated, and internal resistance of this potato series circuit. The general trend that presented itself on my graph was as follows: as current of the circuit increased, the average potential difference decreased. For example, in scenario 1 where current was 0.000847A, potential difference was 0.049V whereas in scenario 5 where current increased to 0.000862A, potential difference decreased to 0.045V. This trend was found to resemble a mostly negative linear trendline, with a relatively high r^2 value of 0.8696 deeming the line an appropriate fit for the data. This implies a negative inversely proportional relationship between current and average potential difference with the equation of the trendline being y = -239.29x + 0.2521. This relationship opposes Ohm’s Law which states that current passing through a conductor is directly proportional with the potential difference across it (Kognity, 2014). However, Ohm’s law does not apply because the resistor in this experiment is variable, or in other words not constant. In addition, the voltage we are measuring is terminal potential difference: the potential difference across the positive and negative terminal of an electric source, which produces a negatively sloped line with respect to current (Kwee, 2018). Thus the negative linear trend is supported by this scientific knowledge. The structure of the equation of the line in the graph directly resembles an arrangement of Kirchoff’s second law (the loop rule) which states: for a closed loop series path, the algebraic sum of all the voltages around any closed loop in a circuit is equal to zero (Kognity, 2014). To apply the loop rule to the circuit in this lab, we must add the potential difference increased across the ideal cell (EMF: labelled E in figure 3), subtract the potential difference lost across the internal resistance (Ir: current
- r in figure 3), subtract the potential difference lost across the external load resistance (IR: current * R in figure 3), and finally equate this to 0. This results in the equation EMF = IR + Ir or EMF = V + Ir since Ohm’s law
Evaluation
1. Validity of the experiment - The data collected in this lab was not consistent. Although the procedure in which the data was collected was consistent, there was a very large range in the data between trials to suggest otherwise. For example, in scenario 4 where current was 0.000859A the range of the values for the 3 trials was 0.004V. Compared to the other 4 trials, this range is 34 times, 25 times, seven times and six times larger in this specific order. Thus, in at least one of the trials in scenario 4, there must have been errors to result in the lack of precision of this data. This can also be observed on the graph as when we calculated the average of scenario 4 and plotted it, it strays most significantly from the trend line and is therefore the biggest visible outlier. This suggests that due to the imprecision of the data collected in the trials of scenario 4, the accuracy was also negatively effected. In addition to this, the ranges of potential difference in scenarios 3 and 5 where current was 0.000857 and 0.000862 respectively, were approximately 5 times larger than the ranges of scenarios 1 and 2. With this information, we can also categorize the ranges of scenarios 3 and 5 as large ranges and assume that possible errors (which will be explored further in this evaluation) caused the inconsistency and thus imprecision of this data. - The negative trend displayed in the graph of Current VS Average Potential difference suggests that as current (A) increases, the terminal potential difference (V) decreases in a linear manner. This matches the expected trend of other experiments posted online (Kwee, 2018). The R^2 value of the data in relation to the trendline is 0.8696; the fact that this number is close to 1 indicates a strong relationship between the independent and dependent variable. This being said, the values of EMF and internal resistance deduced in this lab are far from the expected values of similar experiments. The value for EMF in this lab was 0.2521V but the accepted value online is 0.5V – 0.9V therefore my value is 50.4% lower than being in the accepted range. The value we deduced for internal resistance was 239.29Ω but this is 91.4% less than the accepted value of 2500Ω. This implies that there were definitely some errors in our data collection or calculations, proving this lab to be somewhat invalid. - The largest outliers in my data were evidently the values of average potential difference gathered in scenario 3 and 5 as they deviate from the trendline the most. Most likely, the data for these scenarios or perhaps the data for one of the trials in these scenarios was not collected properly, causing these points on the graph to stray from the expected trend. Overall, we can conclude this lab is not extremely valid. 2. Errors and Improvements
Range of currents tested
- The increments at which i increased the independent variable (current) were too small to be appropriate for this lab. With the largest increment being 0.000015A, the average amount that the current differentiated in each scenario was 0.00000375A. When the current increases an insignificant amount each trial, we will only be able to observe a proportionately small decrease in potential difference. The limited range of current values does not allow the slope nor y-intercept to reach their actual value. Since the slope represents internal resistance of the potato cell and the y-intercept represents the EMF of the potato cell, a smaller slope will result in inaccurate values of both EMF and internal resistance. The small current increments were caused by the narrow range of resistances that the rheostat resistor provides. - To solve this problem, a potentiometer (different type of variable resistor) would be a great alternative to the rheostat resistor in experiments to follow. The potentiometer is a 3 terminal variable resistor and allows for a wider range of resistances and thus a wider range of current than the previous 2 terminal resistors used (John & Ben, 2020). Therefore with a potentiometer we could get higher accuracy in our values for emf and internal resistance. Random Error
- During the second trial of the fourth scenario, Joyce accidentally touched the variable resistor and slid the knob forward a little bit. This caused the current for trials 2 and 3 of scenario 4 to be at a slightly different current than the first trial resulting in a larger potential difference in those two trials (mostly trial 2).
- Preventing random errors is extremely hard because regardless of the number of controlled variables taken into account, there are many factors that lead to random error which cannot be controlled. To prevent the impact of random errors on data more trials can be taken. It would be most beneficial to have at least 5 trials of each scenario, so the averages of potential difference would most accurately represent each scenario. Uncertainty
- To calculate the uncertainty of the average potential difference we took the largest range of all the scenarios and divided it by 2. However, as mentioned previously the largest range was in scenario 4 where it was 35 times larger than the smallest range; therefore we can assume a range of this magnitude must have included errors in data collection of some kind. The errors and lack of consistency in scenario 4 impacts the accuracy of the vertical error bars and the uncertainty of the average potential difference measured in this lab since the uncertainty was calculated using the largest range. The vertical error bars are so large that the minimum line has a positive slope of 17.933 while the maximum and trend line both have negative slopes that correctly
- My lab partner and I completed the trials in different sittings. We completed scenarios 1 and 2 in one period, scenarios 3 and 4 in another period, and finally scenario 5. Although we completed the scenarios in different periods we did not take into account the position (depth and placement) of the electrolytes. We were not aware that the distance between the electrolytes and the surface area of electrolyte inserted in the potato affects internal resistance and current (Toppr, n.d.). Instead of making precise measurements, we just punctured the electrolytes into the potato randomly each time which exposes a major flaw in our method. As seen on the graph, the average potential difference values from scenarios 3 and 4 where current was 0.000847A and 0.000851A respectively, are outliers which could very well have resulted from the inconsistency of the depth and distance between electrolytes. - As a solution to this, next time I would measure the distance between the electrolytes and the distance I insert each strip of metal into the potato. The best solution would be to complete all the trials in one sitting or to leave the metal strips in the potato and store it somewhere safe to ensure that the depth and distance between the strips are exactly the same for each trial. 3. Further Inquiry
- If I were given more time to work on this lab, my next step would be to take measurements in order to find the short circuit current of my series circuit. After some research during the lab, I came across this equation: internal resistance = EMF / short circuit current (BBC, n.d.). This equation suggests that we should be able to calculate EMF or internal resistance using the other value if the short circuit current is found. The use of short circuit current along with this equation could provide another way to validate the values of EMF and internal resistance which I have deduced in this lab and provide another strong data point in my evaluation of this lab.
- An extension of this lab I would like to carry out in the future is creating another potato circuit to power relatively medium sized LED light bulbs (not the tiny bulbs we have in our classroom). In a recent initiative led by Haim Rabinowitch, he and his colleagues have been pursuing the idea of potato power to deliver energy to people cut off from the electricity grids (Kalan, 2013). They argue this idea can supply remote towns and villages lighting. I would like to explore this topic by doing experiments on the most optimal current (which produces the brightest lighting without overloading the circuit) to investigate how Rabinowitch and his team would determine this in preparation for their potential distribution of potato battery kits to developing areas.
Bibliography
- Cells, batteries, and internal resistance. (n.d.). Retrieved April 18, 2020, from https://app.kognity.com/study/app/physics-hl-2016/electricity-magnetism/electric-cells/ cells-batteries-internal-resistance/
- Electrical sources and internal resistance - Electrical sources and internal resistance - Higher Physics Revision - BBC Bitesize. (n.d.). Retrieved April 16, 2020, from https://www.bbc.co.uk/bitesize/guides/zxx66sg/revision/
- John, C., & Ben. (2020, April 9). Difference Between Potentiometer and Rheostat, A detailed Comparison. Retrieved from http://www.circuitstoday.com/difference-between-potentiometer-and-rheostat
- Kwee, C. (2018, March 1). Measuring e.m.f and Internal Resistance (The Line Graph Method). Retrieved April 17, 2020, from https://www.youtube.com/watch?v=gkwrPyl0dCA
- Potato power: the spuds that could light the world. (2013, November 12). Retrieved April 19, 2020, from https://www.bbc.com/future/article/20131112-potato-power-to-light-the-world
- Toppr. (n.d.). Electromotive Force, Terminal Voltage and Internal Resistance of Cell. Retrieved April 16, 2020, from https://www.toppr.com/content/concept/electromotive-force-terminal-voltage-and-inte rnal-resistance-of-cell-209603/
