Six Lemons in a Series/Parallel Charging a 4.4 Farad Capacitor, NO Load Resistor SECTION #1 - The experimental design 1a. The goal of this experiment is to see what voltage I can obtain with the lemon battery in a series/parallel configuration, with No Load Resistor in the circuit, which will charge up two 2.2 Farad Super Capacitors. 1b. Secondly, I wanted to see how long I could run a 4700Ω load resistor from just the stored up capacitor voltage, i.e., no battery connected in the circuit. 1c. Thirdly, I wanted to see how long I could run the experiment after charging the capacitors and connecting in a 4700Ω load resistor, while still maintaining the battery in the circuit. 2. A diagram of the battery configuration is presented in Section 2 below. Part #1/Section 3: lemons in series/parallel{2 banks, 3, two 2.2F capacitors in parallel, No load resistor in the circuit, i.e., SW1 is open. {The data is presented in Table 1a, in the columns under the grey headers. Previous expt - brown header} Part #2/Section 4: Disconnected the positive terminal and connected in load resistor. Part #3/Section 5: Recharging of Super Capacitors, No Load Resistor Part #4/Section : Connecting in Load Resistor, while battery is still connected to the circuit. Part #5/Section 7: Discharge experiment. 3. The lemons were frozen over night and then allowed to thaw for several hours before the experiment. 4. The negative electrodes are Zn plated washers, 3.7cm diameter (part #245). 5. These washers were new (not used in any other experiment), thus had a clean layer of Zn plating.. Positive electrodes are Canadian Silver Dollars (80%Ag / 20%Cu), years - 1958 through 195. 7. I connected two 2.2 Farad electrolytic Super Capacitors to my lemon battery configuration, which theoretically should be able to store 4.4 Farads of charge (or 4,400,000 μf or 4.4 million microfarads). The device number: 2.5DMB2R2M8X1 CAP, ALU ELEC: Manufacturer specifications: 2.2F @ 2.5V. 8. The experiment did not have a load resistor during the initial charging of the capacitor, as in previous experiments. 9. Experiments were run continuously, i.e., once connected to the battery, the experiment was allowed to run for the indicated time period before the positive terminal of the battery was disconnected. 10. My design also uses a germanium diode at the negative side of my battery configuration. The device number is 1N34A. I measured the V F (forward voltage) and found it to be 0.31 Volts. 11. Electrical measurements were taken at several points: (i) Circuit current at point "a" (I circuit ). (ii) Voltage across each capacitor, and. (iii) Charging current (I charging ) at point "b". 12. Additionally, when the current at point "b" is equal approximately 0 Volts during the charging phase, I will assume that the capacitors are fully charged (when there is no load resistor in the circuit). 13. At the end of each experiment, the charge was drained from the capacitor by disconnecting the Positive terminal and by using an additional resistor of lower value, in parallel with the load resistor, in order to SAFELY drain off the stored up charge. I use the symbol " " to mean "in parallel with". 14. Discharge experiments used the following resistor in parallel with the load resistor: 100Ω nominal. 15. The number of Couls of charge and Capacitance is reported at the end of this document (done in Excel). This was done by using the current (amps) at point "b" and the time (seconds). 1. In addition, I calculated the number of Couls of charge generated when recharging the battery in Part 3/Section #5. 17. The table in Section #8 contains data from all experiments to date with the 2.2 Farad Super Capacitors. 18. The term "I" was used in the tables when V cap 2 was identical to V cap 1. SW = switch #1. 19. Voltage dropped by the diode during the experiment was measured with an analog meter. 20. An analog meter was used at some points in the experiment, thus, those values are not as accurate as the digital measurements. 21. Table 8, Notation: 1 Cap = one capacitor and 2 Caps = two capacitors.
SECTION #2 - The experimental diagram, Six Lemons in Series/Parallel 4700Ω load resistor switch 1 (SW1) A = Ammeter, point "a" A = Ammeter, point "b" A A - + 1N34A diode - + 2.2 F Caps Cell 5 = 0.97V Cell 3 = 0.97V Cell 2 = 0.97V - + - + - + - + - + - + Cell = 0.97V Cell 4 = 1.03V Cell 1 = 1.0V V battery = 2.8V
SECTION #3: Data for Part #1 - Initial Charging of the Capacitors Table 1a - Six Lemons in Zn Plated Washers, No Load Resistor, Two x 2.2 Farad Capacitors Time (min) I charging @ "b"; ma I charging @ "b"; ma ** See note (1) % of V max I circuit @ "a"; ma Instantaneous {OL} > 2mA {OL} > 2mA --- --- --- ---- 0.5 1.524 1.421 0.138 8. 0.139 N/A 1 1.445 1.359 0.152 9.5 0.152 N/A 3 1.449 --- 0.203 --- I N/A 5 1.504 1.312 0.20 --- I N/A 7 1.477 1.308 0.305 --- I N/A 10 1.444 1.294 0.378 24 I N/A 15 1.354 --- 0.493 --- I N/A 20 1.274 1.18 0.589 --- I N/A 25 1.187 --- 0.78 --- I N/A 30 1.10 1.07 0.758 47 I N/A 35 1.034 1.014 0.82 --- I N/A 40 0.98 --- 0.888 --- I N/A 50 0.851 0.89 0.99 2 I N/A 55 0.802 --- 1.043 --- I N/A 0 0.759 0.794 1.087 --- I N/A 70 0.79 --- 1.13 --- I N/A 80 0.14 0.7 1.229 --- I N/A 85 0.580 --- 1.257 --- I N/A 90 0.55 0.34 1.285 --- I N/A 100 0.524 --- 1.334 83 I N/A 110 0.480 0.558 1.379 --- I N/A 115 0.42 --- 1.400 --- I N/A 120 0.445 0.532 1.419 --- I N/A 130 0.418 0.511 1.455 91 I N/A 140 0.390 0.484 1.48 --- I N/A 150 0.3 0.41 1.515 95 I N/A 15 0.33 --- 1.554 97 I N/A 180 0.312 --- 1.587 99 I N/A 187 0.302 --- 1.00 100 I N/A Note (1): The data (current @ "b", brown header) comes from the previous experiment {RETEST}, where two 2.2 Farad capacitors were charged up with a load resistor in the circuit; thus, current from the battery was charging the capacitors and flowing through the load resistor at the same time. Table 1b: Part #1 - Battery Data Voltage @ start: V cell 1 = 1.0V, V cell 2 = 0.95V, V cell 3 = 0.97V, V cell 4 = 1.03V, V cell 5 = 0.97V, V cell = 0.97V ** Voltage data before positive electrode is connected: and = 0.119V Voltage (V d ) across diode @ 34 min = 0.32V, @ 5 min = 0.27V, @ 10 = 0.23V, @ 135 min = 0.21V{Analog} Estimated # Couls & Farads: Charge =.959 Couls, V = 1.00Volts, Capacitance = 4.35 Farads Estimated # electrons transferred in experiment = 4.34 x 10 19 Voltage across the battery before start of experiment = 2.8V {analog meter}.
SECTION #3: Discussion of Data for Part #1, Six Lemon Battery (Series/Parallel) - No Load 1. In this experiment, the load resistor was not in the circuit during the charging phase of the experiment, i.e., SW1 was "open". Thus, all of the current supplied by the battery went to charging the capacitors. 2. At the start of the experiment, Table 1a above, the circuit was drawing more than 2mA and 35 minutes later, it was still drawing about 1mA (1.034mA). 3. At the last time point, 187 minutes, the current at "b" decreased to 0.302mA; thus, the capacitors were not fully charged, i.e., if fully charged, the current would decrease to zero or near zero ma. 4. The voltage across both capacitors reached 1.00V. 5. Table 1a includes data from the previous post, i.e., data in the column with the brown header. In this experiment, the circuit contains a 4700Ω load resistor, thus current is going to charge the capacitor and is flowing through the load resistor. From this data, it can be seen that the current at "b" at the start and for the next 35 minutes is lower than in the circuit that does not have a load resistor during charging, e.g., at 0.5 minutes the current is 1.421mA versus 1.524mA and at 35 minutes, it is 1.014mA versus 1.034mA.. From the 50 minute time point onwards, the data is just the opposite, i.e., the current is 0.89mA versus 0.851mA and at 150 minutes, it is 0.41 versus 0.3mA. This makes sense because in the experiment where the load resistor is in the circuit during charging, more current is required to drive the total circuit (i.e., resistor plus capacitors); whereas, in the case where there is no load resistor in the circuit during charging, once the capacitors reach a certain point, current is required only to charge the capacitors. 7. It took 50 minutes to reach about 1V on both capacitors (0.99V) or 2% charged. 8. It took another 100 minutes to reach about 1.5V (1.515V) or 95% charged. 9. It took approximately 3 hours to reach 1.V. 10. The symbol "I" in the V cap 2 column indicates that the voltage across the second capacitor was identical to the voltage across V cap 1. Since SW1 is "open", there is no current flowing through the load resistor, thus, is labelled N/A. 11. It should be noted that the capacitors had 0.119V before that start of the experiment. The reason for this is that these capacitors take a long time to fully drain the charge. At the end of my experiments for each post, I drain the charge safely from the capacitors and furthermore, connect in a dead short cable in order to further drain the capacitors, for about 10 minutes. But, after sitting for one week, one can see that there still is a voltage on the capacitors, indicating that a dead short across the capacitors for 10 minutes was not enough to completely drain the capacitors (within the 10 time frame). 12. As found previously, the voltage drop across the diode ranges from 0.32V-0.21V. 13. For this experiment,.959 Couls of charge were transferred and using a final voltage of 1.00V, this is equivalent to 4.35 Farads of capacitance. 14. Additionally, 4.34 x 10 19 electrons were transferred in the experiment. 15. It should be noted that the voltage developed by the cell Series/Parallel battery was 2.8V before the start of the experiment, which is very close to the theoretical voltage of 3.0V. SECTION #4: Discussion of Data for Part #2, 1. For this discussion, see Table 2a below. 2. In Part 2, after the charging of the capacitors, I disconnected the positive terminal of the battery and then closed SW1; thus, current can flow only from the negative side of the capacitors, through the load resistor, to the positive side of the capacitors. 3. The reason for this experiment is to see how long I can run a 4700Ω load, just from the capacitors alone, before the voltage drops below 1.5V. 4. From Table 2a below, it can be seen that the experiment can run for about 20 minutes (1.493V) and still deliver about 300μA (0.310mA). 5. Furthermore, I can run the load for about 40 minutes before the voltage drops below 1.4V and still delivers about 300μA (0.292mA).. Any load that can run on 1.3 volts, can be run for at least 0 minutes 7. More specifically, 1.5V is reached in 18 minutes (312μA) and 1.4V in 41 minutes (291μA). 8. Thus, these are the limitations of running off the capacitors alone.
SECTION #4: Data for Part #2 - Disconnect Battery - Connect in 4700Ω Load Resistor Table 2a - Disconnect Battery - Connect in Load Resistor, Two x 2.2 Farad Capacitors Time (min) % of V start I circuit @ "a"; ma % I start Prior to start 1.599 100 1.599 ---- ---- Instantaneous 1.597 ---- I 0.332 100 0.5 1.595 ---- I 0.331 1 1.592 99. I 0.331 99.7 3 1.580 ---- I 0.328 5 1.59 98 I 0.32 98 7 1.558 ---- I 0.324 10 1.542 9 I 0.321 97 15 1.517 ---- I 0.315 20 1.493 93 I 0.310 93 25 1.471 ---- I 0.305 30 1.448 91 I 0.301 90. 35 1.428 ---- I 0.297 40 1.407 ---- I 0.292 50 1.3 85 I 0.284 85.5 55 1.347 ---- I 0.280 0 1.327 83 I 0.27 83 Reached 1.5V @ 18 min, 30 secs {I = 0.312 ma} Reached 0.30mA @ 31 min, 7 secs {V = 1.445 volts} Reached 1.4V @ 41 min, 40 secs {I = 0.291 ma} SECTION #5: Discussion of Data for Part #3, 1. For this discussion, see Table 3a below. 2. In Part 3, I re-charged the capacitors to the highest level that I could, in a reasonable period of time, i.e., in this case, I managed to get the voltage to 1.553 Volts after 4 minutes of charging. 3. It only took 15 minutes to reach 1.4V, but took an additional 35 minutes to reach about 1.5V. 4. Data in the columns under the brown headers comes from Table 1a above, i.e., the original charging data. I tried to present data from Table 1a as a comparison, by choosing voltages that were similar and compared the current being drawn by the capacitors for charging. 5. 0.5 minute time point in Table 3a: Table 1a data: 1.334V @ 0.524mA Table 3a experiment: 1.333V @ 0.514mA Thus, it is observed that the currents are very similar.. 15 minute time point in Table 3a: Table 1a data: 1.400V @ 0.42mA Table 3a experiment: 1.405V @ 0.354mA Thus, in the recharging of the capacitors, the battery is not able to supply the same current as in the original charging of the capacitors. This makes sense, because the original charging lasted 187 minutes and would have depleted or "drained" the battery to a point where it could not deliver the current to charge the capacitors. 7. Further evidence for this fact is that I never did reach the 1.00V that I had obtained with the initial charging cycle. But it does show that the battery can continue to supply current for charging.
SECTION #5: Data for Part #3 - Recharging the Capacitors Table 3a - Recharging of the Two 2.2 Farad Capacitors, with No Load Resistor Time (min) I charging @ "b"; ma Table 1a I charging @ "b" Table 1a Time (min) 0 min 0.000 1.327 1.327 --- --- 0.5 0.514 1.333 I 1.334 0.524 100 1 0.47 1.33 I --- --- --- 3 0.422 1.349 I --- --- --- 5 0.402 1.30 I --- --- --- 10 0.374 1.384 I 1.379 0.480 110 15 0.354 1.405 I 1.400 0.42 115 20 0.351 1.425 I 1.419 0.445 120 25 0.329 1.444 I --- --- --- 30 0.314 1.42 I --- --- --- 35 0.304 1.478 I --- --- --- 40 0.290 1.492 I 1.48 0.390 140 50 0.28 1.520 I 1.515 0.3 150 55 0.259 1.532 I --- --- --- 0 0.251 1.544 I --- --- --- 2 0.247 1.549 I --- --- --- 4 0.244 1.553 I 1.554 0.33 15 Note: Data from Table 1a above was added (data under brown headers) for comparison purposes. SECTION #: Data for Part #4 - Connecting in load while battery is still in circuit Table 4a - Connecting Load Resistor into the Circuit after Recharging the Capacitors, Battery still Connected Time (min) I charging @ "b"; ma % of V max I circuit @ "a"; ma Table 2a % of V max I circuit @ "a"; ma, Table 2a 0 min 0.280 1.555 100 1.555 0.324 --- --- --- 0.5 0.272 1.55 100 I 0.323 1.595 100 0.331 1 0.29 1.555 100 I 0.323 1.592 99.8 0.331 5 0.257 1.548 99.5 I 0.322 1.59 98.3 0.32 10 0.253 1.539 98.9 I 0.320 1.542 9.7 0.321 20 0.247 1.524 98 I 0.317 1.493 93. 0.310 25 0.245 1.517 97. I 0.315 1.471 92 0.305 30 0.243 1.510 97 I 0.314 1.448 91 0.301 45 0.237 1.490 95.8 I 0.310 --- --- --- 0 0.230 1.470 94.5 I 0.305 1.327 83 0.27 SECTION #: Data for Part #4 - connecting in load while battery is still in circuit, 1. The discussion comes from data in Table 4a above. 2. I recharged the capacitors to 1.555 (lime colored cells). Then I closed SW1; thus, current was flowing through the 4700Ω load resistor and the battery was still connected to the entire circuit (resistor, capacitors and diode).
SECTION #: Data for Part #4 - connecting in load while battery is still in circuit, 3. The voltage is then compared to the voltage obtained while the load resistor is running from the capacitors alone, data in columns with yellow headers. 4. From the 45 minute time point, the voltage has decreased to 1.490V, 95.8% of the starting voltage; whereas, the voltage from the Table 2a data (yellow headers) shows that the voltage at 20 minutes is 1.493 volts or 93.% of the starting voltage. 5. Thus, charging up the capacitors and connecting in the load resistor (with the battery still connected), is able to maintain a voltage for a longer period of time than just the capacitors alone.. Note that the currents are the same 0.310mA (because the voltages are the same). 7. At 0 minutes, the voltage has dropped to 1.470V or 94.5% of the starting voltage @ 305μA (blue cells); whereas, in the case where the load resistor is running from the capacitors alone, the voltage at 0 minutes has dropped to1.327v or 83% of the starting voltage (yellow cells). 8. The point being, one can charge up the capacitors first (without a load resistor) to 1.V, then connect in a load and still keep the battery connected, which should allow one to run your project for a longer period of time than if the project were run on the capacitors alone. SECTION #7: Discussion of Data for Part #5, Six Lemon Battery (Series/Parallel) Table 5 - Part #5: Discharge of 2.2 Farad Capacitor through 4700 Ohm 100 Ohm, ( 9.7Ω) Discharge Time (minutes) (Volts) (Volts) I circuit, "a"; ma Power (μw) Power (μw) previous post, see note below 0 1.420 13.85 19,7 13,530 {at start} 0.5 1.400 12.98 18,127 --- 1 1.312 12.09 12,972 10,247 3 1.002 9.23 9248 032 5 0.755 7.01 5293 3499 10 0.383 3.53 1352 882 15 0.257 1.298 334 242 20 0.187 0.942 17 123 30 0.100 0.509 51 34 Note: The power delivered from the same battery configuration, i.e., Zn plated washers, cells in S/P, two 2.2F capacitors is presented from a previous post (circuit had a load resistor in the circuit while the capacitors were being charged). Data in column under green header. SECTION #7: Discussion of Discharge Data for Experiment #1, Table 5 1. Note: The capacitors were recharged to 1.505V before the discharge experiment was started. 2. Both capacitors discharged at the same rate, as noted by. 3. At the instant the 100Ω resistor is connected into the circuit, the power delivered by the two capacitors is on the order of 20mW (19,7μW). 4. At 3 minutes, the capacitors are still delivering just under 10mW (9248) and 10 minutes later, it is still delivering 1mW (1352μW). 5. Even after 30 minutes, the capacitors were still not fully discharged.. The power delivered from this experiment is considerably larger than in the previous post, i.e., 19mW versus 13.5mW at the start of the discharge experiment (time = 0 minutes). -------------------------------------------- CONTINUED ON NEXT PAGE -----------------------------------------------------------
SECTION #8: Summary of Current Experiment and Previous Posts Summary of Data from Series and Series/Parallel Battery Configurations, 2.2Farad Super Capacitors # Configuration # of Cells V cap 1 Zn washers, 2 Caps {2 banks, 3 1.00 I charging / I circuit, max x 100 N/A {no load resistor during charging} Time (min) Coulombs # of Electrons transferred Farads 187.959 4.3 x 10 19 4.35 2a 2b Zn washers, 2 Caps Zn washers, 2 Caps {2 banks, 3 {2 banks, 3 # of Couls of charge delivered by the battery, based on I @ "b" 7.173 4.5 x 10 19 ---- 1.271 19% 10 5.24 3.3 x 10 19 4.14 3 Zn washers, 1 Cap {2 banks, 3 1.35 133% 130 3.031 1.9 x 10 19 2.24 4 5 7 8 Series, Zn nails, 1 Cap Series, Zn nails, 1 Cap Series, Zn nails, 1 Cap Zn nails, 1 Cap Zn nails, 1 Cap 2 0.350 274% 48 0.18 3. x 10 18 1.7 3 0.5 129% 85 1.185 7.4 x 10 18 1.81 4 0.957 183% 90 1.821 1.1 x 10 19 1.90 4 {2 banks, 2 {2 banks, 3 0.800 187% 90 1.37 8.5 x 10 18 1.71 1.00 159% 90 1.919 1.2 x 10 19 1.91 SECTION #8: Discussion of Data from all Experiments with 2.2 Farad Super Capacitors 1. From line #1, the maximum voltage obtained was 1.00V, the charge transferred is.959 Couls and had an equivalent capacitance of 4.35F. This is considerably better than line 2b (which was the same configuration as line 1, with the exception that line 2b had a load resistor in the circuit during charging). 2. The total number of Couls of charge transferred, including data from Table 1a and 3a: Total Couls =.959 + 1.151 = 8.11 Couls! 3. Number of electrons transferred = 8.11 Couls/(1.02 x 10-19 Couls/electron) = 5.1 x 10 19 electrons. SECTION #9: Lessons Learned 1. Charging up the capacitors without a load resistor will allow one to store more charge on the capacitors as opposed to charging the capacitors with a load resistor in the circuit. 2. A load can be run directly from the charged up capacitors alone. 3. Preferably, the capacitors should be charged up to the necessary voltage required for the project load and then the load can be connected into the circuit, while the battery is still in the circuit, see Table 4a. 4. Six lemon cells in a series/parallel configuration, with Zn plated washers (#245) and Ag CDN$ can charge two Super Capacitors to 1.00V and store.959 Couls of charge, equivalent capacitance of 4.35F. 5. When charged to 1.505V, 4.35F can deliver between 20mW to 1mW of power for a period of 10 minutes.
SECTION #10 - Calculations of Coulombs & Farads, Cells in Series/Parallel Table : Battery Using Zn Plated Washers - No Load Resistor EXPERIMENT #14, Part No 1 Calculation of Charge and Farads in Capacitor time ma @ b Curr in Amp time, sec Coul 0 0.5 1.524 0.001524 30 0.04572 1 1.445 0.001445 30 0.04335 3 1.449 0.001449 120 0.17388 5 1.504 0.001504 120 0.18048 7 1.477 0.001477 120 0.17724 10 1.444 0.001444 180 0.25992 15 1.354 0.001354 300 0.402 20 1.287 0.001287 300 0.381 25 1.187 0.001187 300 0.351 30 1.103 0.001103 300 0.3309 35 1.034 0.001034 300 0.3102 40 0.98 0.00098 300 0.2904 50 0.851 0.000851 00 0.510 55 0.802 0.000802 300 0.240 0 0.759 0.000759 300 0.2277 70 0.79 0.00079 00 0.4074 80 0.14 0.00014 00 0.384 85 0.58 0.00058 300 0.174 90 0.55 0.00055 300 0.195 100 0.524 0.000524 00 0.3144 110 0.48 0.00048 00 0.288 115 0.42 0.00042 300 0.138 120 0.445 0.000445 300 0.1335 130 0.418 0.000418 00 0.2508 140 0.39 0.00039 00 0.234 150 0.3 0.0003 00 0.219 15 0.33 0.00033 300 0.1008 180 0.312 0.000312 300 0.093 187 0.302 0.000302 420 0.1284 Total Coul.959 # electrons 4.34E19 Volts 1.00 Farads 4.35 -------------------------------------------- CONTINUED ON NEXT PAGE -----------------------------------------------------------
SECTION #11: Table - Recharging of the Capacitors EXPERIMENT #14, Part No 3 Calculation of Charge and Farads in Capacitor time ma @ b Curr in Amp time, sec Coul 0 0.5 0.514 0.000514 30 0.01542 1 0.47 0.00047 30 0.01428 3 0.422 0.000422 120 0.0504 5 0.402 0.000402 120 0.04824 10 0.374 0.000374 180 0.0732 15 0.354 0.000354 300 0.102 20 0.351 0.000351 300 0.1053 25 0.329 0.000329 300 0.0987 30 0.314 0.000314 300 0.0942 35 0.304 0.000304 300 0.0912 40 0.29 0.00029 300 0.087 50 0.28 0.00028 00 0.108 55 0.259 0.000259 300 0.0777 0 0.251 0.000251 300 0.0753 2 0.247 0.000247 120 0.0294 4 0.244 0.000244 120 0.02928 Total Coul 1.151 # electrons 7.18E18