Lab 6 Formal Report-2



Cégep John Abbott College *

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Electrical Engineering


Dec 6, 2023





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March 27 th , 2023 Lab 6: Is my battery still good? Formal lab report Abstract This experiment determined the internal resistance and the EMF of a battery to conclude whether it was in good working condition. Connecting the battery to a circuit with a variable resistor, the data collected states a linear relation between current and terminal voltage, with the slope representing the internal resistance and the y-intercept being the EMF of the battery found through experimentation. The EMF value found was 7.586V and compared to the ideal value of 9V resulted in a percent difference of 13%. This concludes the battery is not in a good condition. Introduction The objective of this experiment is to determine whether the tested battery is in good condition by determining its EMF and internal resistance. A battery has an EMF (ε) and an internal resistance (r). Figure 1: composition of a battery In a circuit, the terminal voltage of a battery is the total change in potential between the terminals of the battery, made of both the EMF and the voltage used by the battery. The terminal voltage is the actual voltage the battery supplies to a circuit, and it is always lower than the EMF of the battery. An ideal battery would only consist of an EMF, however, with true batteries, an internal resistance must be accounted for and when connecting a voltmeter to the terminals of the battery, we are measuring its terminal voltage. Terminal voltage (V T ) is calculated with the formula ? ? = ? − 𝐼? , where the values of ? and ? are constants, terminal voltage and current are both variables where ? ? is linearly dependant on 𝐼 . In the absence of current, the “ideal battery” voltage can be measured since there is no internal resistance to take into account ( ? ? = ? − 0 ). If placed in a circuit with a load resistor ( Figure 2 below) , the presence of a load resistor will provide current to the battery and therefore will now have internal resistance, making V T < ε.
Figure 2: Circuit with real battery and load resistance. The slope created by graphing terminal voltage (V T ) in relation to current ( A ) is the internal resistance of the battery and its EMF, ? ? = −?𝐼 + ? and should decrease linearly. When the resistance is 1Ω, the current is calculated to be proportional to voltage by the formula ? = 𝐼? . When R is 1, ? = 𝐼 , which allowed us to find the experientially measured EMF and internal resistance through the use of the capstone app and the rheostat. A variable resistor was used as it allows for more variables to be measured by providing a variety of currents to the battery.
Methods 1. We created the circuit as per the diagram, while making sure to properly link up the black and red channels to the voltage sensor so that we achieve positive values on the Capstone software. Figure 3: circuit diagram of experimental setup 2. We input the proper settings on the Capstone software to ensure accurate data collection for this experiment. The Voltage sensor was selected as the mode of input for both Channel A and B. The sampling frequency for collecting data was set at 20Hz to record data 20 times per second. The “Table and Graph” menu is selected to display the data collected. The graph plots terminal voltage over current. 3. We first test the rheostat slider to confirm the device was functioning as intended, so that the data collection process goes smoothly. Moving the slider changed the resistant values. 4. Data collection was a process of doing multiple steps in quick succession. Firstly, the circuit is closed by closing the switch. Then by clicking record on the software, the data is collected. We move the slider slowly and precisely, taking three to four seconds to reach the other end. Once the rheostat reaches the end, the data collection is stopped on the software, and the switch is opened again to stop the battery from draining. 5. We exported the data collected by the Capstone software into Excel to help with analyzing the data to ensure the experiment went accordingly. The excel sheet shows a table with recorded values for the three to four seconds of doing the experiment. The first column shows the current while the second column shows the terminal voltage. 6. If the battery used in the experiment is in good condition, the graph would show a linear trend downwards with the y-intercept representing the battery’s voltage. If the battery is in bad condition, the values for the terminal voltage would be very low, making an almost horizontal line, meaning the y- intercept would give a value significantly lower than the battery’s listed voltage. Otherwise, the data collection may need to be repeated to ensure the graph represents a scenario that makes sense. Repeating the experiment several times ensures that nothing went wrong in the data collection process. Once the circuit and Capstone software have been set up correctly, only steps 4 through 5 would need to be repeated.
Data/Results Table 1: current (A) and terminal voltage (V) measured through variable resistor of 0-22 Ω. Current (A) Terminal voltage (V) 1.438 2.311 1.431 2.297 1.424 2.286 1.418 2.275 1.413 2.265 1.408 2.255 1.403 2.247 1.399 2.239 1.395 2.232 1.391 2.225 1.388 2.219 1.384 2.212 1.381 2.207 1.377 2.202 1.374 2.199 1.370 2.198 1.366 2.198 1.362 2.198 1.355 2.208 1.335 2.270 1.334 2.265 1.332 2.258 1.331 2.252 1.331 2.24 1.319 2.273 1.313 2.288 1.309 2.292 1.304 2.300 1.295 2.328 1.281 2.372 1.246 2.495 1.213 2.621 1.186 2.723 1.155 2.839 1.131 2.933 1.115 2.999 1.100 3.056 1.092 3.087 1.077 3.145 1.054 3.233 1.037 3.302 1.015 3.387
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