Purpose The purpose of this lab will be to determine how capacitors behave in RC circuits and to observe the change in τ (tau).
Description/Background The RC Circuit describes a circuit that consists of a resistor(s), a capacitor(s), and a voltage input into the circuit. The RC Circuit will be set up as the following, where a resistor and capacitor will be in series and a galvanometer will be in parallel to capacitor. Using PASCO Capstone software, the changing voltage and the resulting rate of change of the voltage across the capacitor will be shown. From the recorded data, students can calculate for the time constant of RC circuits as well as fundamentally observe the effects of a capacitor.
Materials ● ● ● ● ●
AC/DC Electronics Lab Board: Capacitors, Resistors, Wire Leads D-cell Batteries Galvanometer 100 kΩ Resistor and another resistor of a different value 100 μF Capacitor and another capacitor a different value
Procedure 1. Connect the circuit shown in Figure 1.1, using a 100k Ω resistor and a 100 μF capacitor. Connect the Galvanometer so the black “ground” lead is on the side of the capacitor that connects to the negative terminal of the battery and set it so that it reads to a maximum of 1.5 V DC. 2. Start with no voltage on the capacitor and the switch off. If there is remaining voltage on the capacitor, use a piece of wire to “short” the two leads together, draining any
2 remaining charge. (Touch the ends of the wire to points B and C as shown in Figure 1.1 to discharge the capacitor). 3. Open the pasco software application on the computer, and choose the option that states “Data and Table” and connect the galvanometer. 4. Now start recording on Pasco interface and close the switch by pushing and holding the button down. Observe the voltage readings on the Galvanometer, the voltage across the capacitor. How would you describe the manner in which the voltage changes? 5. Stop previous recording. Next: a. Make sure to continue holding switch even after stopping the recording b. Connect a wire between points A and C in the circuit to allow the charge to drain back through resistor c. Start new recording and let go of the switch observing the graph of voltage as the capacitor discharges 6. Stop previous recording and sketch first Pasco recording onto Graph 1.1. Do the same for the second graph which was discharging but instead record it in Graph 1.2. 7. Record the resistance and capacitance from first trial into Table 1.1. 8. Observe the voltage readings on the Galvanometer as the charge flows back. How would you describe the manner in which the voltage falls? 9. Repeat steps 3-5 until you have a good feeling for the process of charging and discharging of a capacitor through a resistance. 10. Now repeat steps 3-6, but this time replace the 100 μF capacitor with the one of different value. 11. Fill out Trial two in Table 1.1 with the new resistor and capacitor values. 12. Repeat steps 3-6 with a different resistor but using the same initial capacitor of 100 μF. 13. Fill out Trial three in Table 1.1 with the new resistor and capacitor values. 14. Optional: Use the new resistor and new capacitor (Not the initial 100 kΩ and 100 μF) and repeat steps 3-6 and see how circuit varies *Before we continue it is time to derive an equation The equation for an RC circuit discharging is v = v0(e-t/(RC)). To solve for RC which is Tua just divide and take the natural log. ln(v/v0) = -t/(RC) So RC = t/[ln(v/v0)] 15. Make sure the table on the Pasco Interface has three columns. Voltage X Time and the third column needs to be created by the physicists performing the lab. To create the column you must click the third icon on the upper left corner of the table area. If you roll the mouse over it, it should say “Create new calculations on selected column data. 16. As shown in screenshot below a new column will appear and now in the blank bar below ([Table title here]) after Calc(some #)= enter the equation shown in the screenshot. To access the natural log function right click in blank text area and go under function then scientific and search for LN and by right clicking you will also be able to enter [Voltage(Volts)] function by going under data to put into equation. As for V initial this indicates the initial voltage or the first reading in the Voltage column. For this entire
3 process of the Calc(some #) column you will be using the graph of the first time of discharging. 17. If done correctly the third column will create a set of values that represent the points on a graph of a function that can be used to determine the tau. The points calculated create a graph where the slope of it is equal to -1/(tau). So to determine the value of tau simply take the absolute value of -1/(slope). Best way to find the slope of the calculated values
is to select the values and graph them on the Pasco interface. After being graphed use the slope tool in the upper tool boxes to determine slope at any point on graph. 18. To graph on the pasco interface simply click and drag another graph onto the screen and when choosing units plot Calc(some #) vs time. 19. This is what the data table and graphs may look like after following previous few steps:
20. After successfully finding tau for first trial find tau for the next 2 or 3 trials and record them in Table 1.1.
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Figure 1.1
Data Collection Graph 1.1 Time Charging (Make sure to Mark max V values and to use different lines to differentiate which graph represents which trial)
Graph 1.2 Time Discharging (Make sure to Mark max V values and to use different lines to differentiate which graph represents which trial)
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Table 1.1 Resistance
Capacitance
Time Constant (Tau)
Trial 1 Trial 2 Trial 3 Trial 4 (Optional)
Analysis Questions 1. According to actual calculations it is known that if one used a 100k Ω resistor and a 100 μF capacitor that tau should be 10 seconds. Compare the results of your first trial to 10 seconds. Is it the same if not explain why it might not be the same?
2. What did you observe happened to tau when resistance was changed from either larger to smaller value? What did you observe happened to tau when capacitance was changed from either a larger or smaller value? What is the relationship between tau resistance and capacitance?
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3. What would happen to the value of tau if instead of having the resistor and capacitor in series they were in parallel?
4. Would it be possible to do the same Tau calculation with the data table for the graph of charging the capacitor if so how would you go about doing so?
