PHYSICS LAB. Capacitor. Date: GRADE: PHYSICS DEPARTMENT JAMES MADISON UNIVERSITY. Revision November Capacitor 21

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1 PHYSICS LAB Capacitor Printed Names: Signatures: Date: Lab Section: Instructor: GRADE: PHYSICS DEPARTMENT JAMES MADISON UNIVERSITY Revision November 2002 Capacitor 21

2 Blank page Capacitor 22

3 CHARGING AND DISCHARGING CAPACITORS 1 Purpose: To study capacitors (charging, discharging and combining in series and parallel). Equipment: Multi-meter, computer and application programs (Data Logger, Datafit, Excel, ULI), 2 Capacitors (10µf), 1 Resistor (10MΩ), 1.5 Volt battery, capacitance meter and wire. (Note: The old capacitance meter (AC powered) gives a better value of C (~11.5µf compared to about 10 µf for the battery powered meters). Sample circuits have been built. Examine the circuits as a preparation for each section of the lab. The circuits have switches feel free to activate any circuit. Do not however rewire these sample circuits. Part I A. Charging. Note - When a battery, resistor and capacitor are connected in series (an RC circuit), current from the battery will charge up the capacitor to the value of Q. Where Q = CV Q = charge (Coulombs), V = Volts, C = capacitance (farads). 1. Use the voltmeter to measure the EMF (voltage) of the battery and record it. (Start an Excel spreadsheet.) 2. Use the ohmmeter to measure the value of the resistor and record it. 3. Draw a circuit diagram for a charging capacitor (Use pencil and paper or computer drawing tools). 4. Build the circuit, but do not make the final connection to the battery. Be sure to match the polarity of the capacitor with the battery (+ to +). 5. Connect the voltmeter so that the voltage is read across the capacitor. At this point, the voltage should read zero. 6. Now make the final connection to the battery. The voltage as read by the voltmeter should increase. The capacitor is now charging. 7. Remove one connection to the battery. Place a shorting wire on both sides of the capacitor. The voltage on the capacitor should now read zero. Part I B. Recording Data for a Charging Capacitor. 8. Replace the voltmeter with the connections to the computer I/O board (Port 1). 9. Run the program Data Logger. (Set port 2 off. Display on, update screen with voltage.) 10. Record the voltage across the capacitor vs time of a charging sequence. Plot the results in a spreadsheet. Include a textbox description of the process. Part II A. Discharging. 1 K.L. Giovanetti Copyright: James Madison University Capacitor 23

4 Use a capacitance meter, your instructor will need to show you how, to measure the capacitance of your two capacitors. Record these on your data sheets and use them as your theoretical values for capacitance. Note - A discharging capacitor behaves similarly to one that is charging, except that the battery must first be connected in parallel with the capacitor, rather than in a series and then removed to begin the discharging sequence. 11. Draw a circuit diagram for a discharging capacitor. Label each component with a letter and provide a key in the explanation lines below. (Use paper or computer drawing tools.) 12. Build the circuit with the voltmeter connected across the capacitor. 13. Charge the capacitor and then break the connection so that the capacitor discharges through the resistor. Note the drop in voltage. Describe the results in your report. Part II B. Recording Data for A Discharging Capacitor. 14. Record voltage vs. time for a discharging sequence. Start data logger. Start the capacitor discharging by removing the battery. REMOVE VOLTMETER FROM CIRCUIT. 15. Copy the data to an excel spreadsheet or analyze it with the Logger Pro options. A special excel template, capacitors.xls, has been prepared for student use. (Look in the excel files folder on the server.) The voltages recorded do not have a simple straight-line dependence on time. To analyze this data we will use a Datafit [ function a*exp(b*x), where a= V o, b=α] -(α t) V=V o e Where α and V o are the constants determined in the fit, V and t are the recorded data. The fitting routine will also estimate the uncertainty in the parameters estimated. 17. Enter data so that the measured times are in the column labeled x-value and the measured voltages are in the column y-values. Perform fit. 18. Record the fit parameter α and Vo on the summary worksheet. 19. Use the spreadsheet formulas to generate a curve based on α and Vo. Plot this curve and the data together. 20. Repeat the above measurement at 3 times. Enter the data on the sheets ds2, ds3 Copy the fitted parameters to the summary worksheet. Capacitor 24

5 21. When you have completed three measurements create a summary table with the parameters and their uncertainties. Calculate the mean and standard deviation of the parameters and compare the SD based on the three measurements with the uncertainties from the fit. Comment in a text box on this comparison. 22. Calculate the capacitance C of your capacitor using the mean value for the parameter α (part 21). ( α =1/RC ). Since you have measured R you can now calculate C. Predict the uncertainty in C based on the uncertainty in R and the uncertainty in α. 23. Repeat the above steps for a second capacitor. You may choose to do only one measurement. For all the remaining capacitance measurements you may use the percent uncertainty for capacitor 1 as your error and record just one measurement to determine α. Part III. Capacitors in Series and Parallel. Series: 1/C total = 1/C 1 + 1/C 2 Parallel: C total = C 1 + C 2 The above formulas indicate that a pair of capacitors may be treated as a single capacitor with a capacitance give by the formulas. Two capacitors can be placed in the discharging circuit (parallel or series) and the data recorded and analyzed. Use the above methods for a discharging capacitor to measure the total capacitance for 2 capacitors in series. Repeat for 2 capacitors in parallel. Do the resulting values for C agree with calculated values? COMMENT One part of the circuit that has been neglected in this experiment is the resistance of the voltmeter and the interface. The digital meter has a 10 MΩ internal resistance which causes a 10% reduction in the overall discharging resistance. The ULI has 200 MΩ resistance which will cause a 0.5% reduction. Record battery voltage, resistor value, capacitance values and estimates of error. Charging capacitor circuit diagram, and plot. (no fit necessary). Discharging Capacitor data sets 1,2,3, fit results, data and fit plotted. Comparison of above 3 datasets. (Fit uncertainty vs SD) Measurements for C2, C1&C2 in parallel and series. Summary table for C1, C2, parallel and series. Values + uncertainties. Compare C1 and C2 to theoretical Compare parallel and series with theoretical Capacitor 25

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