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EE 211 Networks and Digital Logic Lab Fall 2009 Lab 9 - RC Time Constant Measurements Lab performed on Thursday, Nov. 19. Prelab due at the start of class on Thursday, Nov. 19. Lab Report due Friday, December 4. 100 90 80 70 Capacitor voltage 60 50 40 30 20 10 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Time in seconds Figure 2. Capacitor voltage versus time for Vs = 100 volts and = 1 second Prelab for Lab 9 RC Time Constant Measurements Prelab due at the start of class on Thursday, Nov. 19. Names ______________________ ______________________ ______________________ 1. Given the equation for capacitor voltage in Figure 1: where Vs is the DC source voltage (a constant), T = time in seconds, and = time constant in seconds, where and the equation for capacitor current: Show all the steps to compute the capacitor current in Figure 1 as a function of Vs, and the initial current, I0, where = initial current in amps The answer is: . 2. Using , , R = 1000 ohms, Vs = 10 volts, and C = 1 µF, how long will it take for the capacitor voltage to reach 5 volts? 3. It takes about 5 time constants for the capacitor to reach 99% of its final value. Suppose you want to design a charging system that will charge to 99% of the final value using a capacitor of C = 22000 µF in 10 seconds. The source voltage is 10 volts. (a) What value of resistor would you use? (b) What is the initial current? (c) What is the initial power in the resistor? Lab Session Lab 9 RC Time Constant Measurements Lab performed on Thursday, Nov. 19. Prelab due at the start of class on Thursday, Nov. 19. Lab Report due Monday, November 30. Names ______________________ ______________________ ______________________ Parts: large polarized electrolytic capacitor 1 kohm resistor, rated at 1 W or higher Connecting leads and gator clips Wires Tools: Screwdriver Wire cutter Wire stripper Test equipment: DMM Power supply 1. Select one of the large capacitors. Set the capacitance meter to 15 volts. Measure the capacitance of the selected capacitor using the capacitance meter. In Table 1, record the nominal and measured capacitance and the rated voltage of the capacitor. 2. Select a 1 kΩ resistor rated for at least 1 Watt. Measure its resistance. In Table 1, record the nominal and measured resistance. Table 1 – Measured and Nominal Component Values Capacitor Resistor Measured Rated Nominal Measured Capacitor Nominal capacitance in voltage in resistance in resistance in number Capacitance in µF µF volts ohms ohms 3. From the measured resistance and capacitance, calculate the time constant in seconds, using Calculated time constant = ____________ seconds 4. Theoretically it takes about 5 time constants for the capacitor voltage to rise to a value that is within 1 % of the source voltage. Calculate five time constants using Calculated 5 time constants = ____________ seconds 5. Follow these steps to connect the circuit in Figure 3 below. (a) Set the power supply to 25 volts. (b) Cut a wire about 2 feet long and strip off about 2 inches of insulation from each end. (c) Insert one end of the wire into the COM terminal of the power supply. Hand tighten the COM terminal to the wire. (d) Insert the other end of the wire around the negative (-) terminal of the capacitor. Leave about an inch of bare wire exposed near the capacitor negative terminal. Use a screw driver to tighten the terminal. (e) Use a screwdriver to secure one end of the resistor to the positive terminal of the capacitor. Leave about an inch of bare wire from the resistor exposed, so as to have access to the positive terminal. (f) Use an alligator lead to connect the other end of the resistor to the positive terminal (+25 V)of the power supply. (g) Use an alligator lead jumper as the short circuit across the capacitor. You can actually clip onto the exposed wires at each capacitor terminal. (h) Alligator clip the digital multimeter (DMM) leads across the capacitor and set the DMM to measure DC voltage. Figure 3. RC Charging Circuit showing a short circuit as the initial setup. 6. Using a laptop, navigate to the instructor’s website, paws.wcu.edu/radams. Then click on the EE211 link. Then download the lab instructions for this lab. Copy and paste Table 2 into MS Excel. Now get ready for some serious sustained data taking! This is best done with a partner, but can be done successfully by one person. You will need a watch, or use the laptop clock. The instant you remove the alligator jumper, the current (which had been flowing through the jumper) flows into the capacitor. This is time t = 0, and you will begin recording data every 15seconds after that instant. 7. Have someone at the laptop keyboard, someone watching the clock, and someone reading the capacitor voltage. Every 15 seconds, the clock watcher should count down “ 3, 2, 1, 0” as the seconds tick towards the next 15 seconds. At the count of “0” the voltage reader should announce the capacitor voltage, and the laptop person should record the announced voltage in Excel. Helpful hint: If you select “Change date and time settings” the laptop clock will remain in the window as you enter data in the spreadsheet. Table 2 – Timed Electrical Measurements for the RC Circuit Capacitor Voltage (volts) Calculated Calculated Time (mm:ss) Resistor Trial 1 Trial 2 Average Current (mA) Voltage 0 0:15 0:30 0:45 1:00 1:15 1:30 1:45 2:00 2:15 2:30 2:45 3:00 3:15 3:30 3:45 4:00 4:15 4:30 4:45 5:00 5:15 5:30 5:45 6:00 8. When you are finished recording data for the first trial, press the Output On/Off button on the power supply to set the power supply to 0 volts. The capacitor voltage should start to decrease. Connect the alligator lead jumper across the capacitor to short it out. BE CAREFUL--- THERE WILL BE A SPARK – KEEP YOUR EYES PROTECTED!! A fully charged capacitor is ideally suited for igniting explosives. The small resistance of the wire connected to the explosive creates a very short time constant so that most of the capacitor energy is delivered to the explosive in a very short time. Remember when Wylie Coyote always pressed on this big handle to set off the ACME explosive to try to get the Road Runner? He was likely discharging a capacitor that was connected electrically to the dynamite. 9. Press the Output On/Off button again to resume the 25 volts at the power supply output. 10. Repeat step 7 to record trial 2 data in the Excel spreadsheet. 11. Insert the appropriate equation into Excel to compute the average capacitor voltage in volts. 12. Insert the appropriate equation into Excel to compute the calculated resistor voltage in volts. 13. Insert the appropriate equation into Excel to compute the calculated current in mA. Post-Lab Session Lab 9 1. Include the EXCEL Table from the lab experiment in the Data Analysis/Results section of the lab report. 2. Construct another table that compares theoretical versus experimental capacitor voltage as a function of time. See Table 3 below. Theoretical capacitor voltage is calculated using , where VS is the power supply voltage and is the time constant. Use the value computed in step 3 of the lab instructions as the value for Use to calculate percent error. Include this table in the Data Analysis/Results section of the lab report. Table 3 – Comparison of Theoretical and experimental capacitor charging Average Theoretical Time experimental capacitor % error (seconds) capacitor voltage voltage 0 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225 240 255 270 285 300 315 330 345 3. Construct a single figure, with two graphs on it. You will plot resistor voltage vs. time and capacitor voltage vs. time. Use Microsoft Excel or MATLAB to graph your results. (Note: The resistor voltage starts at Vs and exponentially decays to nearly 0 volts. The capacitor voltage starts at 0 volts and exponentially grows to nearly Vs volts.) Two simple graphs to assist you in constructing your own is shown in Figure 4. The time axis goes out a bit longer than the six minutes specified in your experiment. Figure 4: Example final graph of data 4. After the graphs have been completed, do the following: a. Describe the capacitor voltage behavior from 0 through 5, in terms of initial and final voltage magnitude, linearity and rate of change. b. Describe the resistor voltage behavior from 0 through 5, in terms of initial and final voltage magnitude, linearity and rate of change. c. To how many volts has Vc charged in one time constant? d. To what % has the capacitor charged to at this point? e. Using the equation , show the calculation of Vc for a time equal to one time constant. f. How many volts are across the resistor at the end of one time constant? What % is this of the total possible voltage change? g. Make sure the graphs agree with the data in tables 2 and 3. h. Calculate the values of capacitor and resistor voltage at 4 minutes. i. What do you conclude about the accuracy of your results?
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