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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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