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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

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
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
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.