1. CTU: EE 331 - Circuit Analysis II: Lab 3: Capacitor Charging and Discharging 1
Colorado Technical University
EE 331 – Circuit Analysis II
Lab 3: Capacitor Charging and Discharging
November 2009
Loren Karl Schwappach
Student #06B7050651
This lab report was completed as a course requirement to obtain full course credit in EE331 Circuit Analysis II at Colorado
Technical University. This lab report investigates the time constant calculations and charging/discharging equations for simple and
complex RC circuits. Thevenin’s theorem is further utilized to simplify and solve complex RC circuits. Hand calculations are verified
using P-Spice schematic calculations to determine viability of design prior to the physical build. P-Spice diagrams and calculations are
then verified by physically modeling the design on a bread board and taking measurements for observation. The results were then
verified by the course instructor. If you have any questions or concerns in regards to this laboratory assignment, this laboratory
report, the process used in designing the indicated circuitry, or the final conclusions and recommendations derived, please send an
email to LSchwappach@yahoo.com. All computer drawn figures and pictures used in this report are my own and of original and
authentic content. I authorize the use of any and all content included in this report for academic use.
the capacitor to measure voltage change and a 20V power
supply was connected while the circuit was connected in the
I. INTRODUCTION discharge position to allow the capacitor to fully discharge.
Next with the power applied the circuit was connected in the
T HE time constant of a simple and complex RC circuit can
be found by the equation . Where is the charging position while the students recorded how long it took
for the capacitor to reach 63.2% of its final voltage (
time constant with the SI unit of seconds, is the equivalent
= 12.6V). This is one charging time constant, tau. Tau is
circuit resistance in Ohms and is the capacitance in Farads.
computed using . For the R=10kΩ circuit one
In this lab this equation was verified by comparing the
results after doubling the value of a known resistor in a simple tae = = 4.7s. Next with the capacitor
RC circuit. fully charged the circuit was connected in the discharge
Next a complex RC circuit is built and converted into its position and this time the students recorded how long it took
Thevenin equivalents with respect to charge and discharge. for the capacitor to reach 36.8% of its final voltage (
The of these equivalent circuits are then verified by = 7.4V).
building the complex circuit on a bread board and taking Next the RC circuit was modified using a 20kΩ resistor
readings with respect to the circuit charged and the as a replacement. The multimeter was again connected across
discharging. the capacitor to measure voltage change and a 20V power
supply was connected while the circuit was connected in the
discharge position to allow the capacitor to fully discharge.
II. COMPONENTS Next with the power applied the circuit was connected in the
charging position and discharging positions respectively as
The following is a list of components that were used. completed previously to determine the if the time constant
 A DC power supply capable of 25V. would change double as required by . The
 A digital multimeter for measuring circuit voltage, students again recorded how long it took for the capacitor to
circuit current, resistance, and capacitance. reach 63.2% of its final charging voltage ( =
 A oscilloscope for viewing the input and output 12.6V) and 36.8% of its final discharging voltage (
waveforms of a simple RC circuit with a 1kHz = 7.4V). A table of results obtained follows...
square wave input.
 A signal generator capable of delivering 5V
amplitude 1kHz square waves.
 10kΩ, 20kΩ, 39kΩ, 47 kΩ, and two 100 kΩ
resistors.
 1nF, and two 470 F capacitors.
 Bread board with wires.
III. PROCEDURES AND ANALYSIS Table 1: Results from charging/discharging a simple RC
First a simple RC circuit was built using a 10kΩ resistor circuit with a 10kΩ and then 20kΩ respectively.
and 470 F capacitor. The multimeter was connected across

2. CTU: EE 331 - Circuit Analysis II: Lab 3: Capacitor Charging and Discharging 2
These results closely approximated the results expected
by . A large percentage error was expected due
to the instrumentation used in timing the charge and discharge
(counting) times and because of the large variances in resistors
(+/- 1% to +/- 20%) and capacitors (+/-50%). A P-Spice
model and simulation of this stage and expected results
confirmed our expectations and follows...
Figure 4: P-Spice model of RC with 20kΩ resistor.
Figure 2: P-Spice model of RC with 10kΩ resistor.
Figure 5: P-Spice charging simulation of 20kΩ resistor
RC circuit.
Figure 2: P-Spice charging simulation of 10kΩ resistor
RC circuit.
Figure 6: P-Spice discharging simulation of 20kΩ resistor
RC circuit.
Next an the multimeter was placed in series between the
resistor and the capacitor and the current was checked so the
current from the resistor to the capacitor read as positive
current. The circuit was again charged and discharged so an
observation could be made about the change in direction of
current in each case. The results follow.
Figure 3: P-Spice discharging simulation of 10kΩ resistor
RC circuit.

3. CTU: EE 331 - Circuit Analysis II: Lab 3: Capacitor Charging and Discharging 3
Figure 7: Current direction during capacitor charge and Figure 10: Circuit 2 (discharging): Original circuit
discharge. connected through R3 to ground and reduced to Thevenin
equivalent.
The next stage in the lab was to build the complex circuit
shown below and then reduce and redraw the circuit using its With the modeled charging and discharging circuits
Thevenin equivalent. With the reduced model circuits the reduced to their Thevenin equivalents the time constants were
charging and discharging time constant could be determined obtained using as indicated by the previous
using . respective figures. These time constants were then verified
after measuring the actual capacitor charge and discharge
times. The results of and percentage error was much lower
this time closer to our expected values and are shown in the
table below.
Figure 8: Original unreduced RC circuit.
Table 2: Results from charging/discharging a complex RC
The above circuit was then reduced to two Thevenin circuit.
equivalent circuits (One with the circuit connected to power
Finally one last simple RC circuit was built. The original
and one with the circuit connected through R3 to ground). The
R value had to be modified from 10kΩ to 100kΩ and the
calculations used are included in the figures below.
original C value had to be modified from 10nF to 1nF due to
capacitor availability in lab room. By scaling the capacitor
down a factor of ten and the resistor up a factor of ten the time
constant was preserved by . This RC circuit was
driven by a 5 V, 1 kHz square wave as illustrated by the
completed P-Spice schematic below.
Figure 9: Circuit 1 (charging): Original circuit connected
to power and reduced to Thevenin equivalent.
Figure 31: P-Spice model of simple RC with 100kΩ
resistor.

4. CTU: EE 331 - Circuit Analysis II: Lab 3: Capacitor Charging and Discharging 4
This circuit was then simulated in P-Spice and signal
waveform measurements were taken using an oscilloscope.
The oscilloscope clearly showed the input step functions
being integrated into ramp functions due to the charging and
discharging of the capacitor while the resistor was also slightly
attenuating the signal. The attenuation also hinted that the
circuit was behaving like a low band pass filter. With these
observations the input frequency was increase by a factor of
ten to allow a better picture of the integration and attenuation
taking place. Results of both experiments follow.
Figure 14: Oscillator results taken by camera of input and
output signals for input of 1kHz and 10kHz. The top and
bottom oscillator voltage scales are 2V/div. The top oscillator
time scale is at .2 ms/div (5 div = 1 period). The bottom
oscillator time scale is at 20 s/div (5 div = 1 period).
IV. HAND CALCULATIONS
All hand calculations were illustrated in previous figures.
Figure 12: P-Spice simulation of 1kHz input square wave V. CONCLUSION
(red) and output triangle wave (green). Also illustrates
capacitor charge and discharge. This lab was a success and proved that the time constant
of a simple and complex RC circuit can be found through the
equation . Comparing the results after
doubling the value of the known resistors in a simple RC
circuit confirmed this hypothesis.
It was further successful in proving that the charging and
disharging time constants for a complex circuit can be dirived
by transforming the circuits into their respective Thevenin
equivalents.
Finally, by analyzing the input 1kHz square wave
against the output attenuated triangle wave this lab
demonstrated the selective frequency passing and signal
reshaping posibilities capable of a simple RC circuit.
REFERENCES
[1] R. E. Thomas, A. J. Rosa, and G. J. Toussaint, “The Analysis & Design
of Linear Circuits, sixth edition” John Wiley & Sons, Inc. Hoboken, NJ,
pp. 309, 2009.
Figure 13: P-Spice simulation of 10kHz input square wave
(red) and output triangle wave (green). Also illustrates the
integration and attenuation of higher high frequency
signals.