Week 3 Lab 1 Capacitors in DC Circuits Lab Report
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ECPI University, Virginia Beach *
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Electrical Engineering
Date
Dec 6, 2023
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Electric Circuits Lab
Instructor:
Cameron Ruddy
Capacitors in DC Circuits
Student Name(s):
Brandon Walker
Click or tap here to enter text.
Honor Pledge:
I pledge to support the Honor System of ECPI. I will refrain from any form of academic
dishonesty or deception, such as cheating or plagiarism. I am aware that as a member of the
academic community, it is my responsibility to turn in all suspected violators of the honor code. I
understand that any failure on my part to support the Honor System will be turned over to a
Judicial Review Board for determination. I will report to the Judicial Review Board hearing if
summoned.
Date:
0/18/2023
Contents
Abstract
.......................................................................................................................................................
3
I
ntroduction
................................................................................................................................................
3
Procedures
...................................................................................................................................................
3
Data Presentation & Analysis
.......................................................................................................................
4
Calculations
.............................................................................................................................................
4
Required Screenshots
..............................................................................................................................
4
Conclusion
...................................................................................................................................................
4
References
...................................................................................................................................................
5
2
Abstract
We will be learning in this lab how to measure resistance of capacitors and capacitance of RC
circuits. We will be using function generators and an oscilloscope to help with our
measurements. We will learn the effects of series and parallel in RC circuits time constants with
the use of Vr, and Vc.
I
ntroduction
We will be performing experiments to help us learn what the time constant for a RC circuit is
and why this is important. We find that time constant is t=RxC and this determines the rate of
charging and discharging in the circuit. Capacitors in series combine with the formula
1/ctotal=1/c1+1/c2+1/c3 for how every many capacitors in series. When capacitors are
connected in parallel we use the equation Ctotal=C1+C2… for how every many capacitors in
parallel. Capacitive reactance is how much capacitors resist the flow of AC with the formula
XC=1/2piefC
Procedures
Part I:
1.
Construct
the circuit shown in
Figure 1
in Mutism.
Figure 1: Series RC Circuit
3
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2.
Connect
Channel A of the oscilloscope across the voltage source and Channel B across the
capacitor.
3.
Set
the function generator to
5V
pp
; 100 Hz, Square Wave 50% duty cycle with 2.5 DC
offset
if using a function generator
.
If using clock voltage, set it to 5V
pp
, 100 Hz. The DC
offset can be modeled by using DC mode on the oscilloscope.
4.
Observe
the signals on the scope screen. See
Figure 2(a)
below. (Use Volts/Div and
Time/DIV settings to adjust the signal)
Figure 2(a): Voltage across the Voltage Source and the capacitor
5.
Disable
Channel A, by setting it to 0, while observing Channel B. You should be able to see
the waveform as shown below. Use time base and Channel A scale to adjust the signal.
4
Figure 2(b): Voltage across the capacitor
6.
Change the time base (Sec/Div) until you have a clear waveform on the scope as shown in
Figure 2(c).
Figure 2(c): Voltage across the capacitor
7.
Calculate
the time constant of the RC circuit using the circuit parameter values.
Record
the
result in
Table 1
under calculated value.
5
= R*C
8.
Measuring the time constant with V
C
:
i.
Measure
the peak value of the signal, by placing one of the cursors (T1) at the
peak point ___5.00v______.
ii.
Calculate
the 63% of the above value ___3.15v______.
iii.
Place the second cursor (T2) at the step (ii) value above and T1 at zero just before
the capacitor voltage starts rising as shown in
Figure 3
.
iv.
Observe
the value of T2-T1 on the scope, which is the one time constant, as
shown below.
v.
Record
the result in
Table 1
above under measured value using V
C
.
Figure 5: Measuring RC time constant using V
C
9.
Connect
Channel B of the oscilloscope across the resistor.
10.
You should be able to see the waveform as shown below. (Use Volts/Div and Time/DIV
knobs to adjust the signal)
6
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Figure 6(a): Voltage across the resistor
11. Measuring the time constant with V
R
:
Measure
the peak value of the signal, by placing one of the cursors (T1) at
the peak point ______5.00v___.
Calculate
the 37% of the above value ____1.85_____.
Place the second cursor (T2) at the step (ii) value above.
Observe the T2-T1 value on the scope, which is the one time constant.
Record
the result in
Table 1
above under measured value using V
R
.
7
Figure 6(b): Measuring RC time-constant using V
R
Part II:
12. Place
two capacitors in series as shown in
Figure 7
below.
Figure 7: Series Capacitors
13. Calculate
the total capacitance value and
record
the results in
Table 2
.
C
T
=
1
1
C
1
+
1
C
2
14. Measure
the total capacitance value. Use the following procedure to measure the
capacitance in Multisim.
Connect
the impedance Meter (Simulate>>Instruments>>LabView
Instruments>>Impedance Meter) as shown in
Figure 8
.
Measure
the capacitive reactance, X
C
, as shown in
Figure 8
.
Calculate
the capacitance using the equation,
C
=
1
2
πf X
C
and
record
the value in
Table 2
.
Figure 8: Impedance Meter in Multisim
8
15. Modify
the circuit as shown below, by placing two 0.22µF capacitors in series as in
Figure
8
.
Figure 8: RC circuit with two series capacitors
16. Calculate
the new RC time constant using measured values.
Record
the result in
Table 3.
17. Connect
Channel A of the oscilloscope across the resistor
18.
Adjust the trigger if needed, and you should be able to see the waveform as shown in
Figure 9
below.
Figure 9: Voltage Across the Resistor
19. Repeat
step 11.
Record
the measured time constant in
Table 3
.
9
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Part III:
20. Place
two capacitors in parallel as shown in
Figure 10
below. (
Note:
The 0.001 Ω resistor is
ONLY
required for simulation in Multisim. Without the resistor, the mathematical model will
not converge).
Figure 10: Parallel Capacitors
21. Calculate
the total capacitance value and
record
the results in
Table 4
below.
C
T
=
C
1
+
C
2
22. Measure
the total capacitance value. Use the following procedure to measure the
capacitance in Multisim.
Connect
the impedance Meter (Simulate>>Instruments>>LabView
Instruments>>Impedance Meter).
Measure
the capacitive reactance.
Calculate
the capacitance using the equation,
C
=
1
2
πf X
C
and
record
the value in
Table 4.
23. Modify
the circuit by placing two 0.22µF capacitors in parallel as in
Figure 11.
10
Figure 11: RC Circuit with Parallel Capacitors
24. Calculate
the new RC time constant using measured values.
Record
the result in
Table 5
.
25. Connect
Channel A of the oscilloscope across the resistor.
26.
You should be able to see the waveform as in
Figure 12
below. (Use Volts/Div and Time/DIV
knobs to adjust the signal)
27.
Use the cursors on the oscilloscope to
measure
the time constant (refer to step 11).
Record
the result in
Table 5
under measured value.
Figure 12: Voltage across the resistor
11
Data Presentation & Analysis
Calculated
value
Measured
value using V
C
Measured
value using V
R
Time constant
(
)
220.000uS
274.621uS
220.251uS
Table 1: Calculated and measured time constant values
Calculated Value
Measured Value
Capacitance
0.11uF
0.11uF
Table 2: Series Capacitors
Calculated value
Measured value using V
R
Time constant (
)
110.000uS
109.848
Table 3: Calculated and measured time constant values
Calculated value
Measured value
Capacitance
0.44uF
0.44uF
Table 4: Parallel Capacitors
Calculated value
Measured value using V
R
Time constant (
)
440.000uS
457.880
Table 5: Calculated and measured time constant values
12
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Calculations
Part 1 step 7:
= 220.000uS
Part 2 step 13: C
T
=0.11uF
Part 2 step 14: C
T
=0.11uF
Part 2 step 16:
= 110.000uS
Part 2 step 19:
= 109.848
Part 3 step 21: C
T
=0.44uF
Part 3 step 22: C
T
=0.44uF
Part 3 step 24:
= 440.000uS
Required Screenshots
Figure 13: Screenshot of Waveforms Part 1 Step 8
Figure 14: Screenshot of Waveforms Part 1 Step 11
13
Figure 15: Screenshot of Impedance Meter Part 2 Step 14
Figure 16: Screenshot of Waveforms Part 2 Step 19
14
Figure 17: Screenshot of Impedance Meter Part 3 Step 22
Figure 18: Screenshot of Waveforms Part 3 Step 27
15
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Conclusion
Did your measured results match your calculated values? If not, why not?
Yes my values did match very close to the calculated values.
What happened to the overall capacitance when you went from one series capacitor to
two? (Did capacitance increase or decrease?) When capacitors are added in series the
overall capacitance decreases.
What happened to the overall capacitive reactance when you went from one series
capacitor to two? (Did the capacitive reactance increase or decrease?) The capacitive
reactance increases when capacitors are added in series.
What happened to the time constant when you went from one series capacitor to two?
(Did the time constant increase or decrease?) The time constant decreased since the
overall capacitance decreased.
What happened to the overall capacitance when you went from one capacitor to two
parallel capacitors? (Did the capacitance increase or decrease?) The capacitance
increased when going from one to two parallel capacitors.
What happened to the overall capacitive reactance when you went from one capacitor to
two parallel capacitors? (Did the capacitive reactance increase or decrease?) The
capacitance reactance decreases going from one to two parallel capacitors.
What happened to the time constant when you went from one capacitor to two parallel
capacitors? (Did the time constant increase or decrease?) The time constant increases
going from one to two parallel capacitors.
16
References
Floyd, T. L., & Buchla, D. M. (2019).
Principles of Electric Circuits
(10th Edition). Pearson
Education (US).
https://bookshelf.vitalsource.com/books/9780134880068
17
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