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Lab #2
R-L-C Components
Thompson Nguyen
Bench #8
Basic EE Lab II
Course number (EECE.2070)
Date submitted mm/dd/yyyy
Due date 07/24/2025
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I. SUMMARY
In this lab, the explorations of different electrical components such as a resistor, inductor, and
capacitor will be examined. An oscilloscope will also be used as a voltage-measuring instrument in
order to refine any skills with this tool. The impedance of an element using a current-sensing resistor
will be learned and measured. Comparing the measured and nameplate values of a resistor, inductor,
and capacitor will also be done.
II. EQUIPMENT
Table 1. Equipment Used
Equipment Type
Oscilloscope
Breadboard
Dual-Power Supply
Function Generator
DMM-Bench Top
Details
Make:
Model:
Serial Number:
Make:
Model:
Serial Number:
Make:
Model:
Serial Number:
Make:
Keysight
EDUX-1052G
CN6331335
N/A
N/A
N/A
Gwinstek
GPD-3303D
EL832096
Tektronix
Model:
AFG-1062
Serial Number
1919086
Make:
Keithley
Model:
2110 5 ½ DMM
Serial Number:
8008247
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Table 2. Components Used
Component Type
Decade Resistance
Box
100 Ohm Resistor
1.2k Ohm Resistor
3.3k Ohm Resistor
10 mH Inductor
0.47 uF Capacitor
Details
1x
1x
1x
1x
2x
1x
III. INTRODUCTION
In this lab, components such as a resistor, inductor, and capacitor will be used in order to examine
different measurements and behaviors. Another piece of equipment that is going to be used is the
Analog Discovery kit, which can be used outside of the lab to perform different experiments when
needed. This piece of equipment provides variable voltages directly in the range of -5.0V and +5.0V.
However, if more voltage needs to be applied, the Digilent PowerBrick can be used.
It is known that the reactance of an inductor or capacitor is a function of the applied frequency. This
can be defined using the following equations:
𝑋𝐿 = 2𝜋𝑓𝐿 (1)
And
𝑋𝑐 =
1
(2)
2𝜋𝑓𝐶
For electrical components in series, the total impedance is the sum of the individual impedances.
This is given by the following:
𝑍𝑇 = 𝑍1 + 𝑍2 + 𝑍3 … + 𝑍𝑁 (3)
For resistors in series, the total impedances is the following:
𝑅𝑇 = 𝑅1 + 𝑅2 + 𝑅3 + ⋯ + 𝑅𝑁 (4)
For inductors in series, the total impedance is:
𝑋𝐿 𝑇 = 2𝜋𝑓𝐿𝑇 where 𝐿𝑇 = 𝐿1 + 𝐿2 + 𝐿3 + ⋯ 𝐿𝑁 (5)
It is important to know that the individual and total inductive reactance of inductors is directly
proportional to frequency.
For capacitors in parallel, the total impedance is the following:
1
1
1
1
1
1
2
3
𝑛
𝑋𝐶 𝑇 = 2𝜋𝑓𝐶 where 𝐶 = 𝐶1 + 𝐶 + 𝐶 + ⋯ + 𝐶 (6)
𝑇
𝑇
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Whereas when these components are parallel, the equations are simply the inverse of one another.
In this lab, the root-mean-square will be calculated for various voltage measurements. The rootmean-square measures the magnitude of a varying quantity, in this case an AC sine wave. The root
means square can be calculated using the following equation.
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𝑉𝑅𝑀𝑆 = ( ) 𝐴 = 0.707𝐴 (7), where A is the amplitude of the sinusoidal wave
√2
Using the VRMS value, the Vp as well as the Vp-p values can be calculated using the equations below.
𝑉𝑝 = (√2)(𝑉𝑅𝑀𝑆 ) (8)
𝑉𝑃𝑃 = (2)(𝑉𝑝 ) (9)
Finally, by calculating the Vpp, the peak-to-peak current can be calculated.
𝑉𝑝𝑝
𝐼𝑝𝑝 = 𝑅 (10)
IV. CIRCUIT DESCRIPTION
Figure 1.1 Schematic of first circuit
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Figure 1.2 Physical representation of schematic
In this first circuit, a 1k Ω is connected in series with a 3.3k Ω resistor. From here the function
generator is connected to the corresponding pins at the top of the breadboard to supply a positive and
ground source. The funcntion generator will have a frequency of 500 Hz and an amplitude of 4.0
Vpp. As shown in Figure 1.1, the the 1k Ω resistor is connected to the positive source and the 3.3k
Ω resistor is connected to the ground source. Finally, channel one of the oscilloscope was connected
across the 3.3k Ω resistor. From here the function generator was turned on, and a sine was able to be
generated and measurements were taken accordingly.
Figure 1.3 Schematic of second circuit. A 1.2k Ω resistor is added
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Figure 1.4 Physical representation of schematic
For this next circuit, a 1.2k Ω resistor was added in series with the 3.3k Ω resistor. From here, the
positive end of the oscilloscope was connected to the positive end of the 1.2k Ω resistor and the
ground end of the oscilloscope probe was connected to the ground end of the 3.3k Ω resistor. This
would take measurements across the series resistors.
.Figure 1.5 Schematic of resistor-capacitor circuit
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Figure 1.6 Physical representation of RC circuit
For the next part of the experiment the 1.2k Ω and 3.3k Ω resistors were taken out and replaced with
a 1 μF capacitor. Like the 3.3k Ω resistor in Figure 1.1, it was placed in series with the 100 Ω
resistor. One end was connected to the positive side and the other was connected to the ground via a
jumper wire. From here, the positive end of the oscilloscope was connected to the positive end of the
capacitor and the ground end of the scope was connected to the ground end of the capacitor. The
function generator was also changed to have a frequency of 100 Hz and an amplitude of 4 Vpp.
After everything was changed and connected, the reactance was able to me measured and calculated
using equations above.
Figure 1.7 Schematic with another capacitor added
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Figure 1.8 Physical representation of schematic above
For the next part, a 0.47 μF was placed in parallel with the 1μF capacitor. From here the positive end
of the scope was placed on the positive side of 0.47 μF capacitor and the ground end of the scope
was placed on the ground end of the same capacitor. Since the capacitors are in parallel, the total
capacitance is changed and calculated differently which effects the reactance.
Figure 1.9 Schematic of resistor-inductor circuit
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Figure 1.10 Physical Circuit of schematic
In this last part, both capacitors were taken out of the circuit and then replaced with a 10 mH
inductor making a RL circuit. The positive end of the oscilloscope was connected to the positive end
of the inductor, and the negative end of the probe was connected to the ground end of the inductor.
From here the function generator was set to have a frequency of 2 kHz and an amplitude of 1 Vpp.
Finally, measurements were able to be taken.
V. MEASUREMENTS
Table 1
VRs (DMM)
0.041 V
VRs(Peak)
0.057 V
VRs(P-P_
0.115 V
IP-P
0.00115 A
R
3478.3 Ω
Table 2
RT (Calc)
4438 Ω
VRs (DMM)
0.0301 V
VRs(P-P)
0.0851 V
IP-P
0.000862 A
RT
4637.68 Ω
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Table 3
Parts (b) – (f)
Parts (g) – (j)
VRS (DMM)
0.084 V
0.000335 V
IP-P
0.00239 A
0.00000960 A
XC (meas)
225.941 Ω
Xc (calc)
1619 Ω
1082 Ω
C
0.983 μF
1.47 μF
Table 4
Parts (b) –
(f)
Parts (g) –
(j)
VRS (DMM)
0.140 V
VRS (p-p)
0.395 V
Ip-p
0.004 A
Xc (meas)
250 Ω
Xc (calc)
125.66 Ω
C
9.99 mH
0.00870 V
0.0246 V
0.000249 A
4016 Ω
62.83 Ω
0.005 H
Snapshot 1: Scope of first resistor circuit
Snapshot 2: Scope of single inductor circuit
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Snapshot 3: Scope of series inductor circuit
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VI. DISCUSSION
In this lab, R-L-C experimented with and observed using various tools and techniques. Different
values were measured such as resistance and VRMS values which are important when determining
voltage values. The VRMS value allows for the calculations of the VP and VPP values as seen in Table
1 - 4. The VRMS value is measured by using the bench-top multimeter and looking at the AC voltage
reading. The value that it reads is the effective value of the respective AC signal. This value is
always changing because the signal that is outputted is a sine wave and by using equations (8) and
(9) Vp and Vpp can be calculated.
When looking at AC circuits with inductors or capacitors, the reactance of these components was
calculated. The reactance is the opposition that an element presents to a change in current. Elements
that are reactance rely on frequency to be calculated like in equations (1) and (2). It is important
know that when calculating the reactance of a component, the units is in ohms.
For the first part of the lab, a 100 Ω resistor was placed in series with a 3.3k Ω resistor as seen in
Figure 1.2. As seen in Table 1, the voltage across the 100 Ω resistor was measured using the
multimeter, which was also the VRMS value. Since the VRMS value was taken, the Vp and Vpp values
were calculated using the equation (8) and (9). By getting the Vpp calculation, the Ipp (peak to peak
current) can be calculated using equation (10). The peak-to-peak current measures the difference
between the maximum positive and maximum negative values of an AC waveform. Finally, the total
resistance of the circuit can be calculated by diving 4 by the peak-to-peak current as shown in Table
1. Since the two resistors are in series, the sum of the two would equal the total resistance which is
what is shown in that table.
Afterwards, another resisor of value 1.2k Ω was added to the circuit and put into series with the 3.3k
Ω resistor. The same procedure was done, however the total resistance has a different value and the
oscilloscope probe was connected acrosss the 3.3k Ω resistor and the 1.2k Ω resistor. As seen in
Table 2, the total resistance that was calculated first was 4438 Ω. Then after using the VRMS value to
calculate for Vpp, Vp, and Ipp, the resistance value was calculated using the same technique as before.
The total resistance came out to be 4637.68 Ω.
Next, instead of having a resistors across the circuit, capacitors are used to create a RC circuit. As
seen in Figure 1.6 a capacitor with value of 1 μF is placed in series with the 100 Ω reistor. The
oscillocope probe was then connected across the capacitor and displayed onto the oscilloscope. From
here the VRMS value was taken in order to calculate for Vp, Vpp, and Ipp as seen in Table 3. After the
values were taken, the reactance of the capacitor was also calculated using equation 2. The value that
was calculated came out to 1619 Ω. Finally, when rearranging the same equation to find capacitance,
it is seen that the capacitance is 0.983 μF which is about what the value of the capacitor that was
used is.
After this step was done, a second capacitor with value of 0.47 μF was placed in parallel with the
1μF capacitor. When calculating for the total capacitance it is important that the proper equation is
used, which is equation (6). The same steps were done and the the numbers that were calculated and
proven were shown in Table 3.
Finally, for the last step, the capacitors were taken out and replaced with a 10 mH inductor as shown
in Figure 1.9. For this procedure, the setup was similar to the previous steps, where the oscilloscope
probe was connected across the inducotr. As seen in Table 4, the same values that were calculated in
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the previous steps were caluclated, however the reactance was done differently. Using equation (1),
the reactance was calculated then used to see if it would equal the total inductance, which was
proven in Table 4. The last and final step that was done in the procedure was another 10 mH
inductor being added but this time in series with the original one. In order to compute the total
induactance, the two were added together. Then the same steps were done in to calculate for the
reactance and total inductance values.
VII. CONCLUSION
This lab experimented with different types of AC circuits including resistor, resistor-capacitor, and
resistor-inductor circuits. By experimenting with these circuits, different values were able to be
measured and obtained such as VRMS, Vp, Vpp and more. These values are important in calculating
more values such as peak-to-peak current as well as reactance values. All of which are important in
the analyzation of AC waveforms and observing their behaviors. The oscilloscope and function
generator were important as well in the physical representations of these waveforms as well as
seeing how different frequencies affect vban output.
VIII. QUESTIONS
N/A
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REFERENCES
[1] R. L. Boylestad, Laboratory Manual to Accompany Introductory Circuit Analysis, 11th ed.
Pearson, 2007.
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