Series RL Circuits
Add Abstract, Introduction and Conclusion to the Inductors in DC Circuits Lab. Input calculation
Electric Circuits Lab
Series RL Circuits: Phase Angle, Phase Lead, and Inductors as Differentiators
I.
Objectives:
After completing this lab experiment, you should be able to:
1. Understand the effect of frequency on inductive reactance.
2. Measure the impedance of an RL circuit.
3. Measure the phase angle and phase lead of an RL circuit using the oscilloscope.
4. Draw the impedance and voltage phasor diagrams.
5. Understand how an inductor differentiates current.
II.
Parts List:
1. Resistors 100 Ω, 1 kΩ, 10 kΩ.
2. Inductors 1 µH, 100mH.
III.
Procedures:
Part I
:
1.
Connect the following circuit.
Figure 1: RL Circuit
2.
Connect one DMM across the resistor and one DMM across the inductor.
Set both DMMs to read AC Voltage.
Measure the voltage drop across each component.
Record the result in
Table
1.
3. Use Ohm’s law to
calculate the current flowing through the resistor. Since the circuit in
Figure 1 is a series RL circuit, the same current will flow through the inductor and the resistor.
Record the result in
Table 1.
Total current I =
4.
Calculate the inductive reactance using Ohm’s law.
Record the result in
Table 1.
Inductive Reactance XL =
5. Finally,
calculate the inductive reactance using the inductive reactance equation.
Record the result in
Table 1.
Inductor L1
Voltage across, R
845.958 mV
Voltage across, L
533.246 mV
Total Current, I
0.846 mA
Inductive Reactance, XL
630.35 ohms
Computed Reactance, XL
628.32 omhs
Table 1: Calculated and measured values
6.
Adjust the function generator frequency following the steps in
Table 2. Use the DMM to
measure the voltage across the resistor and the inductor.
Record your measurements.
Frequency (in Hz)
VR
(measured)
VL
(measured)
I =
XL =
XL = 2πfL
(calculated)
300
982.58 mV
185.81 mV
0.9856 mA
189.10 ohms
188.50 ohms
1k
845.958 mV
533.246 mV
0.846 mA
630.35 ohms
628.32 ohms
3k
467.467 mV
833.996 mV
0.468 mA
1.78 kΩ
1.88kΩ
5k
302.425 mV
953.161 mV
0.302 mA
3.15 kΩ
3.14 kΩ
7k
221.027 mV
975.265 mV
0.221 mA
4.41 kΩ
4.40 kΩ
9k
173.593 mV
984.811 mV
0.174 mA
5.66 kΩ
5.66 kΩ
11k
142.743 mV
989.751 mV
0.143 mA
6.92 kΩ
6.91 kΩ
13k
121.133 mV
992.626 mV
0.121 mA
8.20 kΩ
8.17 kΩ
15k
105.174 mV
994.442 mV
0.105 mA
9.47 kΩ
9.43 kΩ
Table 2: Calculated and measured values
7.
Plot the graph for
Frequency vs. VL.
(Use Word or Excel to create the plot)
Figure 2. Plot of Frequency vs. Inductor Voltage
Part II:
8.
Build the circuit in
Figure 2.
Figure 2: Series LR Circuit
9.
Set the voltage source amplitude to
1.5 VP and
frequency to
25 kHz, sine wave
10.
Connect Channel A of the oscilloscope across the resistor and
measure the peak voltage drop (VR).
Record the result in
Table 3.
11. Use Ohm’s law to
calculate the peak current flowing through the resistor. Because it is a series circuit, the same current will flow through the inductor.
Record the result in
Table 3.
Total current I =
VR
I
VL
XL
ZT
1.133 V
0.113 mA
1.786 V
15.80 kΩ
13.27 kΩ
46.49ᶿ
Table 3: Calculated and measured values
12.
Connect Channel B of the oscilloscope across the inductor and
measure the peak voltage drop (VL).
Record the value in
Table 3 above.
13.
Calculate the inductive reactance using Ohm’s law.
Record the result in
Table 3.
Inductive Reactance XL =
14. Now,
calculate the total impedance (ZT) value using the equation.
Record the result in
Table 3.
Total Impedance (ZT) =
15.
Calculate the phase angle between VR and VS using the formula.
Record the result in
Table 3. Also, record this value in
Table 4 under Phase Angle calculated value.
Phase angle,
Part III: Phase Angle and Phase Lead Measurement
Phase Angle
16.
Connect Channel B of the oscilloscope across the voltage source and
run the simulation. Channel A should still be connected across the resistor.
17. The waveforms should look like the ones shown in
Figure 4.
Figure 4: VS and VR waveforms
18. Obtain a stable display showing a couple of cycles for Channel B (which is showing VS) and disable Channel A by setting it to 0.
19.
Measure the time period (T) of the source voltage.
Record the result in
Table 4. (Use the cursors to measure the period on the scope it will show as T2-T1). Remember that the period is the time taken to complete one cycle). See
Figure 5.
Figure 5: Measuring time period (T)
Type of Angle
Measured
Period (T)
Time difference (∆t)
Measured Angle
Calculated Angle
Phase angle θ
40 ms
6.4 ms
57.6
57.6
Phase Lead Φ
Table 4: Phase angle and phase lead measurements
20. Now set the oscilloscope to view both the channels.
21. Adjust the amplitude of the signals using Channel A and Channel B V/Div scale until both channels appear to have the same amplitude as seen on the scope face. (as close as possible)
22. Spread the signals horizontally using the Timebase (Sec/Div) control until both signals are just visible across the screen as shown.
23.
Measure the time duration between the two signals (∆t) and record the result in
Table 4. (Use cursors as shown in
Figure 6)
Figure 6: Measuring the time difference
24.
Calculate the phase angle using the formula and record the result in
Table 4.
Phase angle, θ = (∆t/T) * 360°
Phase Lead
25.
Connect your circuit as shown in
Figure 7. When the output of an RL circuit is taken across the inductor, the circuit is called an RL lead circuit. The output voltage in an RL lead circuit will lead the input voltage.
Figure 7: RL Lead Circuit
26.
Calculate the phase lead using the equation. Notice the similarity to the equation for the phase angle. The phase lead angle and phase angle of an RL circuit are complementary angles. (Their sum is 90°.) Use R and XL values from
Table 3.
Phase Lead,
27.
Measure the time period (T) of the source voltage (as in Step 19). Record this value in
Table 4.
28. Now set the oscilloscope to view both the channels.
29. Adjust the amplitude of the signals using Channel A and Channel B V/Div scale until both channels appear to have the same amplitude as seen on the scope face. (as close as possible)
30. Spread the signals horizontally using the Timebase (Sec/Div) control until both signals are just visible across the screen as shown in
Figure 6.
31.
Measure the time duration between the two signals (∆t) and record the result in
Table 4.
32.
Calculate the phase lead using the formula and record the result in
Table 4.
Phase lead, θ = (∆t/T) * 360°
33.
Plot the Voltage and Impedance Phasor Diagrams. Clearly indicate the phase angle and the phase lead.
Electric Circuits Lab
Instructor: ———–
Series RL Circuits
Student Name(s):
Click or tap here to enter text.
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: 1/1/2018
Contents
Abstract 3
Introduction 3
Procedures 3
Data Presentation & Analysis 4
Calculations 4
Required Screenshots 4
Conclusion 4
References 5
Abstract
(This instruction box is to be deleted before submission of the Lab report)
What is an Abstract?
This should include a brief description of all parts of the lab. The abstract should be complete in itself. It should summarize the entire lab; what you did, why you did it, the results, and your conclusion. Think of it as a summary to include all work done. It needs to be succinct yet detailed enough for a person to know what this report deals with in its entirety.
Objectives of Week 2 Lab 2:
· Understand the effect of frequency on inductive reactance.
· Measure the impedance of an RL circuit.
· Measure the phase angle and phase lead of an RL circuit using the oscilloscope.
· Draw the impedance and voltage phasor diagrams.
· Understand how an inductor differentiates current.
Introduction
(This instruction box is to be deleted before submission of the Lab report)
What is an Introduction?
In your own words, explain the reason for performing the experiment and give a concise summary of the theory involved, including any mathematical detail relevant to later discussion in the report. State the objectives of the lab as well as the overall background of the relevant topic.
Address the following items in your introduction:
· What is Impedance for an RL circuit? (Give formula)
· What is phase angle for an RL circuit? How is it calculated?
· What is phase lead for an RL lead circuit? How is it calculated?
· How/why does an inductor differentiate current? Give formula.
Procedures
Part I
:
1.
Connect the following circuit.
Figure 1: RL Circuit
2.
Connect one DMM across the resistor and one DMM across the inductor.
Set both DMMs to read AC Voltage.
Measure the voltage drop across each component.
Record the result in
Table 1.
3. Use Ohm’s law to
calculate the current flowing through the resistor. Since the circuit in
Figure 1 is a series RL circuit, the same current will flow through the inductor and the resistor.
Record the result in
Table 1.
Total current I =
4.
Calculate the inductive reactance using Ohm’s law.
Record the result in
Table
1.
Inductive Reactance XL =
5. Finally,
calculate the inductive reactance using the inductive reactance equation.
Record the result in
Table 1.
6.
Adjust the function generator frequency following the steps in
Table 2. Use the DMM to
measure the voltage across the resistor and the inductor.
Record your measurements in
Table 2.
7.
Plot the graph for
Frequency vs. VL.
Part II:
8.
Build the circuit in
Figure 2.
Figure 2: Series LR Circuit
9.
Set the voltage source amplitude to
1.5 VP and
frequency to
25 kHz, sine wave
10.
Connect Channel A of the oscilloscope across the resistor and
measure the peak voltage drop (VR).
Record the result in
Table 3.
11. Use Ohm’s law to calculate the peak current flowing through the resistor. Because it is a series circuit, the same current will flow through the inductor.
Record the result in
Table 3.
Total current I =
12.
Connect Channel B of the oscilloscope across the inductor and
measure the peak voltage drop (VL).
Record the value in
Table 3.
13.
Calculate the inductive reactance using Ohm’s law.
Record the result in
Table 3.
Inductive Reactance XL =
14. Now,
calculate the total impedance (ZT) value using the equation .
Record the result in
Table 3.
Total Impedance (ZT) =
15.
Calculate the phase angle between VR and VS using the formula . Record the result in
Table
3 above. Also, record this value in
Table 4 under Phase Angle calculated value.
Phase angle,
Part III: Phase Angle and Phase Lead Measurement
Phase Angle
16.
Connect Channel B of the oscilloscope across the voltage source and
run the simulation. Channel A should still be connected across the resistor.
17. The waveforms should look like the ones shown in
Figure 4.
Figure 4: VS and VR waveforms
18. Obtain a stable display showing a couple of cycles for Channel B (which is showing VS) and disable Channel A by setting it to 0.
19.
Measure the time period (T) of the source voltage.
Record the result in
Table 4. (Use the cursors to measure the period (on the scope it will show as T2-T1). Remember that the period is the time taken to complete one cycle). See
Figure 5.
Figure 5: Measuring time period (T)
20. Now set the oscilloscope to view both the channels.
21. Adjust the amplitude of the signals using Channel A and Channel B V/Div scale until both channels appear to have same amplitude as seen on the scope face. (as close as possible)
22. Spread the signals horizontally using the Timebase (Sec/Div) control until both signals are just visible across the screen as shown .
23.
Measure the time duration between the two signals (∆t) and record the result in
Table
4. (Use cursors as shown in
Figure 6)
Figure 6: Measuring the time difference
24.
Calculate the phase angle using the formula and
record the result in
Table
4.
Phase angle, θ = (∆t/T) * 360°
Phase Lead
25.
Connect your circuit as shown in
Figure 7. When the output of an RL circuit is taken across the inductor, the circuit is called an RL lead circuit. The output voltage in an RL lead circuit will lead the input voltage.
Figure 7: RL Lead Circuit
26. Calculate the phase lead using the equation . Notice the similarity to the equation for the phase angle. The phase lead angle and phase angle of an RL circuit are complementary angles. (Their sum is 90°.) Use R and XL values from Table 3.
Phase Lead,
27.
Measure the time period (T) of the source voltage (as in Step 19).
Record this value in
Table 4.
28. Now set the oscilloscope to view both the channels.
29. Adjust the amplitude of the signals using Channel A and Channel B V/Div scale until both channels appear to have the same amplitude as seen on the scope face. (as close as possible)
30. Spread the signals horizontally using the Timebase (Sec/Div) control until both signals are just visible across the screen as shown in
Figure 6.
31.
Measure the time duration between the two signals (∆t) and
record the result in
Table 4.
32.
Calculate the phase lead using the formula and
record the result in
Table 4.
Phase lead, θ = (∆t/T) * 360°
33.
Plot the Voltage and Impedance Phasor Diagrams. Clearly indicate the phase angle and the phase lead.
Part IV: The Inductor Differentiates Current
34.
Construct the following RL circuit in Multisim. Set the triangular current source to 1mA and 1ms.
Figure 8: Differentiator Circuit
35.
Connect Channel A across the resistor and Channel B across the inductor. (Note: change one or both trace colors to better observe the two signals)
36. Your signals should look like the example in
Figure 9.
Figure 9: Inductor as a differentiator waveforms
37. Channel A will show the voltage across the resistor. This signal can be used to find the circuit current using Ohm’s law.
38. Channel B shows the voltage across the inductor. Show that this signal satisfies the following equation on the piecewise differentiable intervals.
39. Refer to
Figure 10 to answer the following questions.
Figure 10: Differentiator values, 0 to 0.5 ms
a. The signal has a period of 1 ms. Write the equation for the circuit current on the interval 0 to 0.5 ms by following the steps.
b. The general equation of a line is
.
We will start by finding vR(t). In this case, y is vR(t) and m is the slope of the voltage. Fill in the values of vR(0.5) and vR(0) to find the slope. Channel A, Cursor T2 gives the resistor voltage at t=0. Channel A, cursor T1 gives the resistor voltage at t = 0.5 ms.
c. Next, find b, the voltage at the beginning of the interval, v(0), expressed in volts.
d. Write the equation for the resistor voltage on the interval of 0 to 0.5 ms using the values above.
e. Find the equation for i(t)
f. Find the equation of vL(t) by differentiating i(t).
g. Compare this value to the vL(t) waveform.
40. Refer to
Figure 11 to answer the following questions.
Figure 11: Differentiator values, 0.5 ms to 1.0ms
a. The signal has a period of 1 ms. Write the equation for the circuit current on the interval 0.5 ms to 1.0 ms by following the steps .
b. The general equation of a line is
.
We will start by finding vR(t). In this case, y is vR(t) and m is the slope of the voltage. Fill in the values of vR(0.5) and vR(1.0) to find the slope. Channel A, Cursor T2 gives the resistor voltage at t = 50 ms. Channel A, cursor T1 gives the resistor voltage at t = 100 ms.
c. Next, find b, the voltage at the beginning of the interval, v(0.5), in volts
d. Write the equation for the resistor voltage on the interval of 0.5 ms to 1.0 ms using the values
e. Find the equation for i(t)
f. Find the equation of vL(t) by differentiating i(t).
g. Compare this value to the vL(t) waveform.
Data Presentation & Analysis
(This instruction box is to be deleted before submission of the Lab report)
This section is the most important section of the report. Data representations and analysis are crucial in the engineering field. This section should include all raw data collected, e.g., voltage and current readings. All results are to be presented in both tabular and graphical forms. All tables must have titles and all Figures must have brief captions.
Inductor L1
Voltage across, R
Voltage across, L
Total Current, I
Inductive Reactance, XL
Computed Reactance, XL
Table 1: Calculated and measured values
Frequency (in Hz)
VR
(measured)
VL
(measured)
I =
XL =
XL = 2πfL
(calculated)
300
1k
3k
5k
7k
9k
11k
13k
15k
Table 2: Calculated and measured values
VR
I
VL
XL
ZT
Table 3: Calculated and measured values
(Use Word or Excel to create the plot and place here.)
Plot 1: Frequency vs. Inductor Voltage
Type of Angle
Measured
Period (T)
Time difference (∆t)
Measured Angle
Calculated Angle
Phase angle θ
Phase Lead Φ
Table 4: Phase angle and phase lead measurements
(Use Word or Excel to create the Phasor Diagrams and place here.)
Plot 2(a) Impedance Phasor Plot 2(b) Voltage Phasor
Calculations
(This instruction box is to be deleted before submission of the Lab report)
Show all of your calculations in this section.
Part I step 3: I =
Part I step 4: XL =
Part I step 5: L =
Part II step 11: I =
Part II step 13: XL =
Part II step 14: ZT =
Part II step 15:
Part III step 24:
Part III step 26:
Part III step 32:
Part IV step 39 b: m =
Part IV step 39 d: vR(t) =
Part IV step 39 e: i(t) =
Part IV step 39 f: vL(t) =
Part IV step 41 b: m =
Part IV step 41 d: vR(t) =
Part IV step 41 e: i(t) =
Part IV step 41 f: vL(t) =
Required Screenshots
(This instruction box is to be deleted before submission of the Lab report)
Place screenshots of measurements in this section.
Figure 12: Screenshot of Waveforms Part 3 Step 10
Figure 13: Screenshot of Waveforms Part 3 Step 12
Figure 14: Screenshot of Waveforms Part 3 Step 19
Figure 15: Screenshot of Waveforms Part 3 Step 23
Figure 15: Screenshot of Waveforms Part 3 Step 27
Figure 16: Screenshot of Waveforms Part 3 Step 31
Conclusion
(This instruction box is to be deleted before submission of the Lab report)
What is a Conclusion?
This section should reflect your understanding of the experiment conducted. Important points to include are a brief discussion of your results, and an interpretation of the actual experimental results as they apply to the objectives of the experiment set out in the introduction should be given. Also, discuss any problems encountered and how they were resolved.
Address the following in your conclusions:
· Were your measured and calculated inductive reactance values in agreement?
· What happened to the inductance and the inductive reactance as you increased the frequency of the voltage source?
· Were your measured and calculated phase angle values in agreement?
· Which quantity leads in a series RL circuit? (Current or voltage) How do you know?
· What happens to phase angle as the frequency increases? What happens to phase angle as the frequency decreases?
· Were your measured and calculated phase lead values in agreement?
· Which quantity leads in an RL lead circuit? (Source voltage or inductor voltage)
· What is the relationship between phase angle and phase lead?
· What happens to the phase lead as the frequency increases? What happens to the phase lead as the frequency decreases?
References
Floyd, T. L., & Buchla, D. M. (2019).
Principles of Electric Circuits (10th Edition). Pearson Education (US).
https://bookshelf.vitalsource.com/books/9780134880068
(2017) National Instruments Multisim (V 14.1) [Windows]. Retrieved from
http://www.ni.com/multisim/
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