# 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.

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

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°

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.

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.

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.

· 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.
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°

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.

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.

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

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.

· 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?
· 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

http://www.ni.com/multisim/

6

image3.wmf

oleObject1.bin

image4.wmf

oleObject2.bin

image5

oleObject3.bin

oleObject4.bin

image6.wmf

oleObject5.bin

image7

image8

image9

image10

image11

image12

image13

image14

oleObject6.bin

oleObject7.bin

image1.PNG

image2.emf

image15

## Calculate the price of your order

Select your paper details and see how much our professional writing services will cost.

We`ll send you the first draft for approval by at
Price: \$36
• Freebies
• Format
• Formatting (MLA, APA, Chicago, custom, etc.)
• Title page & bibliography
• Amendments to your paper when they are needed
• 275 word/double-spaced page
• 12 point Arial/Times New Roman
• Double, single, and custom spacing

Our custom human-written papers from top essay writers are always free from plagiarism.

Your data and payment info stay secured every time you get our help from an essay writer.

Your money is safe with us. If your plans change, you can get it sent back to your card.

## How it works

1. 1
You give us the details
Complete a brief order form to tell us what kind of paper you need.
2. 2
We find you a top writer
One of the best experts in your discipline starts working on your essay.
3. 3
You get the paper done

## Samples from our advanced writers

Check out some essay pieces from our best essay writers before your place an order. They will help you better understand what our service can do for you.

• Analysis (any type)
Political science
APA
• Coursework
APA
• Essay (any type)
Is Pardoning Criminals Acceptable?
Criminal Justice
MLA

## Perks of our essay writing service

We offer more than just hand-crafted papers customized for you. Here are more of our greatest perks.

• Swift delivery
Our writing service can deliver your short and urgent papers in just 4 hours!
• Professional touch
We find you a pro writer who knows all the ins and outs of your subject.
• Easy order placing/tracking
Create a new order and check on its progress at any time in your dashboard.
• Help with any kind of paper
Need a PhD thesis, research project, or a two-page essay? For you, we can do it all.
• Experts in 80+ subjects
• Calculations and code
We also do math, write code, and solve problems in 30+ STEM disciplines.

• ### Is there a possibility of plagiarism in my completed order?

We complete each paper from scratch, and in order to make you feel safe regarding its authenticity, we check our content for plagiarism before its delivery. To do that, we use our in-house software, which can find not only copy-pasted fragments, but even paraphrased pieces of text. Unlike popular plagiarism-detection systems, which are used by most universities (e.g. Turnitin.com), we do not report to any public databases—therefore, such checking is safe.

We provide a plagiarism-free guarantee that ensures your paper is always checked for its uniqueness. Please note that it is possible for a writing company to guarantee an absence of plagiarism against open Internet sources and a number of certain databases, but there is no technology (except for turnitin.com itself) that could guarantee no plagiarism against all sources that are indexed by turnitin. If you want to be 100% sure of your paper’s originality, we suggest you check it using the WriteCheck service from turnitin.com and send us the report.

• ### I received some comments from my teacher. Can you help me with them?

Yes. You can have a free revision during 7 days after you’ve approved the paper. To apply for a free revision, please press the revision request button on your personal order page. You can also apply for another writer to make a revision of your paper, but in such a case, we can ask you for an additional 12 hours, as we might need some time to find another writer to work on your order.

After the 7-day period, free revisions become unavailable, and we will be able to propose only the paid option of a minor or major revision of your paper. These options are mentioned on your personal order page.