Download Inductive Reactance

Inductive Reactance
Electronics
Lesson Plan
Performance Objective
Upon completion of the lesson, students will be able to demonstrate an understanding of inductive reactance
through satisfactory completion of both informal and formal assessments.
Specific Objectives
 Define terms and symbols associated with the lesson.
 List the factors necessary to calculate inductive reactance.
 Select true statements describing current and voltage relationships in RL circuits.
 Recall formulas associated with the lesson.
 Select true statements concerning inductive time constants.
 Complete the labels on a universal time constant chart.
 Solve computations related to the lesson.
 Demonstrate the ability to
o show the effect of inductance in AC circuits; and
o solve the values of an operating RL circuit.
Terms
 RL circuit-a circuit that has both resistance (usually in the form of a resistor, although any circuit will
have some resistance in things like wires, etc.) and inductive reactance. The phase relationship
between voltage and current in this type of circuit will be somewhere between 0 degrees and 90
degrees.
 Resistance- opposition to current flow, which results in energy dissipation.
 Reactance- opposition to a change in current or voltage, which does not result in energy dissipation.
(NOTE: this opposition is caused by inductive and capacitive effects.)
 Impedance- opposition to current including both resistance and reactance. (NOTE: Resistance,
reactance, and impedance are all measured in ohms.)
 Inductive reactance- the opposition to a change in current caused by inductance.
 Power- the rate of energy consumption in a circuit (true power).
 Reactive power- the product of reactive voltage and current in an AC circuit.
 Apparent power- the product of voltage and current in an AC circuit.
 Power factor- the ratio of the true power (watts) to apparent power (volt-amperes) in an AC circuit.
 Phase angle- the angle in degrees or radians that the current leads or lags the voltage in an AC circuit.
 Angular velocity- the rate of change of cyclical motion expressed in units of radians per second.
 Time constant- the time required for an exponential quantity to change by an amount equal to 0.632
times the total change that will occur.
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Time
It should take approximately two, 45-minute class periods to teach the lesson and two 45-minute class periods
to complete the worksheets and the formal assessment.
Preparation
TEKS Correlations
This lesson, as published, correlates to the following TEKS. Any changes/alterations to the activities may result
in the elimination of any or all of the TEKS listed.
Electronics
 130.368 (c)
o (3) The student develops skills for managing a project. The student is expected to:
(A) use time-management techniques to develop and maintain work schedules and
meet deadlines;
(B) complete work according to established criteria; and
(C) participate in the organization and operation of a real or simulated engineering project.
o (5) The student implements the concepts and skills that form the technical knowledge of
electronics using project-based assessments. The student is expected to:
(B) demonstrate an understanding of magnetism and induction as they relate to
electronic circuits; and
(C) demonstrate knowledge of the fundamentals of electronics theory.
o (6) The student applies the concepts and skills to simulated and actual work situations. The
student is expected to:
(B) apply electronic theory to generators, electric motors, and transformers.
Interdisciplinary Correlations
Physics
 112.39 (c)
o (5) Science concepts. The student knows the nature of forces in the physical world. The student
is expected to:
(A) research and describe the historical development of the concepts of gravitational,
electromagnetic, weak nuclear, and strong nuclear forces;
(D) identify examples of electric and magnetic forces in everyday life;
(E) characterize materials as conductors or insulators based on their electrical properties;
(F) design, construct, and calculate in terms of current through, potential difference across,
resistance of, and power used by electric circuit elements connected in both series and
parallel combinations; and
(G) investigate and describe the relationship between electric and magnetic fields in
applications such as generators, motors, and transformers.
Occupational Correlation (O*Net – www.onetonline.org/)
Job Title: Electric Motor, Power Tool, and Related Repairers
O*Net Number: 49-2092.00
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Reported Job Titles: Repair Technician, Maintenance Technician, Mechanic, Electric Motor Winder, Tool
Repair Technician, Power Tool Repair Technician, Service Technician, Electric Motor Repairman, Electro
Mechanic, Motor Mechanic
Tasks










Measure velocity, horsepower, revolutions per minute (rpm), amperage, circuitry, and voltage of units
or parts to diagnose problems, using ammeters, voltmeters, wattmeters, and other testing devices.
Record repairs required, parts used, and labor time.
Reassemble repaired electric motors to specified requirements and ratings, using hand tools and
electrical meters.
Maintain stocks of parts.
Repair and rebuild defective mechanical parts in electric motors, generators, and related equipment,
using hand tools and power tools.
Rewire electrical systems, and repair or replace electrical accessories.
Inspect electrical connections, wiring, relays, charging resistance boxes, and storage batteries,
following wiring diagrams.
Read service guides to find information needed to perform repairs.
Inspect and test equipment to locate damage or worn parts and diagnose malfunctions, or read work
orders or schematic drawings to determine required repairs.
Solder, wrap, and coat wires to ensure proper insulation.
Soft Skills
 Repairing
 Troubleshooting
 Quality Control Analysis
 Complex Problem Solving
 Critical Thinking
 Equipment Maintenance
 Equipment Selection
 Judgment and Decision Making
 Operation Monitoring
 Active Listening
Accommodations for Learning Differences
These lessons accommodate the needs of every learner. Modify the lessons to accommodate your students
with learning differences by referring to the files found on the Special Populations page of this website.
Preparation
 Review the Inductive Reactance slide presentation and notes prior to each class.
 Review and become familiar with the terminology and the example problems.
 Have materials and handouts ready prior to the start of the lesson.
 Before lab, have parts and equipment ready.
References
 Buchla, D. and Floyd, T. (2004). The science of electronics DC/AC. Upper Saddle River, NJ: Prentice Hall.
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
Floyd, T. (2009). Principles of electric circuits: Electron flow version. Upper Saddle River, NJ: Prentice
Hall.
Instructional Aids
1. Inductive Reactance slide presentation and notes
2. Lab Activity #1- Show the Effect of Inductance in AC Circuits
3. Lab Activity #2- Solve for Values of an Operating RL Circuit
4. Assignment #1- Compute Inductive Reactance
5. Assignment #2- Compute Applied Voltage and Impedance of RL Circuit
6. Assignment #3- Compute Power in Reactive Circuits
7. Assignment #4- Compute the Q of Inductors
8. Assignment #5- Solve Time Constant Problems
9. Assignment #1-5 Answer Key
10. Inductive Reactance Exam
11. Inductive Reactance Exam Key
12. Inductive Reactance Written Exam
13. Inductive Reactance Written Exam Key
Introduction
The purpose of this lesson is to help students
 understand how inductive reactance creates opposition to AC current flow in a circuit;
 understand that the amount of opposition depends on the frequency of the AC voltage; and
 use information about the circuit to calculate inductive reactance, phase shift, and power factor.

Say
o Today we are going to talk about inductive reactance.

Ask
o Has anyone ever wondered if there is any difference in the amount of voltage and current in a
circuit for AC voltage versus DC voltage?

Say
o Today we are going to find out that there is, and we are going to learn why the difference happens
and what happens in the circuit when it does. Let’s get started.
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Outline
MI
OUTLINE
I.
Introduction to Inductive Reactance
A. Overview
B. Terms and definitions
C. Symbols and units
D. Description of reactance
II.
Effects of Reactance
A. Reactance stores energy; it does not consume it.
B. There are two types of reactance (capacitive and
inductive).
C. The amount of reactance for both depends on
frequency.
D. Current and voltage change the same way at the
same time for resistance.
E. Current and voltage do not change the same way
at the same time for reactance.
F. The difference is best described as a phase shift
between voltage and current in a reactive circuit.
NOTES TO TEACHER
Slides 1-6
Start slide presentation.
Reactance is not
something a typical
household needs to
deal with, but a
business or factory
does.
Slides 7-12
The mnemonic ELI the
ICE man uses the
symbol E for voltage
(instead of V), which is
no longer standard.
III.
Impedance
A. We look at impedance only in a series RL circuit.
B. Impedance is a combination of resistance and
reactance, but the two values do not directly add
to form impedance.
C. They do not add because the voltage and current
are out of phase.
D. The energy that reactance uses to build the
magnetic field in an inductive device is returned
to the circuit every cycle.
E. Look at the effect of reactance on DC transient
response first before looking at the effect on AC.
Slides 13-22
Transient response
shows that there is a
time effect. AC voltage
is constantly changing
over time. Students will
understand how voltage
versus current change
more clearly once they
see the time response
effect for DC.
IV.
Series RL Circuit
A. Apply the concepts learned in DC transient circuit
response to a circuit with applied AC voltage.
B. Inductance opposes a change in current.
C. This opposition creates a constant and steady
phase difference between voltage and current
for AC voltage at a given frequency.
Slides 23-27
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MI
OUTLINE
NOTES TO TEACHER
D. Students need to calculate inductive reactance
before they can calculate impedance or phase
shift.
V.
AC Circuit analysis
A. Calculating current is a multi-step process.
B. Calculate inductive reactance from the given
information.
C. Use this inductive reactance to calculate
impedance.
D. The impedance formula comes from the
Pythagorean Theorem.
E. Reactance, resistance, and impedance form a
right triangle.
F. Any two values could be used to calculate the
phase angle and the third value using one of the
trigonometric identities.
Slides 28-33
This is the first time
students have seen the
impedance formula.
You may want to
reinforce it by
performing several
calculations using
resistance and
reactance.
VI.
Power and Impedance
A. With reactance, the amount of power drawn
from a power supply is higher than the amount
of power actually consumed.
B. This is a concern to both the power company and
to anyone paying a power bill.
C. Power factor is an important and industrystandard way to measure the difference between
power drawn (apparent power) and power
consumed (true power).
D. Quality factor measures on of the important
values of an inductor.
Slides 34-41
Lab Activities
A. Lab Activity #1-Show the Effect of Inductance in
AC Circuits
B. Lab Activity #2-Solve for Values of an Operating
RL Circuit
Upon completion of the
slide presentation, go
over the lab activities
and have students
complete the activity
handouts.
VII.
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MI
NOTES TO TEACHER
OUTLINE
VIII.
Student Assignments
A. Assignment #1- Compute Inductive Reactance
B. Assignment #2- Compute Applied Voltage and
Impedance of RL Circuit
C. Assignment #3- Compute Power in Reactive
Circuits
D. Assignment #4- Compute the Q of Inductors
E. Assignment #5- Solve Time Constant Problems
Go over Assignments
#1-5 and have students
complete.
IX.
Assessment
A. Inductive Reactance Exam
B. Inductive Reactance Written Exam
Administer exams and
grade with exam
answer keys.
Multiple Intelligences Guide
Existentialist
Interpersonal
Intrapersonal
Kinesthetic/
Bodily
Logical/
Mathematical
Musical/Rhythmic
Naturalist
Verbal/Linguistic
Visual/Spatial
Application
Guided Practice
The students will observe, take notes, ask questions, and perform some calculations under the teacher’s
guidance.
Independent Practice
The students will perform lab and assignment activities. Then the student will answer the discussion question
at the end of each lab activity and turn in for evaluation.
 Lab Activity #1- Show the Effect of Inductance in AC Circuits
 Assignment #1- Compute Inductive Reactance
 Assignment #2- Compute Applied Voltage and Impedance of RL Circuit
 Assignment #3- Compute Power in Reactive Circuits
 Assignment #4- Compute the Q of Inductors
Summary
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Review
The students will be able to define terms and perform calculations involving inductive reactance.
Evaluation
Informal Assessment
The teacher will ask questions and observe students during lab time and as they complete assignments.
Formal Assessment
Students will complete the assignments and take the Inductance Exams.
Enrichment
Extension
The students will be able to rearrange formulas and solve problems using alternative methods.
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Name _____________________________________ Class: _______ Date: ___/___/___
Inductive Reactance
Lab Activity # 1 - Show the Effect of Inductance in AC Circuits
Tools and Materials

Filter choke approximately 2h or larger

75 ohm, 1 watt resistor

DC and AC milliammeter

Multimeter

AC and DC power supplies
R
S1
VS
L
Procedure
1. Connect the 75 ohm resistor and DC ammeter in series with the DC power supply without the inductor
(for now).
2. Adjust the voltage until there are 5 volts across the resistor.
3. Record the ammeter indication _____________; then compute RDC (NOTE: RDC = V/I).
4. Connect the 75 ohm resistor and AC ammeter in series with the AC power supply.
5. Adjust the voltage until there are 5 volts across the resistor; then record the current from the ammeter
______________ and compute RAC (NOTE: RAC = V/I).
6. Compare RDC and RAC and explain differences noted, if any.
7. Connect the filter choke (inductor) and DC ammeter in series with the DC power supply as shown.
8. Adjust the DC power supply until there are 5 volts across the resistor; read the current indication on
the ammeter __________ and compute ZL(DC) (NOTE: Z L (DC) = EL/IL.).
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Name _____________________________________ Class: _______ Date: ___/___/___
9. Repeat Step 8 using the AC ammeter and AC power supply and compute ZL(AC)
(NOTE: ZL(AC) = VL/IL).
10. Compare the current recorded in Step 8 with that recorded in Step 9, and explain any differences
noted.
11. Use the filter choke value (in henries) and the voltage frequency to compute XL.
12. Compare the computed XL (Step 11) with the DC impedance (Step 8) and with the AC impedance
(Step 9).
13. Explain any differences noted.
14. Turn off circuit, disconnect components, and place materials in the proper storage area.
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Name _____________________________________ Class: _______ Date: ___/___/___
Inductive Reactance
Lab Activity Sheet # 2 - Solve for Values of an Operating RL Circuit
Tools and Materials

Filter choke approximately 2h or larger

Resistor, 750 ohms, 5 watts

AC milliammeter

Multimeter

AC power supply, 60 Hz

Switch
Procedure
1. Measure and record the resistance of the inductor (filter choke) with your ohmmeter (NOTE: This is
the DC resistance (RDC) of the coil). _______
2. Measure and record the actual value of the 750-ohm resistor. __________
3. Connect the circuit as shown in the following schematic (Figure 1).
4. Connect an AC voltmeter across the AC power supply, close the switch, and adjust the AC input until
the meter indicates 10 volts.
5. Read and record the voltage across R (VR). _____________________
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Name _____________________________________ Class: _______ Date: ___/___/___
6. Read and record the voltage across L (VL). _____________________
7. Read and record the applied voltage (across both R and L). _________
8. Read and record the current flowing in the circuit (I). ____________
9. Compute the value of XL. __________________________________
10. Add the coil’s DC resistance (Step 1) and the resistor value (Step 2), and then multiply this value by the
circuit current and compare the result with the applied voltage (EA) observed in Step 7.
11. Arithmetically add VR (Step 5) and VL (Step 6), and then compare with VA (Step 7) (Vest = VR + VL).
12. Repeat (Step 11), but use the formula VA = √ VR2 + VL2 . Compare Vest to VA.
12. Multiply the current (Step 8) and the computed value of XL (Step 9), and then compare the result with
VL (Step 6).
13. Make a vector diagram to scale (Figure 2) showing the values of VR,VL, and VA, letting VA be the
hypotenuse of the right triangle formed by sides VR and VL; explain any differences noted.
14. Discuss and explain differences observed with your teacher.
15. Turn off power, disconnect tools and material, and place in the proper storage area.
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Name _____________________________________ Class: _______ Date: ___/___/___
Inductive Reactance
Assignment # 1 - Compute Inductive Reactance
1. Write the formula for computing inductive reactance.
2. Select the unit of measurement inductive reactance is expressed in.
A Henries
B Ohms
C Farads
D Radians
3. Does inductive reactance increase or decrease if the frequency of an applied voltage of an RL circuit is
increased? (Select the correct answer.)
4. Does inductive reactance increase or decrease if the inductance is increased in a given circuit? (Select the
correct answer.)
5. In the following circuits, solve for XL.
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Name _____________________________________ Class: _______ Date: ___/___/___
Inductive Reactance
Assignment # 2 - Compute Applied Voltage and Impedance of RL Circuits
1. Select true statements relating to R-L series circuits by placing an “X” in the appropriate blanks.
_____ a. The current in a series R-L circuit is the same in the inductor as in the resistor (at all times).
_____ b. In a purely inductive circuit, the current lags the applied voltage by 90 degrees (π /2 radians).
_____ c. In a practical circuit containing inductance and resistance, the current will lag the voltage by an
angle somewhere between almost zero and almost 90 degrees.
_____ d. The voltage across the inductor is always in phase with the applied voltage.
_____ e. The voltage across the resistor is always in phase with the applied voltage.
_____ f. The voltage across the resistor is always in phase with the current flowing through the resistor.
_____ g. The applied voltage is the vector sum of the voltage drops across the resistor and the inductor.
_____ h. If 100 volts is applied to a circuit having 50 ohms of resistance and 50 ohms of inductive
reactance, there will be 50 volts across the resistor and 50 volts across the inductor.
2. If there are 10 ohms of resistance in series with 10 ohms of inductive reactance, the circuit impedance will
be _______________ ohms.
3. If there is a 30 volt drop across the resistor and a 40 volt drop across the inductor in a series R-L circuit,
the applied voltage is ________ volts, and the cosine of the phase angle is ___________. (Remember, the
cosine of the phase angle equals VR/VS.)
4. Solve as indicated using the circuit values given.
a.
b.
c.
d.
e.
f.
XL = ___________________
Z = ___________________
I = ___________________
θ = ______________________
VR = ______________________
VL = ______________________
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Name _____________________________________ Class: _______ Date: ___/___/___
Inductive Reactance
Assignment # 3- Compute Power in Reactive Circuits
1. List three ways to compute true power.
a.
b.
c.
2. List three ways to compute apparent power.
a.
b.
c.
3. List three ways to compute reactive power.
a.
b.
c.
4. List three ways to compute power factor (i.e., cosine θ).
a.
b.
c.
5. In a series circuit with only a pure inductor, if there are 100 volts and 10 amperes applied, the true power
consumed is _______________ watts.
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Name _____________________________________ Class: _______ Date: ___/___/___
6. Solve as indicated in the following circuit.
a. XL = ______________________
b.
Z = ______________________
c.
I = ______________________
d. VR = ______________________
e. VL = ______________________
f. PF = ______________________
g. PA = ______________________
h. PT = ______________________
i. PX = ______________________
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Name _____________________________________ Class: _______ Date: ___/___/___
Inductive Reactance
Assignment # 4- Compute the Q of Inductors
1. State the formula for computing Q.
Q = ______________________________
2. Two inductors have the same value of L, but one has more resistance in its windings than the other. Does
the one with the most resistance have the higher or lower Q?
3. Select true statements regarding the Q of inductors by placing an “X” in the appropriate blanks.
_____ a. All inductors have some resistance.
_____ b. High Q coils usually have relatively little resistance.
_____ c. In general, high Q coils have greater energy storage ability than do low Q coils.
_____ d. Since Q equals XL divided by RS, an inductor having a Q of “100” means that it has 100 ohms.
4. A coil is measured with a DC ohmmeter as having 0.5 ohms resistance. If the coil has an XL of 300 ohms,
the Q is ____________.
5. Will increasing the angular velocity slightly increase or decrease the Q of the coil?
6. An inductor has an internal resistance of ½ ohm and is rated at 500 mH. If 10 volts at 60 hertz is applied,
the Q of the inductor is ___________________.
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Name _____________________________________ Class: _______ Date: ___/___/___
Inductive Reactance
Assignment # 5- Solve Time Constant Problems
1. The graph shows which of the following values in a series RL, DC circuit (check the correct statements).
____ a. current increase on curve B
____ b. current increase on curve A
____ c. current decrease on curve B
____ d. current decrease on curve A
2. Refer to the chart. How many time constants are required for
____ a. Current rise to maximum value?
3. Refer to Curve A only in the chart. At 1 TC, what is the percentage of current increase?
___________________________
4. What is the percentage of current increase at 2 TC? _____________________
5. What is the percentage of rise at 3 TC? ____________ 4 TC? ___________.
6. In effect, when the switch is turned off and current starts to decay, it will have dropped to what
percentage of its maximum value at 1TC (the first percentage on the B curve)?
_______________________
7. What is the percentage decay at 2 TC? _______________ 3 TC? ______________
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Name _____________________________________ Class: _______ Date: ___/___/___
8. Using the following circuit and the universal time constant chart, answer the question below the circuit.
a. The maximum current that will flow in the circuit is ____________ amps.
b. The time for one time constant is _____________________________________.
c. The time required to reach the maximum current after switch closure is _______.
d. The time required to reach 19 amperes is _________________ seconds after switch closure.
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Inductive Reactance
Answers to Assignments #1-5
Assignment #1
1. XL = ω L or XL = 2π f L
2. b
3. Increase
4. Increase
5. a. XL = 2π f L = 6.28 x 60 Hz x .02 h = 7.54 Ω
b. XL = 2π f L = 6.28 x 400 hz x 0.025 h x 2 = 125.6 Ω
c. XLT = XL1 + XL2 = 25Ω + 25Ω = 50Ω
d. XL = 2π f L = 6.28 x 500000 Hz x 0.00001 h = 31.4 Ω
Assignment #2
1. a. True
b. True
c. True
d. False
e. False
f. True
g. True
h. False
___________
______________
____
2
2
2
2
2. Z = √ ( R ) + (XL) = √ (10Ω) + (10Ω) = √200 = 14.14 Ω
___________
___________
_____
2
2
2
2
3. VA = √ (ER) + (EL) = √ (30) + (40) = √ 2500 = 50 volts
Phase angle = ER / EA = 30/50 = .6 = 53º
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4. a. XL = 2π f L = 6.28 x 60 Hz x .1274 h = 48 Ω
___________
______________
2
2
b. Z = √ ( R ) + (XL) = √ (20Ω)2 + (48Ω)2 = 52 Ω
c. I = EA / Z = 130 volts / 52 Ω = 2.5 amperes
d. θ = tan-1 ( ) = 67.38°
e. VR = I R = 2.5 a x 20Ω = 50 volts
f. VL = I XL = 2.5 a x 48Ω = 120 volts
Assignment #3
1. a. PT = I2R
b. PT = ERIR
c. PT = VI (PF)
Or EI cos θ
2. a. PA – VI
b. PA = I2Z
c. PA = (V2) / Z
3. a. PX = I2X
b. PX – VXIX
c. PX = VI sin θ
4 a. PF = PT / PA
b. PF = VR / VA
c. PF = R / Z
5. Since there is no resistor, there is no true power. Therefore, answer is 0 watts.
6. a. XL = 2π f L = 6.28 x 60 Hz x 0.5h = 188.4 Ω
___________
_________________
2
2
b. Z = √ ( R) + (XL) = √ (10Ω)2 + (188.4Ω)2
= 188.66 Ω
c. I = VA / Z = 100 v / 188.66Ω = .53 amps
d. VR = IR = 0.53 a x 10 Ω = 5.3 volts
e. VL = IXL = 0.53 a x 188.4 Ω = 99.85 volts
f. PF = R / Z = 10 Ω / 188.66 Ω = 0.053
g. PA = VI = 100v x .53 a = 53 volt-amperes
h. PT = I2R = (0.53 a)2 x 10Ω = 2.81 watts
i. PX = I2XL = (0.53)2 x 188.4 Ω = 52.92 vars
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Assignment #4
1. Q = XL / RS
2. Lower
3.
a. True
b. True
c. True
d. False
4. Q = XL / RS = 300 Ω / 0.5 Ω = 600
5. Increases
6. XL = 2π f L = 6.28 x 60 x 0.5h = 188.4 Ω
Q = XL / RS = 88.4 Ω / 0.5 ΩΩ = 376.8 or 377
Assignment #5
1. b
2. a. 5
3. 63.2%
4. 86.5%
5. 95%, 98%
6. 36.8 %
7. 13.5%, 5%
8. a. I = V / R = 10 volts / ½ Ω = 20 amperes
b. TC = L/R = 0.5 h / 0.5 Ω = 1 second
c. 5TC = maximum current = 5 seconds
d. 19/20 = 95% = 3TC = 3 seconds
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Name _____________________________________ Class: _______ Date: ___/___/___
Inductive Reactance Exam
Match the terms with their correct definitions.
1. Resistance
A Opposition to current caused by voltage or current changes not
resulting in energy dissipation
2. Impedance
B The rate of change of cyclical motion
3. Reactance
C Opposition to current resulting in energy dissipation
4. Inductive reactance
D Opposition to current including both resistance and reactance
5. Angular velocity
E Circuit opposition caused by inductance
Match the terms with their correct definitions.
6. Power
A The product of volts and amperes in an AC circuit
7. Reactive power
B The ratio of true power to apparent power in an AC circuit
8. Apparent power
C The product of reactive voltage and amperes in an AC circuit
9. Power factor
D The angle that the current leads or lags the voltage in an AC circuit
10. Phase angle
E The rate of energy consumption in a circuit
Match the symbols with their correct definitions.
11. XL
A Impedance
12. VARS
B Frequency in hertz
13. Z
C Angular velocity in radians per second
14. f
D Reactive apparent power
15. ω
E Inductive reactance in ohms
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Name _____________________________________ Class: _______ Date: ___/___/___
Match the symbols with their correct definitions
16. X
A Radians in one cycle
17. PF
B Reactance in ohms
18. R
C Power factor
19. 2π
D Resistance in ohms
14. Which of the following is not a factor used to compute inductive reactance?
A 2π - reactive apparent power
B ω - angular velocity
C L - inductance
D f - frequency
15. Which of the following statements is false concerning current and voltage relationships in RL circuits?
A Current lags voltage by 90º in a pure inductive circuit
B Current and voltage are in phase in a pure inductive circuit
C Current and voltage are in phase in a pure resistive circuit
D Current lags voltage between 0º and 90º in an RL circuit, depending upon relative amounts of R and
L present and frequency of applied voltage or current
16. Which of the following statements is true concerning the formula for computing inductive reactance?
AωL
B 2π f L
C Both of the above
D Neither of the above
17. Which of the following statements is true concerning inductive time constants?
A In the RL circuit connected to DC, the current immediately rises to the Ohm’s law value when switch
is closed
B The time required for current to reach maximum value varies inversely with inductance in henries
C One time constant equals L/R
D One time constant equals XL / R
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24
Name _____________________________________ Class: _______ Date: ___/___/___
18. Which of the following statements is false concerning inductive time constants?
A The time required for current to reach maximum value varies inversely with resistance in ohms
B During each time constant, the current rises (or fails) 63.2 percent of the value remaining
C During each time constant, the current rises (or falls) 36.8 percent of the value remaining
D During the universal time constant, voltage acts inversely to current
Match the indicated value to the lettered blank on the universal time constant chart.
19. 98.2
20. 63.2
21. Inductor current rising
22. 36.8
23. 1.8
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25
Name _____________________________________ Class: _______ Date: ___/___/___
Answer the following questions using the Universal Time Constant Chart above.
24. What is the percentage for curve A, at 2TC?
A 95%
B 5%
C 86.5%
D 13.5%
25. What is the percentage for curve B, at 2TC?
A 95%
B 5%
C 86.5%
D 13.5%
26. What is the percentage for curve B, at 4TC?
A 98%
B 2%
C 100%
D 0%
27. What is the percentage for curve B, at 1TC?
A 36.8%
B 63.2%
C 50%
D 86.5%
28. Curve A of the universal time constant chart is called which of the following?
A rising curve
B inductor current rising
C capacitor voltage
D all of the above
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26
Inductive Reactance Exam Answer Key
Match the terms with their correct definitions.
1. Resistance
C
A Opposition to current caused by voltage or current changes not
resulting in energy dissipation
2. Impedance
D
B The rate of change of cyclical motion
3. Reactance
A
C Opposition to current resulting in energy dissipation
4. Inductive reactance
E
D Opposition to current including both resistance and reactance
5. Angular velocity
B
E Circuit opposition caused by inductance
Match the terms with their correct definitions.
6. Power
E
A The product of volts and amperes in an AC circuit
7. Reactive power
C
B The ratio of true power to apparent power in an AC circuit
8. Apparent power
A
C The product of reactive voltage and amperes in an AC circuit
9. Power factor
B
D The angle that the current leads or lags the voltage in an AC circuit
10. Phase angle
D
E The rate of energy consumption in a circuit
Match the symbols with their correct definitions.
11. XL
E
A Impedance
12. VARS
D
B Frequency in hertz
13. Z
A
C Angular velocity in radians per second
14. f
B
D Reactive apparent power
15. ω
C
E Inductive reactance in ohms
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27
Name _____________________________________ Class: _______ Date: ___/___/___
Match the symbols with their correct definitions
16. X
B
A Radians in one cycle
17. PF
C
B Reactance in ohms
18. R
D
C Power factor
19. 2π
A
D Resistance in ohms
14. Which of the following is not a factor used to compute inductive reactance?
A 2π - reactive apparent power
B ω - angular velocity
C L - inductance
D f - frequency
15. Which of the following statements is false concerning current and voltage relationships in RL circuits?
A Current lags voltage by 90º in a pure inductive circuit
B Current and voltage are in phase in a pure inductive circuit
C Current and voltage are in phase in a pure resistive circuit
D Current lags voltage between 0º and 90º in an RL circuit, depending upon relative amounts of R and
L present and frequency of applied voltage or current
16. Which of the following statements is true concerning the formula for computing inductive reactance?
AωL
B 2π f L
C Both of the above
D Neither of the above
17. Which of the following statements is true concerning inductive time constants?
A In the RL circuit connected to DC, the current immediately rises to the Ohm’s law value when switch
is closed
B The time required for current to reach maximum value varies inversely with inductance in henries
C One time constant equals L/R
D One time constant equals XL / R
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28
Name _____________________________________ Class: _______ Date: ___/___/___
18. Which of the following statements is false concerning inductive time constants?
A The time required for current to reach maximum value varies inversely with resistance in ohms
B During each time constant, the current rises (or fails) 63.2 percent of the value remaining
C During each time constant, the current rises (or falls) 36.8 percent of the value remaining
D During the universal time constant, voltage acts inversely to current
Match the numbered label to the lettered blank on a universal time constant chart.
19. 98.2
C
20. 63.2
A
21. Inductor current rising
E
22. 36.8
B
23. 1.8
D
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29
Name _____________________________________ Class: _______ Date: ___/___/___
Answer the following questions using the Universal Time Constant Chart above.
24. What is the percentage for curve A, at 2TC?
A 95%
B 5%
C 86.5%
D 13.5%
25. What is the percentage for curve B, at 2TC?
A 95%
B 5%
C 86.5%
D 13.5%
26. What is the percentage for curve B, at 4TC?
A 98%
B 2%
C 100%
D 0%
27. What is the percentage for curve B, at 1TC?
A 36.8%
B 63.2%
C 50%
D 86.5%
28. Curve A of the universal time constant chart is called which of the following?
A rising curve
B inductor current rising
C capacitor voltage
D all of the above
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30
Name _____________________________________ Class: _______ Date: ___/___/___
Inductive Reactance Written Exam
1. State three formulas for determining true power.
a. _____________________________
b. _____________________________
c. _____________________________
2. State three formulas for determining apparent power.
a. _____________________________
b. _____________________________
c. _____________________________
3. State three formulas for determining reactive power.
a. _____________________________
b. _____________________________
c. _____________________________
4. State four formulas for determining power factor.
a. _____________________________
b. _____________________________
c. _____________________________
d. _____________________________
5. State the formula for determining quality factor (Q) or figure of merit of an inductor.
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Name _____________________________________ Class: _______ Date: ___/___/___
6. Compute the applied voltage and impedance in a series RL circuit in which the voltage across the resistor
is 50 volts, the voltage across the inductor is 120 volts, and the current is 13 milliamps.
a. Applied voltage is ______ volts
b. Impedance is ______ ohms.
S
V
S
R = 20
k
1
L = 100 mH
V = 40 V
f = 8000 Hz
7. From the figure above, find
a. XL =__________ = _________ = _________
b. Z =__________ =__________ = _________
c. I =__________ = _________ = _________
d. VR =__________ = _________ = _________
e. VL =__________ = __________ = _________
8. From the figure on the right, find
S
a. XL =__________ = _________ = _________
b. Z =__________ = _________ = _________
V
S
R =200
Ω =
1
V = 120 V
f = 60 Hz
L = 200
mH
c. I =__________ = _________ = _________
d. VR = __________ = _________ = _________
e. VL = __________ = _________ = _________
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32
Name _____________________________________ Class: _______ Date: ___/___/___
9. From the figure on the right, find
R =30
Ω =
S
a. XLT =__________ = _________ = __________
V
b. Z = __________ = _________ = __________
S
1
V = 50 V
f = 200 Hz
L = 30
mH
c. I = __________ = _________ = __________
d. VL = __________ = _________ = __________
e. θ = __________
S
V
S
R =1
kΩ =
1
V = 150 V
f = 25 kHz
L = 7.5 mH
10. From the figure above, find
a. XLT =__________ = __________ = __________
b. Z = __________ = _________ = __________
c. I = __________ = __________ = __________
d. VL = __________ = __________ = _________
e. θ = __________
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33
Inductive Reactance Written Exam Answer Key
1. State three formulas for determining true power.
a. PT = I2R
b. PT = VRIR
c. PT = EI cos θ or VI (PF) where PF is the power factor
2. State three formulas for determining apparent power.
a. PA = VI
b. PA = I2Z
c. PA = V2 / Z
3. State three formulas for determining reactive power.
a. PX = I2X
b. PX = VXIX
c. PX = VI sin θ where sin θ = VR / VA or R / X
4. State four formulas for determining power factor.
a. PF = PT / PA
b. PF = VR / VS
c. PF = R/Z
d. PF = cos θ where θ is angle between current and voltage
5. State the formula for determining quality factor (Q) or figure of merit of an inductor.
Q = XL / RS where XL is inductive reactance in ohms and RS is series resistance in ohms
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6. Compute the applied voltage and impedance in a series RL circuit in which the voltage across the resistor
is 50 volts, the voltage across the inductor is 120 volts, and the current is 13 milliamps.
a. Applied voltage is __130__ volts
EA = √ (VR)2 + (VL)2 = √ (50)2 + (120)2 = 130 volts
b. Impedance is __10000__ ohms.
Z=
⁄ =
⁄ .
= 10000 Ω
S
V
R = 20
k
1
V = 40 V
f = 8000 Hz
S
L = 100 mH
7. From the figure above, find
a. XL = 2π f L = 6.28 x 8000 x 0.1h = 5027 Ω
b. Z = √ ( R)2 + (XL)2 = √ (20000Ω)2 + (5027Ω)2 = 20622 Ω
c. I =
⁄
=
⁄
= 1.94 ma
d. VR = IR = (0.00194) (20000) = 38.8 volts
e. VL = IX XL = (0.00194a) (5027Ω) = 9.75 volts
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35
R =200
Ω =
S
1
V
L = 200
mH
V = 120 V
f = 60 Hz
S
8. From the figure above, find
a. XL =2ππf L = 6.28 x 60 Hz x 0.002 = 75.4 Ω
b. Z = √( R)2 + (XL)2 = √ (200)2 + (75.4)2 = 213.74 Ω
c. I = VA / Z = 120v / 213.74 Ω = 0.561 amperes
d. VR = IR = (0.561) x (200) = 112.28 volts
e. VL = I XL= (0.561) (75.4) = 42.3 volts
S
1
V
9. From the figure above, find
R =30
Ω =
V = 50 V
f = 200 Hz
S
L = 30
mH
a. XLT = 2π f L = 6.28 x 200 Hz x .03 h = 37.7 Ω
b. Z = √(
+
)= √
+
.
= 48.18 Ω
c. I = VA / XL = 50v / 48.18 Ω = 1.04 amps
d. VL = I XL = (1.04) (37.7 Ω) = 39.1 volts
e. θ = Tan-1(
) = Tan-1(
.
) = 51.5°
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36
S
V
S
R =1
kΩ =
1
L = 7.5 mH
V = 150 V
f = 25 kHz
10. From the figure above, find
a. XL1 = 2π f L = 6.28 x 25000 Hz x .0075 h = 1178 Ω
b. Z = √(
+
)= √
+
= 1545.3 Ω
c. I = VS / Z = 150v / 1545.3 Ω = 0.097 amps or 97 ma
d. VL = IXL = (0.097 a) (1178 Ω) = 114.3 volts
e. θ = Tan-1(
) = Tan-1(
) = 49.7°
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37