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ELTR 115 (AC 2), section 2
Recommended schedule
Day 1 Topics: Power in AC circuits Questions: 1 through 20 Lab Exercise: Lissajous figures for phase shift measurement (question 71)
Day 2 Topics: Power factor correction Questions: 21 through 40 Lab Exercise: Power factor correction for AC motor (question 72)
Day 3 Topics: Alternator construction and introduction to polyphase AC Questions: 41 through 55 Lab Exercise: Power factor correction for AC motor (question 72, continued)
Day 4 Topics: AC motor construction and polyphase AC circuits Questions: 56 through 70 Lab Exercise: work on project
Day 5 Exam 2: includes Lissajous figure phase shift measurement performance assessment
Practice and challenge problems Questions: 74 through the end of the worksheet
Impending deadlines Project due at end of ELTR115, Section 3 Question 73: Sample project grading criteria
ELTR 115 (AC 2), section 2
Skill standards addressed by this course section
EIA Raising the Standard; Electronics Technician Skills for Today and Tomorrow, June 1994
C Technical Skills – AC circuits C.01 Demonstrate an understanding of sources of electricity in AC circuits. C.04 Demonstrate an understanding of basic motor/generator theory and operation. C.05 Demonstrate an understanding of measurement of power in AC circuits. C.30 Understand principles and operations of AC polyphase circuits.
B Basic and Practical Skills – Communicating on the Job B.01 Use effective written and other communication skills. Met by group discussion and completion of labwork. B.03 Employ appropriate skills for gathering and retaining information. Met by research and preparation prior to group discussion. B.04 Interpret written, graphic, and oral instructions. Met by completion of labwork. B.06 Use language appropriate to the situation. Met by group discussion and in explaining completed labwork. B.07 Participate in meetings in a positive and constructive manner. Met by group discussion. B.08 Use job-related terminology. Met by group discussion and in explaining completed labwork. B.10 Document work projects, procedures, tests, and equipment failures. Met by project construction and/or troubleshooting assessments. C Basic and Practical Skills – Solving Problems and Critical Thinking C.01 Identify the problem. Met by research and preparation prior to group discussion. C.03 Identify available solutions and their impact including evaluating credibility of information, and locating information. Met by research and preparation prior to group discussion. C.07 Organize personal workloads. Met by daily labwork, preparatory research, and project management. C.08 Participate in brainstorming sessions to generate new ideas and solve problems. Met by group discussion. D Basic and Practical Skills – Reading D.01 Read and apply various sources of technical information (e.g. manufacturer literature, codes, and regulations). Met by research and preparation prior to group discussion. E Basic and Practical Skills – Proficiency in Mathematics E.01 Determine if a solution is reasonable. E.02 Demonstrate ability to use a simple electronic calculator. E.05 Solve problems and [sic] make applications involving integers, fractions, decimals, percentages, and ratios using order of operations. E.06 Translate written and/or verbal statements into mathematical expressions. E.09 Read scale on measurement device(s) and make interpolations where appropriate. Met by oscilloscope usage. E.12 Interpret and use tables, charts, maps, and/or graphs. E.13 Identify patterns, note trends, and/or draw conclusions from tables, charts, maps, and/or graphs. E.15 Simplify and solve algebraic expressions and formulas. E.16 Select and use formulas appropriately. E.17 Understand and use scientific notation. E.26 Apply Pythagorean theorem. E.27 Identify basic functions of sine, cosine, and tangent. E.28 Compute and solve problems using basic trigonometric functions.
F Additional Skills – Electromechanics B.01e Types of motors.
Questions
Question 1
Power is easy to calculate in DC circuits. Take for example this DC light bulb circuit:
110 V
I = 2.4 A
Calculate the power dissipation in this circuit, and describe the transfer of energy from source to load: where does the energy come from and where does it go to? file 02171
Question 2
A generator is coupled to a bicycle mechanism, so that a person can generate their own electricity:
Generator
Load
The person pedaling this bicycle/generator notices that it becomes more difficult to pedal when the generator is connected to a load such as a light bulb, or when it is charging a battery. When the generator is open-circuited, however, it is very easy to spin. Explain why this is, in terms of work and energy transfer. file 02172
Question 3
If the power waveform is plotted for a resistive AC circuit, it will look like this:
Time
e
i
e
i p
What is the significance of the power value always being positive (above the zero line) and never negative (below the zero line)? file 02174
If the power waveform is plotted for an AC circuit with a 90 degree phase shift between voltage and current, it will look something like this:
Time
e
i
e
i
p
What is the significance of the power value oscillating equally between positive (above the zero line) and negative (below the zero line)? How does this differ from a scenario where there is zero phase shift between voltage and current? file 02175
Calculate the current in this circuit, and also the amount of mechanical power (in units of ”horsepower”) required to turn this alternator (assume 100% efficiency):
Alternator
480 VAC
60 Hz
9.02 mH
file 00768
A student is pondering the behavior of a simple series RC circuit:
5 VAC
XC = 4 kΩ
R = 3 kΩ
I = 1 mA
4 V
3 V
It is clear by now that the 4 kΩ capacitive reactance does not directly add to the 3 kΩ resistance to make 7 kΩ total. Instead, the addition of impedances is vectorial:
√ XC 2 + R^2 = Ztotal
ZC + ZR = Ztotal
(4kΩ 6 − 90 o) + (3kΩ 6 0 o) = (5kΩ 6 − 53. 13 o)
It is also clear to this student that the component voltage drops form a vectorial sum as well, so that 4 volts dropped across the capacitor in series with 3 volts dropped across the resistor really does add up to 5 volts total source voltage:
VC + VR = Vtotal
(4V 6 − 90 o) + (3V 6 0 o) = (5V 6 − 53. 13 o)
What surprises the student, though, is power. In calculating power for each component, the student arrives at 4 mW for the capacitor (4 volts times 1 milliamp) and 3 mW for the resistor (3 volts times 1 milliamp), but only 5 mW for the total circuit power (5 volts times 1 milliamp). In DC circuits, component power dissipations always added, no matter how strangely their voltages and currents might be related. The student honestly expected the total power to be 7 mW, but that doesn’t make sense with 5 volts total voltage and 1 mA total current. Then it occurs to the student that power might add vectorially just like impedances and voltage drops. In fact, this seems to be the only way the numbers make any sense:
PC = 4 mW
PR = 3 mW
Ptotal = 5 mW
However, after plotting this triangle the student is once again beset with doubt. According to the Law of Energy Conservation, total power in must equal total power out. If the source is inputting 5 mW of power
In this circuit, three common AC loads are modeled as resistances, combined with reactive components in two out of the three cases. Calculate the amount of current registered by each ammeter, and also the amount of power dissipated by each of the loads:
Fluorescent lamp Incandescent lamp Induction motor
A A A
120 VAC, 60 Hz
10 μF 0.25 H
If someone were to read each of the ammeters’ indications and multiply the respective currents by the figure of 120 volts, would the resulting power figures (P = IE) agree with the actual power dissipations? Explain why or why not, for each load. file 00770
Question 12
A very important parameter in AC power circuits is power factor. Explain what ”power factor” is, and define its numerical range. file 02173
Question 13
Power calculation in DC circuits is simple. There are three formulae that may be used to calculate power:
P = IV P = I^2 R P =
V 2
R
Power in DC circuits
Calculating power in AC circuits is much more complex, because there are three different types of power: apparent power (S), true power (P ), and reactive power (Q). Write equations for calculating each of these types of power in an AC circuit:
file 02181
Calculate the power factor of this circuit:
C = 0.1 μF
400 Hz
32 V
R = 7.1 kΩ
file 02179
Question 15
Explain the difference between a leading power factor and a lagging power factor. file 00774
Question 16
In this circuit, three common AC loads are represented as resistances, combined with reactive components in two out of the three cases. Calculate the amount of true power (P ), apparent power (S), reactive power (Q), and power factor (P F ) for each of the loads:
Fluorescent lamp Incandescent lamp Induction motor
A A A
120 VAC, 60 Hz
10 μF 0.25 H
Also, draw power triangle diagrams for each circuit, showing how the true, apparent, and reactive powers trigonometrically relate. file 00772
If an electrical device is modeled by fixed values of resistance, inductance, and/or capacitance, it is not difficult to calculate its power factor:
R
L
Electric
motor
(model)
V
P.F. =
R
R^2 + (ωL)^2 In real life, though, things are not so simple. An electric motor will not come labeled with an ideal- component model expressed in terms of R and L. In fact, that would be impossible, as the resistance R in the circuit model represents the sum total of mechanical work being done by the motor in addition to the energy losses. These variables change depending on how heavily loaded the motor is, meaning that the motor’s power factor will also change with mechanical loading. However, it may be very important to calculate power factor for electrical loads such as multi-thousand horsepower electric motors. How is this possible to do when we do not know the equivalent circuit configuration or values for such a load? In other words, how do we determine the power factor of a real electrical device as it operates?
Large electric motor
Power conductor
Power conductor
Of course, there do exist special meters to measure true power (wattmeters) and reactive power (”var” meters), as well as power factor directly. Unfortunately, these instruments may not be readily available for our use. What we need is a way to measure power factor using nothing more than standard electrical/electronic test equipment such as multimeters and oscilloscopes. How may we do this?
Hint: remember that the angle Θ of the S-Q-P ”power triangle” is the same as the angle in a circuit’s Z-X-R impedance triangle, and also the same as the phase shift angle between total voltage and total current. file 02180
Suppose that a single-phase AC electric motor is performing mechanical work at a rate of 45 horsepower. This equates to 33.57 kW of power, given the equivalence of watts to horsepower (1 HP ≈ 746 W). Calculate the amount of line current necessary to power this motor if the line voltage is 460 volts, assuming 100% motor efficiency and a power factor of 1. Now re-calculate the necessary line current for this motor if its power factor drops to 0.65. Assume the same efficiency (100%) and the same amount of mechanical power (45 HP). What do these calculations indicate about the importance of maintaining a high power factor value in an AC circuit? file 02182
file 01480
Question 22
Lissajous figures, drawn by an oscilloscope, are a powerful tool for visualizing the phase relationship between two waveforms. In fact, there is a mathematical formula for calculating the amount of phase shift between two sinusoidal signals, given a couple of dimensional measurements of the figure on the oscilloscope screen. The procedure begins with adjusting the vertical and horizontal amplitude controls so that the Lissajous figure is proportional: just as tall as it is wide on the screen (n). Then, we make sure the figure is centered on the screen and we take a measurement of the distance between the x-axis intercept points (m), as such:
m n
n
Determine what the formula is for calculating the phase shift angle for this circuit, given these dimensions. Hint: the formula is trigonometric! If you don’t know where to begin, recall what the respective Lissajous figures look like for a 0o^ phase shift and for a 90o^ phase shift, and work from there. file 01481
An oscilloscope is connected to a low-current AC motor circuit to measure both voltage and current, and plot them against one another as a Lissajous figure:
A B Alt Chop Add
Volts/Div A
Volts/Div B
DC Gnd AC
DC Gnd AC
Invert (^) Intensity Focus
Position
Position
Position
Off
Beam find
LineExt.
AB
Norm ACDC AutoSingle Slope
Level
Reset
X-Y
Holdoff
LF RejHF Rej
Triggering Alt Ext. input
Cal 1 V Gnd Trace rot.
Sec/Div 1 0.5^ 0.2 0. 105
2 20
50 m20 m 5 m10 m 2 m
1 0.5^ 0.2 0. 105
2 20
50 m20 m 5 m10 m 2 m
5 m^ 1 m 100 m25 m 500 m (^1) 2.
250 μ (^50) μ 10 μ 2.5 0.5 μ μ 0.025^ 0.1^ μμ off
Rshunt
AC motor
The following Lissajous figure is obtained from this measurement:
From this figure, calculate the phase angle (Θ) and the power factor for this motor circuit. file 02183
A large electrical load is outfitted with a wattmeter to measure its true power. If the load voltage is 7. kV and the load current is 24 amps, calculate the load’s apparent power (S). Calculate the power factor and also the phase angle between voltage and current in the circuit if the wattmeter registers 155 kW at those same voltage and current values. Draw a ”power triangle” for this circuit, graphically showing the relationships between apparent power, true power, and phase angle. file 02187
Question 26
The power factor of this circuit is as low as it can possibly be, 0:
L = 0.25 H
30 V
400 Hz
Calculate the apparent, true, and reactive power for this circuit:
- S =
- P =
- Q = Now, suppose a capacitor is added in parallel with the inductor:
L = 0.25 H
30 V
400 Hz
C = 0.47 μF
Re-calculate the apparent, true, and reactive power for this circuit with the capacitor connected:
Calculate the line current and power factor in this AC power system:
240 VAC
60 Hz
A
Ammeter
Z = 5 Ω ∠ 34 o
Now, calculate the line current and power factor for the same circuit after the addition of a capacitor in parallel with the load:
240 VAC
60 Hz
A
Ammeter
270 μF Z = 5 Ω ∠ 34 o
file 00643
Question 28
It is in the best interest of power distribution systems to maintain the power factors of distant loads as close to unity (1) as possible. Explain why. file 01885
Question 29
The ”power triangle” is a very useful model for understanding the mathematical relationship between apparent power (S), true power (P ), and reactive power (Q):
P
S Q
Explain what happens to the triangle if power factor correction components are added to a circuit. What side(s) change length on the triangle, and what happens to the angle Θ? file 02184
