Non-commercial
Joint Stock
Company
ELECTRICAL ENGINEERING THEORETICAL BASES 1
DC & AC linear electric circuit analysis
Methodological guidelines and assignments for calculation graphical works № 1…3
for the baccalaureate 5B071800 – “Electrical Power Engineering” specialty
Almaty 2015
Almaty
University of
Power
Engineering &
Telecommunications
Electrical Engineering
Theoretical Bases Department
2
AUTHORS: A.S. Baimaganov, S.J. Kreslina. Electrical Engineering Theoret-
ical Bases 1. DC & AC linear electric circuit analysis. Methodological guidelines
and assignments for CGW № 1…3 for the baccalaureate 5B071800 – “Electrical
Power Engineering” specialty. – Almaty: AUPET, 2015. – 16p.
Provides methodological guidelines and assignments for Calculation Graph-
ical Works of the “Electrical Engineering Theoretical Bases 1” course for the next
sections: “DC linear electric circuit”, “Single-phase sinusoidal current linear electric
circuit”.
Calculation graphical assignments are intended for the second-year students
by baccalaureate 5B071800 – “Electrical Power Engineering” specialty.
Illustration 30, tables 9, references 8 items.
Reviewer: Foreign Languages department head Ph.D. V.S. Kozlov
Printed according plan Publishing of Non-commercial JSC “Almaty Universi-
ty of Power Engineering &Telecommunications” on 2015 yr.
В© Non-commercial JSC
“Almaty University of Power Engineering &Telecommunications”, 2015 yr.
3
Contents
Introduction ....................................................................................................... 4
Requirements ..................................................................................................... 4
1 CGW в„–1 DC brunched linear electric circuit analysis ................................. 6
1.1 Assignment............................................................................................... 6
1.2 Methodological guidelines ....................................................................... 6
2 CGW в„–2 Analysis of a single-phase sinusoidal current brunched linear
electric circuit with a single source ............................................................................. 9
2.1 Assignment............................................................................................... 9
2.2 Methodological guidelines ....................................................................... 9
3 CGW в„–3 Single-phase sinusoidal current brunched linear electric circuit
analysis ...................................................................................................................... 12
3.1 Assignment............................................................................................. 12
3.2 Methodological guidelines ..................................................................... 12
References ....................................................................................................... 15
4
Introduction
Calculation Graphical Works (CGW) is an essential component in the study
“Electrical Engineering Theoretical Bases 1” (EETB1) course. Performing CGW
allows the student to apply theoretical principles in practical calculations, to gain
the skills of independent circuit analysis that ultimately contribute to the successful
mastering of the EETB1 course.
This brochure contains assignments and methodological guidelines for three
CGW on the main sections of the EETB1, which should be studied in 3-rd semester.
CGW в„–1 is devoted to calculation of a DC branched linear electric circuit by
using the basic circuit analysis methods.
CGW в„–2 and CGW в„–3 are devoted to calculation of the single-phase sinus-
oidal current linear electric circuits by using a complex method.
Variant of original data is determined by the first letter of the surname, last
and penultimate digit of the credit book number and by the year of enrollment (even
or odd).
Requirements:
- CGW should be included next sections: introduction, assignment, procedure
of calculation, results presentation, conclusion and list of references;
- choose the original assignment data according to your variant, assignments
text should be rewritten to the explanatory note completely unabridged;
- each stage of a CGW should be named, all tasks are performed on only one
side of a sheet (size A4);
- in an explanatory note to be presented not only calculation formulas and fi-
nal results, but also text with explanations, needed intermediate calculations, that
allow to understand and verify your actions;
- variant number, academic group, surname and initials of the student should
be written on the title page; a template of the title page represented on the next
page;
- it is necessary to write appropriate units for the parameters, having a partic-
ular of dimension;
- put a dot over complex parameters, that are a time function;
- underline a complex parameters, that are not time function, such as imped-
ance and admittance;
- do not change of names of the nodes, parameters, resistors, inductances, ca-
pacitances and of the arbitrarily taken current and voltage positive directions;
- plots of instantaneous values, phasor, topographic and circle diagrams to be
performed on the pasted sheets of graph or checkered paper, or by using computer
applications;
- it is necessary to sign coordinate axes name and the names of variable on
the graph, also choose a scale so that would be convenient to use a graph or dia-
gram;
- circuit diagrams in the explanatory note should be done in pencil using a
ruler, or by using computer applications.
5
Template of the title page:
REPUBLIC OF KAZAKHSTAN
NON-COMMERCIAL JOINT STOCK COMPANY
ALMATY UNIVERSITY OF POWER ENGINEERING &TELECOMMUNICATIONS
Electrical Engineering Theoretical Bases Department
Calculation Graphical Work в„– __
on the “Electrical Engineering Theoretical Bases 1” course
______________________________________
Title of the calculation graphical work
Done by student of the __________ group
academic group code
___________________________
Student’s Surname & Initials
Credit book в„–_________
“___” “___________” 201__yr
Checked by __________________________
Teacher’s Surname & Initials
“___” “___________” 201__yr
Almaty 201__ yr.
6
CGW в„–1 DC brunched linear electric circuit analysis 1
Original data and number of analyzing circuit diagram is presented in the Ta-
bles 1.1…1.3 for a variety of variants. Variants of a circuit diagram is presented on
the Figures 1.1…1.10. Choose the original data and circuit diagram according to
your variant and enter it at the very beginning of the explanatory note.
Assignment 1.1
a) Make a system of equations by the Kirchhoff's laws.
b) Calculate of the currents in all circuit branches by applying mesh analysis
and nodal analysis. Compare the results obtained by applying these techniques.
Make up a conclusion.
c) Make a power balance equation. Check an accuracy with which it is exe-
cuted.
d) Calculate of a single current (indicated in Table 1.3) by applying
Thevenin’s theorem. Compare the result with the values of that current obtained in
the mesh analysis and nodal analysis.
Methodological guidelines 1.2
a) A circuit diagram should not include elements with zero parameters.
b) It is appropriate to replace the current source by the equivalent voltage
source (but not necessarily) before applying the mesh currents analysis, or the nodal
potentials analysis.
c) Before applying a nodal analysis the potential of one of the nodes adjacent
to the branch without resistance to be taken equal to zero. Then the potential of an-
other node will be equals to this branch EMF, taken with the appropriate sign.
References: [R1] – 3.12…3.18, 5.11, 5.12, 5.17; [R2] – 1.5…1.12, 2.5…2.8;
[R3] – 2.1…2.26; [R4] – chapter 1; [R5] – chapter 1; [R2] – 1.1…1.6; [R3] – 1…6.
Table 1.1
Enrollment year
Last digit of the credit book number
even
9
1
2
3
4
5
6
7
8
odd
0
8
7
6
5
4
3
2
1
Circuit в„–
1.1
1.3
1.4
1.5
1.6
1.7
1.8
1.9
1.10
Р•
1
, V
100
0
200
150
0
0
0
250
0
Р•
2
, V
0
200
180
0
150
0
180
200
150
Р•
3
, V
120
150
0
200
180
100
250
100
0
Р•
4
, V
250
0
0
250
200
150
200
0
250
Р•
5
, V
0
100
250
0
0
200
0
0
120
Р•
6
, V
200
250
150
180
120
220
150
200
100
Table 1.2
7
Enrollment year
Penultimate digit of the credit book number
even
9
1
2
3
4
5
6
7
8
odd
0
8
7
6
5
4
3
2
1
R
1
, Ω
30
60
30
20
100
60
90
30
70
R
2
, Ω
70
20
80
50
80
50
70
80
50
R
3
, Ω
90
50
60
70
20
20
90
60
30
R
4
, Ω
40
70
90
30
90
80
30
20
250
R
5
, Ω
60
90
40
100
40
60
50
50
100
Table 1.3
Enrollment year
First letter of the surname
even
ДЛСЮЧШ
ЕАЖНУ
МБОЗФЫ
ВИПХЩТ
ГКРЭЦЯ
odd
ГКРЭЦЯ
ДЛСЮЧШ
ЕАЖНУ
МБОЗФЫ
ВИПХЩТ
J, A
2
5
3
4
6
Calculate current
I
1
I
2
I
3
I
4
I
5
Figure 1.1 Figure 1.2
Figure 1.3 Figure 1.4
8
Figure 1.5 Figure 1.6
Figure 1.7 Figure 1.8
Figure 1.9 Figure 1.10
9
CGW в„–2 Analysis of a single-phase sinusoidal current brunched line-2
ar electric circuit with a single source
Original data and number of analyzing circuit diagram is presented in the Ta-
bles 2.1…2.3 for a variety of variants. Variants of a circuit diagram is presented on
the Figures 2.1…2.10. Choose the original data and circuit diagram according to
your variant and enter it at the very beginning of the explanatory note.
Electric circuit with mixed compound is powered by a single sinusoidal volt-
age source рќ‘ў
(
рќ‘Ў
)
= рќ‘€
рќ‘љ
в€™ sin рќњ”рќ‘Ў,
where рќњ” = 2рќњ‹рќ‘“.
RMS (root mean square) voltage рќ‘€ = рќ‘€
рќ‘љ
/
в€љ
2.
Assignment 2.1
a) Calculate of the inductive X
L
and capacitive X
C
reactance, complex imped-
ance of each branch Z
1
, Z
2
, Z
3
and an equivalent whole circuit impedance Z
eq
.
b) Calculate of the RMS complex values of the currents in all branches and
write there instantaneous values.
c) Build a voltage phasor diagram combined with a current phasor diagram.
Methodological guidelines 2.2
a) Note that a complex inductive reactance is positive and capacitance –
negative.
b) To calculate the currents in parallel branches it is convenient to use a cur-
rent divider formula.
References: [R1] – 4.1…4.5, 5.1…5.7; [R2] – 3.1…3.12, 4.1…4.4; [R3] –
3.1…3.18; [R4] – chapter 2, 3; [R5] – chapter 2; [R3] – 7…9.
Table 2.1
10
Enrollment year
Last digit of the credit book number
even
9
0
1
2
3
4
5
6
7
8
odd
0
9
8
7
6
5
4
3
2
1
Circuit в„–
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
U, V
100
120
90
80
50
110
70
115
75
125
R
1
, Ω
90
120
130
0
90
40
120
100
110
40
R
2
, Ω
110
0
0
85
0
110
95
0
0
130
R
3
, Ω
0
80
90
100
150
100
75
95
80
0
Table 2.2
Enrollment year
Penultimate digit of the credit book number
even
9
0
1
2
3
4
5
6
7
8
odd
0
9
8
7
6
5
4
3
2
1
f, Hz
600
700
800
900
1000
700
900
600
1000
800
L
1
, mH
35
25
20
15
10
30
20
40
15
30
L
2
, mH
40
20
15
18
20
25
10
30
20
25
L
3
, mH
30
35
25
10
15
18
15
35
10
20
Table 2.3
Enrollment year
First letter of the surname
even
РђРЇ
УЮФ
РљРҐ
БЛЦ
Р’РњР§
ТЭИ
Р–РЎР—
ДОЩ
ЕПР
ГНШ
odd
ГНШ
РђРЇ
ЕПР
УЮФ
ДОЩ
РљРҐ
БЛЦ
Р–РЎР—
ТЭИ
Р’РњР§
C
1
, ОјF
2,0
3,5
3,0
1,0
0,8
2,0
2,2
2,5
1,8
1,5
C
2
, ОјF
1,5
2,5
2,0
1,8
2,0
2,5
3,2
2,0
1,5
2,5
C
3
, ОјF
2,5
2,0
1,5
2,5
3,0
3,5
1,5
2,8
2,0
3,0
Circuit diagram variants:
Figure 2.1 Figure 2.2
11
Figure 2.3 Figure 2.4
Figure 2.5 Figure 2.6
Figure 2.7 Figure 2.8
Figure 2.9 Figure 2.10
12
CGW в„–3 Single-phase sinusoidal current brunched linear electric cir-3
cuit analysis
Original data and number of analyzing circuit diagram is presented in the Ta-
bles 3.1…3.3 for a variety of variants. Variants of a circuit diagram is presented on
the Figures 3.1…3.10. Choose the original data and circuit diagram according to
your variant and enter it at the very beginning of the explanatory note.
Assignment 3.1
a) Make a system of equations by the Kirchhoff's laws in two forms: differen-
tial form – for instantaneous values and symbolic form – for complex values.
b) Calculate of the complex RMS values of the currents in all circuit branches
by applying two techniques: mesh analysis and nodal analysis. Compare the results
obtained by applying these techniques. Make a conclusion.
c) Write the equations of active and reactive power balance. Check the accu-
racy with which they are executed.
d) Build a voltage phasor diagram combined with a current phasor diagram.
Methodological guidelines 3.2
a) Before applying the mesh currents analysis, or the nodal potentials analysis
it is appropriate to replace two parallel branches with passive elements with one
equivalent.
b) Power balance can be made for a complex, active and reactive power. Ap-
parent power balance equation is not made.
c) Building of a topographical diagram the point of zero potential is to be
placed in the origin of the complex plane, and from the same point build the cur-
rents phasor diagram.
References: [R1] – 5.1…5.8, 5.1…5.7; [R2] – 3.13…3.17, 4.5…4.6; [R3] –
3.19…3.23; [R4] – chapter 2, 3; [R2] – 2.1…2.6; [R3] – 10…11.
Table 3.1
Enrollment year
Last digit of the credit book number
even
9
0
1
2
3
4
5
6
7
8
odd
0
9
8
7
6
5
4
3
2
1
Circuit в„–
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
E
1
, V
100
50
75
0
50
110
70
90
0
0
П†
e1
, deg
30В°
90В°
–60°
0В°
90В°
45В°
120В°
–60°
0В°
0В°
E
2
, V
0
0
0
90
100
0
95
0
75
50
П†
e2
, deg
0В°
0В°
0В°
30В°
60В°
0В°
90В°
0В°
–60°
–30°
E
3
, V
50
90
110
100
0
75
0
50
100
120
П†
e3
, deg
–90°
60В°
120В°
45В°
0В°
30В°
0В°
90В°
120В°
60В°
Table 3.2
13
Enrollment year
Penultimate digit of the credit book number
even
9
0
1
2
3
4
5
6
7
8
odd
0
9
8
7
6
5
4
3
2
1
R
1
, Ω
15
20
10
25
45
15
5
15
50
15
X
L1
, Ω
10
25
10
40
15
40
15
15
35
10
X
C1
, Ω
20
10
25
20
40
20
30
10
40
20
R
2
, Ω
20
45
20
10
30
25
15
10
20
15
X
L2
, Ω
15
20
10
5
45
5
50
10
25
45
X
C2
, Ω
30
10
5
15
15
20
15
35
10
20
Table 3.3
Enrollment year
First letter of the surname
even
РђРЇ
УЮФ
РљРҐ
БЛЦ
Р’РњР§
ТЭИ
Р–РЎР—
ДОЩ
ЕПР
ГНШ
odd
ГНШ
РђРЇ
ЕПР
УЮФ
ДОЩ
РљРҐ
БЛЦ
Р–РЎР—
ТЭИ
Р’РњР§
R
3
, Ω
20
35
15
25
10
5
20
25
15
35
X
L3
, Ω
15
25
20
15
20
45
30
20
5
15
X
C3
, Ω
50
5
10
45
30
35
20
5
20
40
Figure 3.1 Figure 3.2
Figure 3.3 Figure 3.4
14
Figure 3.5 Figure 3.6
Figure 3.7 Figure 3.8
Figure 3.9 Figure 3.10
15
References
Basic references
1 Демирчян К.С., Нейман Л.Р., Коровкин Н.В. Теоретические основы
электротехники. Том 1. – СПб.: Питер, 2009. – 512 с.
2 Денисенко В.И., Зуслина Е.Х. Теоретические основы электротехники:
Учебное пособие. – Алматы: АИЭС, 2000. – 83 с.
3 В.И. Денисенко, С.Ю. Креслина. Теоретические основы электротех-
ники 1. Конспект лекции (для студентов всех форм обучения специальности
050718 – Электроэнергетика). – Алматы: АИЭС, 2006. – 63 с.
4 Бессонов Л.А. Сборник задач по теоретическим основам электротех-
ни-ки. – М.: Высшая школа, 2000. – 528 с.
Additional references
5 Зевеке Г.В., Ионкин П.А., Нетушил А.В., Страхов С.В. Основы теории
цепей. – М.: Энергоатомиздат, 1989. – 528 с.
6 Бессонов Л.А. Теоретические основы электротехники. – М.: Гардари-
ки, 2006. – 701 с.
7 Шебес М.Р., Каблукова М.В. Задачник по теории линейных электри-
чес-ких цепей. – М.: Высшая школа, 1990. – 544 с.
8 Сборник задач и упражнений по теоретическим основам электротех-
ни-ки/ Под ред. П.А. Ионкина. – М.: Энергоиздат, 1982. – 768 с.
2015 yr. publishing plan 53 position
16
Aliaskar Baimaganov
Svetlana Kreslina
ELECTRICAL ENGINEERING THEORETICAL BASES 1
DC & AC linear electric circuit analysis
Methodological guidelines and assignments for calculation graphical works № 1…3
for the baccalaureate 5B071800 – “Electrical Power Engineering” specialty
Editor: V.S. Kozlov
Standard expert: N.M. Moldabekova
Circulation 25 copies Printout paper
Signed to publication _____________ Layout size 60 С… 84 1/16 в„–1
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