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Файл:Theoretical fundamentals of electrical engineering. P.II. Transients in linear electrical circuits with lamped parameters. A collection of advanced pr
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71
500t
i(t)=5-5 e A
−
.
At the second time interval
12
t t t
:
500t
i(t)=8,59 e A
−
.
At the third time interval
2
tt
:
500t
i(t)= 52,32 e A
−
−
.
Problem 3.65.
For the circuit shown in Fig. 3.65a, it is known:
r 100 =
;
C 200 μF=
;
voltage pulse acts on the circuit input (Fig. 3.65b)
11
1
21
U
e (t) t, t 0,t ;
t
e(t)
e (t)=3 U, t t ;
=
=
U=100 V
;
1
t =10 ms
.
Calculate the transient current in the capacitor at
1
tt
.
Fig. 3.65
Answer:
At the time interval
1
tt
100t
2
i (t) 7,15 e A
−
=
.
Problem 3.66.
For the circuit shown in Fig. 3.66, it is known:
r 10 Ω=
;
L 0,1 H=
;
an exponential voltage
30t
e(t) 20 e V
−
=
is supplied to the input of the circuit.
Calculate the transient current in the coil.
72
Fig. 3.66
Answer:
30t 50t
2
i (t) 5 e 5 e A
−−
= −
.
73
REFERENCES
1. Zadachnik po teoreticheskim osnovam jelektrotehniki [Problem book on theoretical fundamentals
of electrical engineering]. K.M. Polivanov, Eds. Moscow, Jenergija, 1973, 304 pages. (in
Russian).
2. Sbornik zadach i uprazhnenij po teoreticheskim osnovam jelektrotehniki [A collection of
problems and exercises on the theoretical fundamentals of electrical engineering]. A tutorial for
universities. P.A. Ionkin, Eds, Moscow, Energoizdat, 1982, 768 pages. (in Russian).
3. Shebes M.R. Sbornik zadach i uprazhnenij po teoreticheskim osnovam jelektrotehniki [Theory of
electrical circuits in exercises and problems]. Textbook for electrical and radio specialties of
universities. Moscow, Vysshaja shkola, 1973, 656 pages. (in Russian).
4. Sbornik programmirovannyh zadach po teoreticheskim osnovam jelektrotehnik [A collection of
programmed tasks on the theoretical fundamentals of electrical engineering]. N.G. Maksimovich,
Yu.E. Batranina, Eds. Publishing House of Lviv National University, 1967, 571 pages. (in
Russian).
5. Vlasov S.P., Kosarev B.I., Kruchinin E.V. Collection of problems with solutions on the
theoretical fundamentals of electrical engineering (Problem book), Part V, Transients in linear
circuits with lamped parameters. Moscow, MIIT, 2014, pages 64. (in English).
6. Nikolayev S.S., Pishchikov V.I. Sbornik olimpiadnyh zadach po teoreticheskoj jelektrotehnike
[Collection of problems of increased complexity in theoretical electrical engineering]. Moscow,
"Znak", 2000, 168 pages (in Russian).
7. Vorotnikov V.S., Gorokhova N.A. Sbornik zadach s reshenijami po teoreticheskim osnovam
jelektrotehniki chast' II [Collection of problems with solutions on the theoretical fundamentals of
electrical engineering] part II. Moscow, MIIT, 1977. (in Russian)
8. Theoretical fundamentals of electrical engineering. Part I. DC and AC linear electrical circuits:
Advanced problems for students of electrical specialties and specializations of the university.
Revised edition. Vlasov S.P., Volyntsev V.V., Kosarev B.I., Kruchinin E.V., Simakov A.V.
Moscow, RUT (MIIT), 2022, 180 pages. (in English)
74
CONTENT
PREFACE 3
3. Transients in linear electrical circuits with lamped parameters 5
3.1. Electrical circuits with inductive coils 5
3.2. Electrical circuits with capacitors 17
3.3. Electrical circuits with two energy storage devices 25
3.3.1 Use of the Law of Conservation of Energy 25
3.3.2 Calculation of circuit parameters and transient processes 28
3.3.3 Circuits satisfying the condition of indifferent resonance of currents 44
3.4. Ill-posed problems 54
3.5. Determining the degree of characteristic polynomial 61
3.6. Duhamel’s integral method 63
REFERENCES 73
75
Educational and methodological edition
Vlasov Stanislav Petrovich
Volyntsev Valery Vyacheslavovich
Kruchinin Evgeny Vladimirovich
Theoretical fundamentals of electrical engineering
Part II.
Transients in linear electrical circuits with lamped parameters.
Problem Book
Advanced problems for students of electrical specialties and specializations of the university.
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