1.1 model)
1,
a
b
10BA
SE-T
wall
plate
2,(circuit model)
sR
LR
sU
1 3
(a) (b)
(c)
1.2
(reference direction)
1,
t
q
t
qi
t d
dlim)t(
0Δ
d e f

Δ
Δ
1kA=10
3A
1mA=10-3A
1? A=10-6A
A kA
mA?A
( ),
A
A B
B
i
( )
A B
i i
i > 0 i < 0
AA BB
iAB,A B
i
A B
iAB
A B
U
dq
dW
U
d e f
V ( ) kV mV?V
2,
q
W
q?
0
4C a b
8J b c
12J
(1) b a b c
Uab Ubc;
(2) c
a
c
b
VqW aba 248
0?b?
VqWqW bccbc 3412
VU baab 202
VU cbbc )( 330
(1) b
a b
c
VqW aca 54 128
0?c?
VqW bcb 3412
VU baab 235
VU cbbc 303
(2) c
()
U < 0> 0
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+ +
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U
(1)
(2)
(3)
U
U+
A B
UAB
u i
3,
i
+ - +-
i
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(1)
(2) (
3
A B
i
U
A
B
A
B
1.3
1,
t
wp
d
d?
ui
t
q
q
w
t
wp
d
d
d
d
d
d
W () (Watt )
J () (Joule )
q
wu
d
d?
t
qi
d
d?
2,
u,i
P=ui
P>0 ( )
P<0 ( )
p = ui
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P<0 ( )
u,i
+
-
i
u
+
-i
u
5
6
4
1
2
3
I2 I3
I1
+
+
+
+ +
+
- -
-
U6
U5U4
U3
U2
U1
U1=1V,
U2= -3V,
U3=8V,U4= -4V,
U5=7V,U6= -3V
I1=2A,I2=1A,
I3= -1A
WIUP 221111
WIUP 62)3(122
WIUP 1628133 WIUP 3)1()3(366
WIUP 7)1(7355
WIUP 41)4(244
t t0
ttttR uipW 00 dd ξξ
3,
1
2
3
4
1.4
d
u i
1.5 (resistor)
2.
R
ui
0?),( iuf i
u
1,
ui
VCR
R?( ) (Ohm )
(Ohm’s Law)
GuRui
iuR?
u
i
G S( ) (Siemens )
u i R
u
i
+ -
Riu?
(2)
(3)
(1) ( R
u? –R i i? –G u
R
u
i
+-
3,
p? –u i? –(–R i) i? i2 R
–u(–u/ R)? u2/ R
p? u i? i2R?u2 / R
R
u
i
+-
R
u
i
+ -
t0 t
ttttR uipW 00 dd ξξ
R
i
u
+
–
4,
00 ui
G o r R 0
00 ui
0 G o r R
u
i
1.6 (independent source)
i
1,
i
Su
+ _
(1)
(2)
u
i
)(tuS
R
i
-
+
Su
R
ui S?
)( Ri 0
)( 0 Ri
1
+
_
i
u
+
_S
u
+
_
i
u
+
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u
iuP S?
iuP S?
2
iuP S?
iuP S?
5R
+
_
i
+_
Ru
+
_
10V5V
Vu R 5510 )(
ARui R 155
WRiP R 5152
WiuP SV 1011010
WiuP SV 5155 )(5W
P P
u
2,
u
Si
+ _
(1)
(2)
u
i
)(tiS
)( 00 Ru
)( Ru
R
u
-
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SRiu?
1
SuiP?
2
uiP S?
u
+
_
Si SuiP?
SuiP?
u
+
_
Si
Ai 2
Vu 5?
WuiP SA 10522
WiuP SV 10255 )(10W
P P
+
_
u
+
_
2A5V
i
1.7 ( )
(controlled source or dependent source)
+ –
1,
CCCS
,
2,
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+
_
u2
i2
_u1
i1
+
12 ii
g,
VCCS )
u1 g
+
_
u2
i2
_
i1
+ 12 gui?
VCVS
u1
+
_
u2
i2
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i1
+ +
-
12 uu
,
ri1
+
_
u2
i2
_u1
i1
+ +
-
CCVS
12 riu?
r,
bi
ci
bc ii
bi?
bi ci
u25i
1
+
_
u2_u1=6V i1
+
+ -
3?
Ai 2361
V
iu
4610
65 12


’
KCL KVL
(b)
b=3
a
n=2
b
+
_
R1
uS1 +
_
uS2
R2
R3
1
(branch)
i3
i2
i1 b=5
l
l=3
+
_
R1
uS1 +
_
uS2
R2
R31 2
3
KCL
m
k
ti
1
0)(? iior
1i
5i
4i
3i
2i
054321 iiiii
54321 iiiii
1
3
2
5i
6i
4i
1i
3i
2i
0641 iii
0542 iii
0653 iii
0321 iii
KCL
1 KCL
2 KCL
3 KCL
–U1–US1+U2+U3+U4+US4= 0
KVL
m
k
tu
1
0)(? uuor
I1
+
US1
R1
I4
_ +U
S4 R4
I3
R3
R2 I2
_ U
3
U1
U2
U4
U2+U3+U4+US4=U1+US1
–R1I1+R2I2–R3I3+R4I4=US1–US4
KVL
a
Us
b
-
+
+
+
U2
U1 Sab UUUU 21
1 KVL;
2 KVL
3 KVL
KCL KVL
KCL KVL
KCL KVL
KCL KVL
KCL KVL
i1=i2?
3.
A
B
+
_
1
1
1
1
1
13 +
_2
i2i1
UA =UB
I = 0
1.
A
B
+
_
1
1
1
1
1
13 +
_2
2,i1
Ai 523 )(
A3
A2?
i
3
3
5
1
4
1
Vu 1552010
V5

u
V10
V20
2
+
+ -
- 4V
5V
i =?
+
+-
-
- 4V
5V
1A
+ -u =?
Ai
i
3
543
Vu 1275
3?
3?
10V
+
+
- -
1A
-10V
I =?
10?
5,4V
+
-
10A
U =?
2?
6,+ -
3A
I1
I
10V
++
- -
3I2
U=?
I =05?7.
5?
- +
2I2
I2
5? +-
++
-
I1
U=?
8.
R2
I1
R1US
12 IRU
111 RUII S
)1(11
R
UI S
)1(
1
2
R
URU S
)1(1
2
1 R
UIUP S
SS
22
1
2
2
2 )1( R
URP S
o
)1(1
2
R
R
U
U
S
)1(
2
1
20
R
R
P
P
S
usu
iO
i
+
_ u
+
_
Su
SR
iRuu SS
0?SR
is
u
iO
S
S R
u
ii
SR
u
+
_
Si SR
i
6.1 (capacitor)
_q+ q
1.
uq
0?),( quf
q
u
q u q
~ u
2,
C
u
+q -q
t a n uqCorCuq
C,F ( )
(Farad ),?F p F
q
uO
t
uC
t
qi
d
d
d
d
C
u
i
u i
VCR
(1) i u,u
(2) u ( ) i =0
(3) i u
.
1 u i;
2 u(t0)
)( d
dd )(


t
t
t
t
tt
ξi
C
u
id ξ
C
ξi
C
ξi
C
tu
t
0
0
0
0
1
111
VCR
3,
t
uCuuip
d
d
(1) u>0 d u/d t>0 i>0 q?
p>0,
(2) u>0 d u/d t<0 i<0 q?
p<0,.
u i
1
2
t0 t
)(2 1)(2 1)(21)(21 022022 tqCtqCtCutCuW C
0
2
1
2
1
2
1
2
1
ξ
2
1
22
0
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)()()(d
d
d
)(
tq
C
tCu
CutCuCuξ
ξ
u
CuW
u
t
t
C
)(tus C 0.5F
ii P (t) W (t)
21 t /s
2
0
u/V
uS (t),


st
stt
stt
t
tu
s
20
2142
102
00
)(



st
st
st
t
dt
du
Cti
s
20
211
101
00
)(
21 t /s
1
i/A
-1



st
stt
stt
t
titutp
20
2142
102
00
)()()(
21 t /s
2
0
p/W
-2



st
stt
stt
t
tCutW
C
20
212
10
00
2
1
2
2
2
)(
)()(
21 t /s
1
0
WC/J


st
st
st
t
ti
20
211
101
00
)(
21 t /s
1
i/A
-1
d0d )( 0 t ttξCξCtcust 00 2201111

t
C tdutu 1 24150
11?)(
.
)()(st 21
t?2 t
C dutu 2 0050
12?
.
)()(
6.2 (inductor)
i (t)
+ -u (t)
t)N?(t)
1.
i
0?),( if?
i
i ~
i
2,
t a n )()( iLortLit
L,L H ()
(Henry )?H m H
iO
+ -u (t)
i L
td
tdiL
td
dtu
)(
)(
u i
VCR
(1) u i,i
(2) i ( ) u =0
(3) u i
.
+ -u (t)
i L
1 u i;
2 i(t0)
)( d
ddd )(


t
t
t
t
tt
ξu
L
i
ξu
L
ξu
L
ξu
L
ti
t
0
0
0
0
1
111
VCR
3,
i
t
iLuip
d
d
(1) i>0 d i/d t>0 u>0 p>0,
(2) i>0 d i/d t<0 u<0 p<0,
u i
1
2
t0 t
)()()()( 022022 2 12 12121 tLtLtLitLiW L
0)(
2
1
)(
2
1
)(
2
1
)(
2
1
)ξ(
2
1
d
d
d
22
0)(
222





t
L
tLi
LitLiLiξ
ξ
i
LiW
i
t
t
L
C L
i
u
q
(1)
(2) u-i q-? C-L i-u,
(3) C L,? q
* R G,
I=U/R? U=I/G
U=RI? I=GU
22
2
1
2
1
L
LiW
t
i
Lu
Li
L
d
d
22
2
1
2
1
d
d
q
C
CuW
t
u
Ci
Cuq
C