§ 6-2 The source-free series circuit
)(012
2
stAeii
Cdt
diR
dt
idL ???????
? ???? tt c ti d tCRidtdiLKVL 0 0)(1,0?
012 ??? CRsLs
),LC,LR( d 2200 12 ????? ????
djLCL
R
L
R
L
CLRRs ????? ??????????????? 2
0
22
2
2,1
1)
2(22
/4
The over-damped response----
The critically-damped response----
The under-damped response---- )s i nco s()(
21 tBtBeti ddt ??? ?? ?
tsts eAeAti 21 21)( ??
)()( 21 AtAeti t ?? ? ?
?? c?
R
)(ti
L
C
Example 1:
)(:
.2)0(,2)0(
,
401
1
,2 0 0 0,1:
tiF i n d
VmAi
FCRHLIf
c ??
???
?
?
20000220 ??? ??? d
AtBtBeti t )2 0 0 0 0s i n2 0 0 0 0c o s()( 2110 00 ??? ?
10001220002 ???? LR?
20025
10401 11
11
6
0 ?
??
??
?LC
?
Solution:
?? c?
R
)(ti
L
C
313 102102)0( ?? ????? Bi
)20000s in20000c o s()( 211000 tBtBeti t ??? ?
)2 0 0 0 0s in2 0 0 0 0c o s102()( 231000 tBteti t ??? ??
)2 0 0 0 0c o s2 0 0 0 02 0 0 0 0s i n40()( 21 00 0 tBtedt tdi t ??? ?
)2 0 0 0 0s i n2 0 0 0 0c o s102(1 0 0 0 2310 00 tBte t ??? ??
2)0()0()0(22000 00)( 2 ???????? L RiLBtdt tdi cL ??
tAetiB t 2 0 0 0 0c o s102)(0 10 0032 ???????
e n v e l o p eo n e n t i a le x pe t ??? ?? 10003102
te 1 0 0 03102 ????
)(ti
t
?? c?
R
)(ti
L
C
iL(0)=0.002
vC(0)=2
Time
0s 1.0ms 2.0ms 3.0ms 4.0ms 5.0ms
I(C1)
-2.0mA
0A
2.0mA
tAeti t 2 0 0 0 0c o s102)( 10003 ????
L1
1H
1
2
C1 0,0 0 2 5 u
R1
2k
I
0