§ 6-3The complete response of the RLC circuit
The complete response is written as the sum of the
forced and the natural response,and the initial
conditions are then determined and applied to the
complete response to find the values of the constants.
?
?
?
?
?
?
?
???
?
???
C
i
t
eAseAs
tdt
td
AAV
ctsts
f
)0(
0
)0(
0
)(
)0(
21
2211
21
?
?
tstsnff eAeAtVt 21 21)()( ??? ??
tstsf eAeAVt 21 21)( ????
Example,Find ).t(i),t(ia n d
RLc?
945355
145355
22
2
22
1
?????????
?????????
s
s
ttcn eAeA 921 ?? ??? ? ttc eAeA 9211 5 0 ?? ???? ?
0150150)0()0( 2121 ??????? ?? AAorAAcc ??
0]9[0
9
21 ?????
??
teAeAtdt
d ttc?
5.135.13 21 ??? Aa n dA
VV
S ol u tion
cf 150530
:
???
3152 0 ???? LC,LR ??
108545045 ??????? C )(C ))(i( LCiR )0(5 ??
C
iC )0(?21 9 AA ???
5.135.13 21 ??? Aa n dA
)0()(5.13150)( 9 ????? ?? tVeet ttc?
)0(1 5 0)( ?? tVtc?
Aeeti ttc )9(5.0)( 9?? ????
Aeeti ttL )9(5.09)( 9?? ????
Aeeti ttR )9(5.05)( 9?? ?????
C1
0,037
I
R1
30
L1
3H
1
2
I1
4Ad c
I
I2
5Ad c
I
0
Aeeti ttc )9(5.0)( 9?? ????
Aeeti ttL )9(5.09)( 9?? ????
Aeeti ttR )9(5.05)( 9?? ?????
Time
0s 1.0s 2.0s 3.0s 4.0s
I(L1) I(R1) -I(C1)
-5A
0A
5A
10A