lcr circuit + v0v0 r c 1 2 l v(t) i(t)=0 for t
TRANSCRIPT
![Page 1: LCR circuit + V0V0 R C 1 2 L V(t) I(t)=0 for t](https://reader036.vdocument.in/reader036/viewer/2022062721/56649f205503460f94c386d5/html5/thumbnails/1.jpg)
LCR circuit
+V0
R
C
1
2
L
V(t)
0t
0tfor
V
0tV
0
I(t)=0 for t<0
0ILC1
dtdI
LR
dtId
VCQ
dtdI
LIR
VVVV
0t
2
2
0
0CLR
0
keI
LC1
LR2
t
20
2
LC12
L2R
L2R
t2
t1
21 ekekI
trial solution
characteristic equation
general solution
LC12
0
L2R
![Page 2: LCR circuit + V0V0 R C 1 2 L V(t) I(t)=0 for t](https://reader036.vdocument.in/reader036/viewer/2022062721/56649f205503460f94c386d5/html5/thumbnails/2.jpg)
LCR circuit – initial conditions
Initial conditions I(0), ? 0dtdI
No energy stored 00I0LIW 221
L
0
0C
C2
21
C
V0dtdI
L
VV0dtdI
LR0I
00V0CVW
LV
0dtdI 0
+V0
R
C
L
I(t)
![Page 3: LCR circuit + V0V0 R C 1 2 L V(t) I(t)=0 for t](https://reader036.vdocument.in/reader036/viewer/2022062721/56649f205503460f94c386d5/html5/thumbnails/3.jpg)
LCR circuit 20
2 t2
t1
21 ekekI
overdamped solution
2 20
2,1
LV
kk0dtdI
kk 0kk0I
ekek0tI
021
2121
t2
t1
L2V
k 01
20
2
LC12
0
L2R
tt
CL2
2R
0 ee2
VtI
![Page 4: LCR circuit + V0V0 R C 1 2 L V(t) I(t)=0 for t](https://reader036.vdocument.in/reader036/viewer/2022062721/56649f205503460f94c386d5/html5/thumbnails/4.jpg)
LCR circuit 20
2
critically damped solution
2 20
21
t21 etkkI
0k 00I 1
t221 ektkk
dtdI
LV
dtdI
k 0
0t2
tetLV
tI 0
![Page 5: LCR circuit + V0V0 R C 1 2 L V(t) I(t)=0 for t](https://reader036.vdocument.in/reader036/viewer/2022062721/56649f205503460f94c386d5/html5/thumbnails/5.jpg)
LCR circuit 20
2 t2
t1
21 ekekI
2 20
R
2202,1
j
j
2121
tj2
tj1
t
kk 0kk 00I
ekeke0tI RR
0R 1 R 2
t 0
dI Vj k j k
dt L Lj2V
kR
01
tjtjt
22R
CL
0 RR eej2
1e
V0tI
tsineV
0tI Rt
22R
CL
0
t
tL2
R
e
underdamped (oscillatory) solution
![Page 6: LCR circuit + V0V0 R C 1 2 L V(t) I(t)=0 for t](https://reader036.vdocument.in/reader036/viewer/2022062721/56649f205503460f94c386d5/html5/thumbnails/6.jpg)
LCR circuit 0ILC1
dtdI
LR
dtId2
2
20
2 t2
t1
21 ekekI
overdamped solution
critically damped solution
underdamped (oscillatory) solution
20
2 2,1 β is real
20
2 21 t21 etkkI
20
2 R
2202,1
j
j
LC12
0
L2R
![Page 7: LCR circuit + V0V0 R C 1 2 L V(t) I(t)=0 for t](https://reader036.vdocument.in/reader036/viewer/2022062721/56649f205503460f94c386d5/html5/thumbnails/7.jpg)
LCR circuit 0ILC1
dtdI
LR
dtId2
2
20
2 t2
t1
21 ekekI
overdamped solution
critically damped solution
underdamped (oscillatory) solution
20
2
20
2
20
2
LC12
0
L2R
tt
CL2
2R
0 ee2
VtI
tetLV
tI 0
tsineV
0tI Rt
22R
CL
0
![Page 8: LCR circuit + V0V0 R C 1 2 L V(t) I(t)=0 for t](https://reader036.vdocument.in/reader036/viewer/2022062721/56649f205503460f94c386d5/html5/thumbnails/8.jpg)
CP2 September 2003
![Page 9: LCR circuit + V0V0 R C 1 2 L V(t) I(t)=0 for t](https://reader036.vdocument.in/reader036/viewer/2022062721/56649f205503460f94c386d5/html5/thumbnails/9.jpg)
This way up
![Page 10: LCR circuit + V0V0 R C 1 2 L V(t) I(t)=0 for t](https://reader036.vdocument.in/reader036/viewer/2022062721/56649f205503460f94c386d5/html5/thumbnails/10.jpg)
This way up
![Page 11: LCR circuit + V0V0 R C 1 2 L V(t) I(t)=0 for t](https://reader036.vdocument.in/reader036/viewer/2022062721/56649f205503460f94c386d5/html5/thumbnails/11.jpg)
This way up
![Page 12: LCR circuit + V0V0 R C 1 2 L V(t) I(t)=0 for t](https://reader036.vdocument.in/reader036/viewer/2022062721/56649f205503460f94c386d5/html5/thumbnails/12.jpg)
This way up
![Page 13: LCR circuit + V0V0 R C 1 2 L V(t) I(t)=0 for t](https://reader036.vdocument.in/reader036/viewer/2022062721/56649f205503460f94c386d5/html5/thumbnails/13.jpg)
LCR circuit 0ILC1
dtdI
LR
dtId2
2
20
2 t2
t1
21 ekekI
overdamped solution
critically damped solution
underdamped (oscillatory) solution
20
2
20
2
20
2
LC12
0
L2R
tt
CL2
2R
0 ee2
VtI
tetLV
tI 0
tsineV
0tI Rt
22R
CL
0