Find the current in the RLC circuit, assuming that E(t) = 0 for t > 0 R = 4 ohms; L = .05 henrys; C = .008 farads; Q0 = -1 coulombs; I0 = 2 amperes
Find the current in the RLC circuit, assuming that E(t) = 0 for t > 0 R = 4 ohms; L = .05 henrys; C = .008 farads; Q0 = -1 coulombs; I0 = 2 amperes
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Linear Second-Order Equations
Find the current in the RLC circuit, assuming that E(t) = 0 for t > 0
R = 4 ohms; L = .05 henrys; C = .008 farads; Q0 = -1 coulombs; I0 = 2 amperes
![We have
Pulting all
Let I
the differential equation,
=
the values
d²f
0.05
dt² +
+80.
80 det inte
we
4
dt2
be the trial
Hence general sollution,
have
det s
+
dt
Aext
Hence auxiliary equation,
-> x =
+2500 1 = 0
I(t) =
sollution of
I
0.008
x =
e
L
-802
-40t
d²I
dt²
c
9² +80x + 2500
80
di
R = + = = 0
곧
dt
2
+ R
=0
4x2500
- 40 ± 30
{ c₁cos (30t) + C₂ sin (30+)}
[c1, c₂
are constants ]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F98175f82-a1e3-49ad-8594-ec8a3ac834b0%2Fa400e2aa-ee5f-45ac-ad09-ab2b99dd34cc%2Fuqb0f1_processed.png&w=3840&q=75)
Transcribed Image Text:We have
Pulting all
Let I
the differential equation,
=
the values
d²f
0.05
dt² +
+80.
80 det inte
we
4
dt2
be the trial
Hence general sollution,
have
det s
+
dt
Aext
Hence auxiliary equation,
-> x =
+2500 1 = 0
I(t) =
sollution of
I
0.008
x =
e
L
-802
-40t
d²I
dt²
c
9² +80x + 2500
80
di
R = + = = 0
곧
dt
2
+ R
=0
4x2500
- 40 ± 30
{ c₁cos (30t) + C₂ sin (30+)}
[c1, c₂
are constants ]
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