In an RLC series circuit as shown in Figure 2, R = 40 , L = 1 H, C = 16 x 104 F, and the voltage source is E (t) = 100 cos 10t V. Determine the current i(t) in the circuit using the undetermined coefficients if at the initial time i(0) = 0, and q(0) = 0 C. Hint: Note that R switch L d²q dq 1 +R - += q = E(t) dt² dt dq i = dt Figure 2 and

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(a)
In an RLC series circuit as shown in Figure 2, R = 40 Q2, L = 1 H, C = 16 x 104 F, and
the voltage source is E (t) = 100 cos 10t V.
Determine the current i(t) in the circuit using the undetermined coefficients if at the
initial time i(0) = 0, and q (0) = 0 C.
Hint: Note that
R
d²q
switch
dq 1
+R +=9=
dt c
E (t)
dt²
and
dq
i =
dt
Figure 2
(b)
If R = 130, verify your answer for the current i(t) in part (a) using Laplace
Transforms is
3125
168
416
-125t
e
-5t
i(t)
+ е
sin 10t +
cos 10t
3774
629
629
Hint: Use partial fractions to simplify Q (s).
L
Transcribed Image Text:(a) In an RLC series circuit as shown in Figure 2, R = 40 Q2, L = 1 H, C = 16 x 104 F, and the voltage source is E (t) = 100 cos 10t V. Determine the current i(t) in the circuit using the undetermined coefficients if at the initial time i(0) = 0, and q (0) = 0 C. Hint: Note that R d²q switch dq 1 +R +=9= dt c E (t) dt² and dq i = dt Figure 2 (b) If R = 130, verify your answer for the current i(t) in part (a) using Laplace Transforms is 3125 168 416 -125t e -5t i(t) + е sin 10t + cos 10t 3774 629 629 Hint: Use partial fractions to simplify Q (s). L
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