(a) In an RLC series circuit as shown in Figure 2, R = 40 Q, L= 1 H, C = 16 x 10* 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 ume i(0) = 0, and q (0) = 0 C.
(a) In an RLC series circuit as shown in Figure 2, R = 40 Q, L= 1 H, C = 16 x 10* 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 ume i(0) = 0, and q (0) = 0 C.
Chapter15: Alternating-current Circuits
Section: Chapter Questions
Problem 15.8CYU: Check Your Understanding The resonant angular frequency of an RLC series circuit is 4.0102 rad/s. An...
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Transcribed Image Text:(a)
In an RLC series circuit as shown in Figure 2, R = 40 Q, L = 1 H, C = 16 x 10* 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 ume i(0) = 0, and q (0) = 0C.
Hint: Note that
R
switch
d²q dq 1
+R +
E (t)
1
dt²
L
dt 79 =
and
dq
C
i =
dt
Figure 2
(b)
If R = 130 0, verify your answer for the current i(t) in part (a) using Laplace
Transforms is
3125
1
i(t) =
-e-125t +-e-5t
168
629
-sin 10t +
416
629
cos 10t
3774
Hint: Use partial fractions to simplify Q (s).
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