4. ch13, problem 6 13.6 As displayed in Fig. P13.6, an LC circuit can be mod- eled by the following system of differential equations: d²i, L, (i, - i) = 0 + dr? d'i, 1 L2 i, - i) - (i, - i,) = 0 + dr? d'i, L3 + iz dr? 0 = (! - )-2. where L = inductance (H), 1 = time (s), i = current (A), and C = capacitance (F). Assuming that a solution is of the form i, = 1, sin (@t), determine the eigenvalues and eigenvectors for this system with L= 1 H and C = 0.25C. Draw the network, illustrating how the currents oscillate in their primary modes.
4. ch13, problem 6 13.6 As displayed in Fig. P13.6, an LC circuit can be mod- eled by the following system of differential equations: d²i, L, (i, - i) = 0 + dr? d'i, 1 L2 i, - i) - (i, - i,) = 0 + dr? d'i, L3 + iz dr? 0 = (! - )-2. where L = inductance (H), 1 = time (s), i = current (A), and C = capacitance (F). Assuming that a solution is of the form i, = 1, sin (@t), determine the eigenvalues and eigenvectors for this system with L= 1 H and C = 0.25C. Draw the network, illustrating how the currents oscillate in their primary modes.
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Q:31)
Transcribed Image Text:4. ch13, problem 6
13.6 As displayed in Fig. P13.6, an LC circuit can be mod-
eled by the following system of differential equations:
d'i,
L,
4- i) = 0
+
di?
d'i,
L
- (i, - i)
+
dt?
d'i,
L3
dr?
o = (1 = '» ?-
1
di +--i,) = 0
C3
C2
where L
= inductance (H), t = time (s), i = current (A), and
C = capacitance (F). Assuming that a solution is of the form
i; = 1, sin (@t), determine the eigenvalues and eigenvectors for
this system with L = 1 H and C = 0.25C. Draw the network,
illustrating how the currents oscillate in their primary modes.
L
L2
all
C2
iz
L3
ll
C1
C3
+
FIGURE P13.6
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