Applying the Kirchhoff's second law, show that the system of differential equa- tions is (a) L- dt dle +L+R¡lb =E (1) . dt dl dle +R2- dt =0. dt %3D Use the Laplace transform to solve the system in (a) if R¡ = 102, R2 = 52, %3D (b) L= 1H, C =0.2F, I,(0) =0, I.(0) = 0 and 120, 0<1<2, E(t) = 0, 1> 2.
Applying the Kirchhoff's second law, show that the system of differential equa- tions is (a) L- dt dle +L+R¡lb =E (1) . dt dl dle +R2- dt =0. dt %3D Use the Laplace transform to solve the system in (a) if R¡ = 102, R2 = 52, %3D (b) L= 1H, C =0.2F, I,(0) =0, I.(0) = 0 and 120, 0<1<2, E(t) = 0, 1> 2.
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For b
Transcribed Image Text:Figure 1 shows an electric circuit that can be represented by a system of differential
equations.
R2
4 la
R1
47
FIGURE 1. Electric circuit
If I, and I. describe the currents of the circuit, by Kirchhoff's first law, we can write
la (1) = I, (1) +1. (1).
Transcribed Image Text:(a)
Applying the Kirchhoff's second law, show that the system of differential equa-
tions is
dl
dle
+L
+RIb = E (t),
dt
dt
dl,
dle
+R2
dt
1
= 0.
-R
dt
Use the Laplace transform to solve the system in (a) if R = 102, R2 = 52,
L= 1H, C =0.2F, I,(0) =0, I(0) = 0 and
(b)
120, 0<1<2,
0,
E(t) =
122.
(c)
Calculate the current I.(t).
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