RL Network. The currents in the RL network given by the
Chapter 9, Problem 33E(choose chapter or problem)
RL Network. The currents in the RL network given by the schematic diagram in Figure 9.8 are governed by the following equations:
\(2 l_{1}(t)+90 l_{2}(t)=9\),
\(I_{3}(t)+30 l_{4}(t)-90 l_{2}(t)=0\),
\(60 l_{5}(t)-30 I_{4}(t)=0\),
\(I_{1}(t)=I_{2}(t)+I_{3}(t)\),
\(I_{3}(t)=I_{4}(t)+I_{5}(t)\).
Figure 9.8 RL network for Problem 33
Assume the currents are initially zero. Solve for the five currents \(I_{1}, \ldots, I_{5}\). [Hint: Eliminate all unknowns except \(I_{2}\) and \(I_{5}\), and form a normal system with \(x_{1}=I_{2}\) and \(x_{2}=I_{5}\).
Equation Transcription:
Text Transcription:
2l_1(t) + 90l_2(t) = 9
I_3(t) + 30l_4(t)-90l_2(t) = 0
60l_5(t)-30I_4(t) = 0
I_1(t) = I_2(t)+I_3(t)
I_3(t) = I_4(t)+I_5(t)
I_1, ... , I_5
I_2
I_5
x_1 = I_2
x_2 = I_5
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