Answer: (a) The system of differential equations for the currents i2(t) and i3(t) in the
Chapter 10, Problem 12(choose chapter or problem)
(a) The system of differential equations for the currents \(i_{2}(t)\) and \(i_{3}(t)\) in the electrical network shown in FIGURE 10.4.2 is
\(\frac{d}{d t}\left(\begin{array}{l} i_{2} \\ i_{3} \end{array}\right)=\left(\begin{array}{cc} -R_{1} / L_{1} & -R_{1} / L_{1} \\ -R_{1} / L_{2} & -\left(R_{1}+R_{2}\right) / L_{2} \end{array}\right)\left(\begin{array}{l} i_{2} \\ i_{3} \end{array}\right)+\left(\begin{array}{l} E / L_{1} \\ E / L_{2} \end{array}\right)\).
Use the method of undetermined coefficients to solve the system if \(R_{1}=2 \Omega, R_{2}=3 \Omega, L_{1}=1 \mathrm{~h}, L_{2}=1 \mathrm{~h}\), E = 60 V, \(i_{2}(0)=0\), and \(i_{3}(0)=0\).
(b) Determine the current \(i_1(t)\).
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