Chapter 7.6, Problem 16E

1. (a) In Problem 12 in Exercises 3.3 you were asked to show that the currents i₂(t) and i₃(t) in the electrical network shown in Figure 7.6.8 satisfy

$L\frac{d{i}_2}{dt}+L\frac{d{i}_3}{dt}+R_1{i}_2=E(t)$

$-R\frac{d{i}_2}{dt}+R_2\frac{d{i}_3}{dt}+\frac{1}{C}{i}_3=0.$

Solve the system if R₁ = 10 Ω, R₂ = 5 Ω, L = 1 h, C = 0.2 f,

$E(t)=\{\begin{array}{cc}120,& 0\le t<2\\ 0,& t\ge 2,\end{array}$

i₂(0) = 0, and i₃(0) = 0.

1. (b) Determine the current i₁(t).

FIGURE 7.6.8 Network in Problem 16