Solved: In the circuit in Fig. 8.1, and a) Find for b) Find the first three values of t

Chapter 8, Problem 8.19

(choose chapter or problem)

In the circuit in Fig. 8.1, \(R=5 \ \mathrm{k} \Omega, L=8 \ \mathrm{H}\), \(C=125 \ \mathrm{nF}, V_{0}=30 \mathrm{~V}\), and \(I_{0}=6 \mathrm{~mA}\).

a) Find v(t) for \(t \geq 0\).

b) Find the first three values of t for which dv/dt is zero. Let these values of t be denoted \(t_{1}, t_{2}\), and \(t_{3}\).

c) Show that \(t_{3}-t_{1}=T_{d}\).

d) Show that \(t_{2}-t_{1}=T_{d} / 2\).

e) Calculate \(v\left(t_{1}\right), v\left(t_{2}\right)\), and \(v\left(t_{3}\right)\).

f) Sketch v(t) versus t for \(0 \leq t \leq t_{2}\).