Answer Happy

Problem 3: /40 For the circuit shown below, the switch has been open for a long time before closing at t = 0. t = 0 0.2 A (↑) 30 Ω + b 10Ω m + cvc(t) = K L (t) or a) Develop a second-order differential equation of the form di? (t) dv}(t) dt² dvc(t) dt dt² 4H Lic(t) iz(t) vc(t): 5 mF 2002 ww 2002 + di₂ (t) +b. +ci₂(t) = K dt and use the coefficients of this equation to calculate a and oo and determine if the circuit is overdamped, critically-damped, or underdamped. (10 points) b) Analyze the circuit at t= 0 and determine y(0-), iz(0-), vc(0-), and ic(0-). (5 points) c) Analyze the circuit at t= 0+ and determine vä(0+), iz(0*), vc(0¹), and ic(0*). (5 points) d) Analyze the circuit at t = ∞ and determine y(0), iz(∞), vc(∞), and ic(00). (5 points) e) Determine an expression for i(t) and yc(t) valid for t≥ 0+. (10 points) f) Simulate the circuit for t≥0+ using LTspice XVII and verify that your analytical solutions match those of the simulation. (5 points)