Question

t-0 a SW1 SW2 0.5 Ω 2 1Ω V. R3 20 A T v(t) 0.5 F 0.5 H 0 Find the initial current i(0) through the inductor and the initial voltage v(0) across the capacitor at t 0. b. Write a node equation at node a fort2 0. c. Represent v(t) as a function of i(t) on the series connection of R2 and L. Find dv(t)/dt. Derive a second-order differential equation in i(t) Find the particular solution to the differen- tial equation; or find the final value of i(t), i(o), from the circuit Find the characteristic equation. Find the roots of the characteristic equation. Find the solution of the differential equation i(t) and plot i(t) for tz 0. d. e. f. g. h. i. j. Find v(t) and plot v(t) for t2 0.

Please do the problem if you can do ALL parts.

Answer 1

0.5-n 0.5H clased, sws pened OPenaal iTD 6 ence

nods equotn at node a ta o.5F o.5H Is dt

dt dli5 dt dt dict O-25 dt dut

2 VCt) i (t) by curing equteń ④ 2 3100

hence fhu Ssn dict) dt dt dt

(0-622くcos Cak)ナsin@t íCt) 2t so 2