Question

Function Generatr Inductor Model Ra R, Figure 1 Series RLC Circuit Preliminary This laboratory will demonstrate how varying resistance changes the natural response of a series RLC circuit (Fig. 1). The function generator is modeled as an ideal voltage source v(t) 5 u() V in series with source resistance Rs-50Q. After measurements using an LCR meter, the inductor is modeled as an ideal L 90 mH inductor in series with resistance RL-20Q. The capacitance is C-0.22 μF. 1) Calculate the roots of the characteristic equation and determine the general form of the natural response of the capacitor voltage vo.n(t) for t 0 when the resistor Rar has values of: a) 2200 Ω (overdamped), b) 1209.2043 2 (critically-damped, make roots equal), and c) 330 (underdamped) 2) Find vc(0), dvc/dtl-o, and vc( given no initial energy is stored in the inductor and/or capacitor. 3) Determine expressions for the total capacitor voltage vc) for 20 when the resistor Rvar has values of a) 2200 2, b) 1209.2043 2, and c) 330 2

Answer 1

vtLt) >charatesiche 501 20+2200 0xLo s +2511 2 $+ 50505050 51 0 S2302-1ove damped Oves damP e. Re こ50 t 20 12.01.203 / s4 .1274.2043

ζ2tIY213 351 11st 50 505050 51:0 ş'--커06. 323 3 2 de - ahen t-

3 ยุโ 5/s LC) Ус 2430-2301utt) e A

万 21939 LO (-23029 . (A) (-230 2 ร.1AYナ2193074 Vees) sCat 귀06.323)