Question

You are given the circuit shown below. The switch has been at the position shown for a long time before being moved at t = 0. You are told that C = 0.25F, L = 2H, R1 = 100. LR + VL -+ VR. =O Use the same sort of methodical approach as before: a) Determine i, (0+), vc(0+) and ic(0+) b) Determine di 2007 and doc0* c) Determine the steady-state value for the voltage Vc.final d) Use circuit analysis to write the differential equation for Vout(t) fort > 0 and determine if the system is over, under, or critically damped. e) Write the total solution for vc (t) fort 20 and determine the value of vc (7). syms ilo veo ico Dil DVC vcss da vt Script Save C Reset MATLAB Documentation 1 syms ilo vco ico Dil DVC vcss da vt 2 ile=[];%Please enter the value of Il(+). 3 vc@=[];%Please enter the value of Vc(+). 4 ico=[];%Please enter the value of IC(+). 5 Dil=[];%Please enter the value of dil(+)/dt. 6 DVC=[];%Please enter the value of dvc(+)/dt. 7 VCSS=[];%Please enter final values for capacitor voltage. 8 da=[]; %If the system is under damped, please input -1; %If the system is critically damped, please input @; %If the system is over damped, please input 1. 11 vt=[]; %Enter the voltage across the cpacitor 7 second after the switch closed.

Answer 1

CzOOS: LEGH R, 2 tour Given, > L L R1 to + - SheV va (1) ev steady schate 2 for sime to the circuit reacher, after tome so y short & C open iLolzoA Vecol=18v lav we lchow that Vecot) = Vccov z 12v icot) - ico) - OA for tzoi TVLot) 12V + OV xon of t- RA mmm Cot)=0A VcCot) = 12v ricco Peco+) icot)c 04. (Vecot) & Bv

dicot Vicot) dt a 6 Alsec advertente Irrot) Pecot 0.85 N 0 V/sec Ve final = 24 volte हा source Voltage in capacitor gets Charged to steady state.

& Vout ct) for tzo conte kul Sanaton, 24 - 2.de + i.R, & ve - ie = cave 24 Lei de constrie de + VC de lo + Rutes ou de + Uc z tego that . delen + 2 Vee 481 Yout' ct for tzo roote of Characteristic Equation, S.,2 -&& fan-wov woefie Terrein ve L 7 won over Damped system.

@ Vect = porced tecponce & Natural response value @ t=00 (steady state). Natural response, Suzen & to wor 2-9.5 +/95 2 - 9.5 + 2.061 Si sig -4.561, -0.439 Vect)s Ariesit + As esat z Ai e gessit & As-oueat force resonce Vc z 24v at t ax Vect) = Ai e possit As 20.480 + See at tz ot Vc = 12V 122 Alt Ag + 94 Ait tez-1 - . - . – 4.561t 0 - - 4.561A, 0 - 4.561A, & 0.459 A una – giugat 0.439 As 1 at tzot at teot

solve equation ③ & ņ are get A = 1.278 &-Age – 13.278. -0.430t è solta.B.998 e Dit ct) 1.878 Lot to. Nc 7 2 1.978 è l.so - 13.088 e ~0.489.7 t 24. Nect) - 23.385 volte