Question

For the next set of questions, consider the following circuit. The switch has been open for a long time. At t=0, it is closed. t=0 11 R1 3 1 3 C c IL R2 3 V = Assume the following values: 11=5mA 12=10mA R1=2K R2=2k L1=10mH C1 = luF Find the following: a) 11(0), the initial current through the inductor (in mA): b) The final current thru the inductor after the switch has been closed for a long time (in mA): mA c) Vc(O), the initial voltage across the capacitor (in V): d) The final voltage over the cap after the switch has been closed for a long time (in V): e) The resonant frequency for this circuit (in rad/s): w= rad/s rad/s f) The neper frequency in (rad/s): a = rad/s g) Is this (O)verdamped, (U)nderdamped, or (C)ritically damped (just type O, U, or C):

Answer 1

the crowt When tso aconds and under steady state condition can be drawn as below:- loma */07/20 lom ellele 10mA wa en under steady state Condition, Inductor --Shoot circuited Capacitor — opon ciocwted 77 (0) = 5mA) because entire woent flows through the short circuited Inductor VC(O) = Voltage across a K = 10xd = 20 V VECO) - dov when t so seconds, after switch operation - lomp Vlo) 500 900 sma under Steady state condition after switch operation Inductor short circuited Capacitor - open circuited inductor the two ak2 resistors becomes bent flows Horough shost ridewited inductor Due to short circuit of inductor the two ak2 sesixto redundant and the total worent flows thorough shoor I (O) = 5+10 = 15mA TIL (60) = 15mA Vc (O) = OV because of short circwt across capacitor by the inductor

Final ans were from the above analysis a] I (0) - 5mA DJ I() = 75mA 5J VC (0) =[20v Į Vc (os) = ov = tov for Parallel RLC cirowt (10x10-3) (1x100) Rif2 -22-1 - where heq = RollR2 = Artha - 27. 1. Req=1 kr 2= 2.60).Coo - & L = 1500 rad/sec 2 <0 then under damped system x>0 then over damped 2=0 then critically damped 500 <10000 so under damped system סן