Question

The switch sl has been open and switch s2 is closed. for a long time (Fig. 2) At t= 2 seconds, S2 is opened. Determine ict) fort>o. *=2 O 0 4or 40V ilt)

Answer 1

&t=2see cue 82 ES Tę8lt Solution : Stepi! Here ist) is the indlector current which is stected for to: Tikt) = {(60) +[12(o) [2(o) e th € 40v where, vil loo)= final value of current il(o) = initial value of current ( Here TL(0)=0 Amp, as .. no urrent is there before t=o) • E= time constant for the circuit = [L ) . L res! • Req = Therenin Resistance seen by incluctes. Steps? Here for oto 2 see the circuit is! so {(ou? = (40) = 5 Amp 40 V sont = her = = ILCt) = 57 [0-5Je t'i Tart) = 5(1-e-t) Amp. I step3. when surtch S, closed at t=2see: Son 1219) = 5(1e->) = 4.3233 Amp. 821 &r I so for traseel (new ciocnit o Hero {{ (t') = xí cool + [ilgi ileogethet Helle, 1.600) = - 2.5 Amp - oty token = 878 = 0r5 see Son il t') = 4.5+ [403233 - 2.5] e-t/orso 1 Q(+') = 2.5 + 107333 e 21 Hey t'= (t-2) see en Fict-2) = [Q+5 + 1.7333e -214-2)] 8

Step 4: so, overall indructor current o Ampi tvo 5(1-e-t) Amp; 0<t< Isle 1 (2-5+1-7333 e-2t) Arub; +7, 28ee { (t) = plotting plit 5 + 4-32334-- 2 - t