Question

The voltage of the capacitor vo(t) for t> 0 is known to be vo(t) = 9e-20 V. i1(0) = 5mA. (a) Find i(t) for t 20. (b) How much energy was initially stored in the inductor and capacitor? (c) How much energy was stored at t= in the inductor and capacitor? it) (0) i20 1110 H V.0) 10 kΩ Black box -T gmF

Answer 1

consider the given circuit Nilt) Jit) 13 let) st Fre) lolt) Black IOH MMF Box at Node N, By kirchoff's current law, Nodal ict) - 1,(t)-1(t) - i, ct) Analysis consider the + capacitoy un Laplace domain I t Iols) Vo (8) Vols) Lo(s) Z(s) → lo (s). Vo(s) (5) 9/3+20 1/sc 20t Volt) = qe Vo(s) = 9. 8 + 20 2018) 98c Stro 9c ( S St20 20 9c 1 ( Stro Po (8) = ac ac (! 20 Stro Apply Inverse Laplace transform loct) - 0.0018 ( 86t) - 200 - 20€

5. Volt) = (lok) () ² dl (t) = qe 6-20t -zot 0.90 mA lokr Also, Vo(s) I, (8) Z (8) 2:18) a ) * 5L S+20 0.9 S(S+20) 0.9 208 > 20 (5+20) i ct) = 0.9 uct) - 8200) {(t) = d.our Cult) - & 20t) m. (uce 20 ilt) 1 (t)- 10lt) -ig (t) MA ict): 4:5 (uct) - 2201) - 1.8 (84) - 200201) - 02630+) for to - 20(0) Initially voltage on capacitor Volo) - 90 Vo(o)= av 2 on 2 Energy capacitor a 1 cv² = 1 x L xoxlan 토 current though inductor 1, () = 5mA = 8.1mJ → Ę 2 Li2 x 10 *(5x103) ? Ę = 0.125 m J

At t=00 - 20100) Vo(0) qe 0 At I instant t=0 7 So total € = 2 (M²) = 0 energy stored upto co Ec600) - Ecco) = -8.1mJ i, at t=00, all - – 8.1mJ cis delivered and capacitor energy has no energy At t=0 1,Lt) - 0.045 (uct) -e2016) 0.045 (uct) - 0) ię (00) ² 0.045 At instant too 2 EL LLLICO 3x tox x 10 * (.045) - 10.125mJ So upto t=00 Energy stored E600) – Eco) 10.125mJ - 0.125mJ com J