Question

Find the charge q(t) on the capacitor and the current i(t) in the given LRC-series circuit. 5 h, R 2 1 f, E(t) 20 = 0 A 10 , C 200 V, q(0) 0 C, i(0) q(t) C i(t) A Find the maximum charge on the capacitor. (Round your answer to three decimal places.) C C II

Answer 1

CD Qeeee Re l02 LE-2.5H EU)E 200V Uoiny kvL, lit 9 be the cument at Aime t towin thrngh the circuit, th enne amoumt tchange will be at the Capaclb hlales. o) + R da dt 200 L di dt L da +R oli dt2 d'a 200 dt LC we thave to solut this secondl arder dilferential guation Conplementany functis (CE) 4- R2. RI t LC 2 4 Lo 4 ZC

padicador nlegrat (Ps) deD Nlow thu oo PI r Paut 208 0 Gennal sointron is 94 CFtPI ep 200 C undary Cunditisn to ditimine Now we will ne the A and B. A B+200 C ()40)0 AtR -200 (D i Loo -R 4 LC +EC (3-3 4 LC no calulati 4 and LC and nt thm fn equ-
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lo and 4 2.S 4y20 16- 4i 2.5 becomes equ (-4-41) o ( - t 4i) A + 2A tQAi B-28i bads phnt ane equal to O. Roth imasinaruj and en! nequ this A -B 2A--2o0c tence (-2-2) +74 2121) + 200 l0o C noer ( (-2-2i)t dath 242i) t e -00 C dt +00C

capacitor on the capacttry Marimum chage Since a io thu chage which thi chanje in deus will give the tim fr at maximum. eC 2+2i) t ( 2+2i) + E2-21JA 2-2j) 100 C 200 C 24ai) E2t2i) 2-ai) 2itt 2it e 2421 242 4iA e 222-2) 2t21) (-1-2j) 414 4 t 1) (4- e 1 4t Compariny 31T 2 ht te 3 in equ to get thhe marimum on thi capactor chage -l0 ol 20 SIT +200x1 + e e e + e -Se 2 - 2-

in Coulombs -0e Coo + lo 10 x0.0948 710 J2 Coulombs l0.670 Coculanbs saoreney