Question

Chapter 7, Problem 7.067 Find i(t) for t > 0 in the circuit in the accompanying figure using the step- by-step method. 12 100 X 150 1H OO 21 V (+ it) 603 603 Please round all numbers to 3 significant digits. i(t) = [-**T E A Click if you would like to Show Work for this question: Open Show Work

Answer 1

22 WL Go 362 Solution: Giren circuit diagrom - At to the switch u w in open position therefore the giren circuit is operating at L trendy dlate (woichid due to presence # 21V DC source) Hence inducher it acting as short circuited at this condition- 122 WM 3152 1 21v 13 lorilis2 = 62 26 & G21162=32 Nero, voltage va ei giren by using voltage direder Rule - = (611162) x 21 V (621162) + (101|152) +122 = 3x (211) 3 +6+12 vagy = 3V . and similarly voltage across (10211152) resistor- Vj = (102||152) x 210 [(6169) +(1009158) +12]

- 6 X 210 (3+6+12) () v = Gloet Now the distribution of current is given across the elements- na ,6A = 0:48 TISA Sicrov + JA 7 Đ 6v zlor a lot 210 13A-65A JUA= 70-5A 362 3v Using tel at Node 'A' -|_107 + 0.6A -0.5A =0 TI_10) = -0.14 At t-ot : At switch is closed, since current flowing through inducher cannot change instantly :- [lvos = 110) = -014] for to :~ The switch is in closed position noco, - Tisz ll O2 = or At t=0 % The inducher behaved as short circuited u finding the current through inductor at taos-

122 K 2V (t S60 S67 1 ' 1102 = 인 पणि | ev (2 22 Using Kel at Node 'l - W ++] = 1 ( ) 12. 242H

Now, koos is given as a ix a Vix Ampere les e Comics = 0.4 ampere Now, calculation of time constant ir Replace all the independent energy source by their equivalent resistance - Doc. noltage source acts as shorn circuited Now, IAf steady state) 12. lor NOW, {or { {12r {lor > 622 Here, 6211122, which is equenalent to a single resistor of 6x12 2 - = 72 -42 6+12 18 pedrawing the cioweit - for

New Req is giren as Req = 102 11 [42+ Gr 102 11 102 = 10x10 10+10 Req =52 News Time- constant (e) is given by - てた 2 0-2 second 2 or seconda Now, current litt is given as ilHz 110) + (ilo) - 1)] e . -50-2 = 0.7 + (-0.1 -0.4] e " Set) = 0.7 -0.8 10-2 Ampere Ampere ; valid for to checking - Answer -0 05 -0.7 -0.82 -0.14 Art=t0 .1100) = 0.7 -0.02 = 0.7A Badis fiel