Question

Use the step-by-step method to find i₀(5 ms) in the circuit in the figure below.

4 Ω t = 0 12 Ω 6ΩΣ i. (1) 4 Ω 12v (+ 3Η 3Α H

Please show all work and methods used.

Answer 1

circuit for txo 2.4 10 paralles (4116=24 un w Gri $ 120 & Is 12V 000 3 H 40, 3 A Leler 2H parallel ( 2113 = H) to current Sowce Convert Voltage Source or $42 w 12 ЗА ( wa 4 (3A المهم lo2H 4. 6r I 16A & 12 2 3 4r 1.214 The above circuit is 1st order circuit (ie the circuit consists of single energy storage element).

Current through any element is defined 98 ICt) = 1(a) + f (0) -160))et/ I. C) = I.() + (106)-I(0))etle I. CO) - TBA t =0 circuit at 62 ² 40 Io 3 42 12s 6A 1. 1.211 I. CO) - OA I. Cool - ! circuit as to .64 3 4.0 I. 122 het en GA ↑ 1.24 we can find lom as Current by Kothage devision Rule

I. (0) = 6x (41141112) 6+ (41141112) 6 X 12 = ㅋ 6 + 12 4 3 Io Cool 1.333 A the circuit 'e' is the time constant of Lea 7 = Req Leq こ 1.2 H Let find Req ( this is the resistance from inductor terminals) seen 6 4 4. :12 - Req Req = 4116 + 12116 9.4 +4 Req = 6.42

T - Lea Req = 1.2 6.4 こ 0.1875 sec Hence I. (t) is -tle i. (t) = e + (1. (0) - I.CO Io Cu + b) -t/0.1875 io (t) = 42 + (0-4) e io (t) = 4 (1-é -5.33t A for txo 3 at t = 5ms -5.33*5x103 4 (i-e e - 5*2*5x6 WII io (t=5m) 3 Yo (t=5 ms) - 0.03506 A.