Question

Can you help me do b)?

In the circuit below, a) For t < 0, the switch has been open for a long time, find the inductor current? b) For t > 0, the switch is closed at t=0, find the inductor current using Thevenin's equivalent at the terminals a and b? And sketch the current waveform? c) Then find the steady-state, transient, forced and natural components? 22 V 10 v t=0 X 22 §

Answer 1

for t o the Switch has been open for a long time. Henie Grunt reached Steady state, so indutor alt as Short Circuit Indenfor Coment (460) lov (t IL (0) 2+2 = 24 732 A - for tso, The Cirkuit as follows, open the indufer aunt a,b 22v no and find Thenvenin's equiralent 6 Apply KeL at node the th-10 o 22 2 + - 0 22 22 24th = 32 h = 16v Short the voltage Sources and find cauivalent Resistence to Rh Rth = 2 +2 +3 – 45 2+2

Thevenin's Eauivalent Girluit ir lov T Iby T Lemo 21 6 we know, Cement through the inductors, { 10 = a) + Cizco) - incus dertle inductor where, (6) - Cument Llo) - T - through inductor at t=2 (Steady State Cument) Cement through inductor (at t:o) Constent of the Circuit initial Time At to Induiter become open, Gimont through the indulter. is iol. At t=0, Inductor belone short, circuit as follows. nas 1-met 4 (0) = 2A () = 16 - 4 Time Constant of the Cirmit to 12 = 2 2 = 2 sec Henie, Cument through the inductor for too, is. I, (t) = 4+ (2-4) e- / CIH - 4 - 2e

l(t) 10 t(sec)