Question

Chapter 30, Problem 054 In the figure, 3 = 148 V, R1 = 7.83 2, R2 = 16.92, R3 = 40.0 2, and L = 2.13 H. Immediately after switch S is closed, what are (a) i1 and (b) iz? (Let currents in the indicated directions have positive values and currents in the opposite directions have negative values.) A long time later, what are (c) j1 and (d) 12? The switch is then reopened. Just then, what are (e) 11 and (f) i2? A long time later, what are (9) 1 and (h)iz? RI R$ +8 La (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units (f) Number Units (9) Number Units (h) Number Units

Answer 1

t=0 RI Q. E148V, Ri=7.8382, R2 = 16.950, R2-401, L=2.13H Before switch is closed, current in inducteur coill be 2000. IL CO-) . OA let switch is closed at Immediately after closing switch since includes does not allow sudden change of cocient, curent in incluctor remains 2010 :. Ic 0+ )- II (0-) = OA Herce cosi court is bauen O. R3 Incorron " No worrent flows in incluctor, it is open circuited By ke at node a I= I cot) + Iz - I- Iz [ : IL 60+) =OA applying Kul in closed loop - I Rit I2 R2 = Iz=€ Rita =Y I 2: 148 A = Iz: 5.984 A 7.83+ 16:9) Immediately aftes A Iz R2 I JE E switch S is closed II 5.984A I2- 5.984A b u Ri w (:IIz) long time leter, the incluctor gets fully charged and hence becomes shost cermited. Hence after a long time, circuit A Ills) is drauen as, 군 Iz y R2 and R3 in parallel 1 1+1 = Rear : Rean SR3 R23 of E equivalent resistance B R2 Ro 1 Ro lla?

.. Read 40 R & applying sy Req1:11.8812 į 16.9 Hence circuit is creuenos I Kul in closed loop, E- I Rie Is Requ IĘ Reaa vo B Re Requ -Y I - 148 D o - Ii: 7.5A 7.83€ 11.88) :. 196 = I requsy VAB: 89.200 VAB = I₂ R2 ay I VAB 89.2 Rr 16:9 I2 = 5.278 A applying Kll at node , I = Izt Ila) » Is cool = I- Iz 7.5-5.278) A - Il coo) : 2.22 A - after a velty very long time I= 7.5 I 2 = 5.278A let switch is re-opened at tisec. Since inductor does not allow suelden change of cworent, current in inductor at titis, Il tit) - IL 600) = 2.22 A Hence citawit, immediately fter sreopening Suwitch is bausas, switch is opened, I TO of applying Kluat node A, or Iz + Illtat) R3 A R Tultit) TE R₂ Il ctit) IZ

:. 12 = - Ipctit) a - 2.22A :. (e LG OA I 2.a24 LV after a long time, incluctor gets fully discharged across R Ro and R3, Hence worent through incluctor after a long time. The is zoro ; Iz- - Iult) => I2= OA .. after long time switch of pavado-d16 Bursa I=OA b IL: OA