Question

LWW is(t) = A1 . cos(1000t +90) + A2 cos(2000t -90) Assume the system is in steady state. Find the current ia at times t1 47 ms: ia (t1) = B1 t2= 5m ms: ia (t2) = B2 kia(t) + R2 Given Variables: A1:9A A2:3A L:2 mH C:500 uF R1:10 ohm R2:2 ohm k:3 V/A Determine the following

Answer 1

Thansfermy the aicict nto Ueng phaseAs kIa R2 K,=10-2 R2=2 LO By KCL +Vi-kIS RatjwL V, R.+ tst)9 CosGeoot +96)+3 as (aooot-9) as UO1000 IsI =9190 Vi -k 9 10 = V 10 + JAIO00 X500xio 2tix2o00xRXIO VI +Vi- kxala0 2(क३) 9L20 3x9 Lg0 = V 1 + 2+jR to-JR o+19 +0+7 Vo3+6-j 231 -7.527+j 40 495

Tai 7537+jo-440.495 10-Ja =1.5025+J3749 - 4.04111.84 4.04 Cos(10oot +111.84 A ait) 1 Consdeing put 9Cos(2000t -9o as Tsa = 3-9o J= 200o +(M jao0ox ax1o 3 - 3x 3-90 31-90=Vi 104 a000X 50o K166 3 L-90 +990 R+jT Vi 10J1 o3+ 0-J9 i 6.0R1 + 10.061 Ta3 0.031+Jo o6 =0.0143+J1-9 x103 a014 7-57 az c)=.014 CosCR00ot+.57°A a, t)+daa t 04 as occt +1.84)t at) o.014 as Cao0st +.57 At t=4T ms act) = 404 Cas(ocox 4Txi111-84) +0.014 Cas coox 1TxTo+75 =3.27 A= B At t =5 Tms alt)=404os (00DX5TX 11-8+o.014as (o0ox5Txio+T57 =-2.45 A Ba 1