Question

20 μF 50 cos 2 000t V +) $ 80 Ω $ 100 Ω 40 mH δο 2 sen 4 000t A ξ 60 Ω (+) 24V

Find io using superposition

Answer 1

SUPERPOSITION THEOREM(SPT):

In a linear network with several independent sources,the response in a particular branch when all the sources are acting simultaneously is equal to the linear sum of individual response calculated by taking one independent source at a time.

Note: All the ideal voltage sources are eliminated from the network by shorting the sources,all the ideal current sources are eliminated from the network by opening the sources and do not disturb the dependent sources present in the network.

Fلرمو a 802 n floo.. {loor 40 mit om 50 Gaccount, c 2 sin forot, 24V tas → when 50 los 2000t, v is acting alone; LI(t) = 50 cos 2000t, V. so coszoo Bose CO = 2000 Bad/sec "Loront XL = jwL = (2000)(40x103) b cos X = json 4 x = c - - - - = -325 4. {lbor Req = (bal/80)+(westion Ut) 0 {sor = 63,33 +355der Leiter = 76.61/ 45.88° s. VCA = ū = 5ole → phasor form :ico Soler 16.6114538 = .6 53-4588,4 na konsti) Ghetto) = 0,2176/134.12, A = 0 a = 0.2176 cos(2000t + 134.12"), A

→ when 2 sin 4000t, A source acting alone: xok (ay) T7i 380h {loor i(t) = 2 sin 4000t, A W = 4000 rad/soc X = a + ile 4000x20X10% Xc =-;12.5 & XL = jwL = j(4000)(408167 = 1 1602 or I = 218,A A + Y conversion: -112.52 H7 RV (160)(-j125) 2000 - 2000 Ra= 80+; 147.5 80+j147.5 167,8161.53 Re = 11.921-66.53", z = (5.68-j1o.47),us 112.5) (80) -j looo 1000 270 86+j(47,5 80 +j147. 5 1 67.8161.539 R6 = 5,96/208,47", ir = 45.24–32,84), ve RE = (1160)(RO - 1286096 80 +3147,5 167.8/61.500 Re = 76.28/28.47", 2 -5(67.05 +j36.36), uz

Now, the circuit becomes, 2 = (ice) ( Rether you 3loor =GT) T127,05 +3 36,36 Tiles {bon 61.81 +133.52 460 T 127.05+j 36,367 221.81 +j33.52 132.15/151970 e 224.33/8.590/ box = 1.10187.33%, A → 102 2 4.18) sin ( 4ooot +1871889), A .

when '24V' source acting alone? 80.2 1002 Vs = 24 v Wzo rad/sec XL = or s.c Xc = ou 0.C {for ③ zey {8o.2 oof 24v Elor 163 = 24 100+80+60 M 100 3802 24V 63 = 0.1, A bor i, According to the super position theorem, i = 1 + 12 + los * = Bob +0.2176) cos(2006€ + 134.12) + (1,18) sin(400ot +187.38°), A)