Question

Find v, in the given circuit where P = 90 sin(2t) V. Please report your answer so the magnitude is positive and all angles are in the range of negative 180 degrees to positive 180 degrees. 0.5 H + P 2H ele ell 2 H vo 0.5 F The value of vo(t) = cos(2t+ 1) v.

Answer 1

Solafton O.SH + dan mo P-90 Sint) 24 - 0.5t P. Yo sinat v sinusoidal form 교 P = 9010° v polar form 2 rad /sec. 4-24 XL 2 un د اما 2x22 L2 2H X22= you WM 2 M- IR 0.5H XM 2 2xo.srz 2 ܘܝ |. I a In с 0.56 Xca 2x0.5 - a So This is circuit case of magnetically coupled there will be emf develop in both the loops due to current I, & I and Megnitically complet inductance M? 0.5 Hi current I, the is entering in dot (-) while Iz is dot (") leaving induced emf will be - ve for both loops.

- will Due to cument 1, a emp of JAMII induce în while in loop.it loop will induced. a emf of JXMI 2 Redraw circuit with induced emp loop-f loop- A مدل ji 90L0v Bliv -jin 1, jun jun Apply KVL în loop- 90/o- j Iz + jui, j 41, -j I 90 Lol 2 Apply KvL in loop- I (-ji) Iz at ju Iz rt (-UI) j31, +(ja) 31, +(-1) = 0 1, + 3 12

put 1, 2 312 In eq. jul 313) jI2 = 9010 j 11 12 qOLO' 90LO' A Iz qoco' JI А - 11190 I2 - 8.18 -90* A we can Now have IL through cap. so Current by find ܝܗܘܢ V Vo - ji (12) (14-901) ( 8-18 1190) u vo 8.18 (780° u -180 € +1809 οι Vo 8.18 (+1809 v both are some practically Vo o we This Can base is petar form of op voltage write it's sinusoidal from according to given ile p = qo sin(at) .', Vo 8:18 sin ( 24 +18) No 8.18 sinf 8t +90'+90) v

sin (90+0) as we know that ? Sime Cose Vo 8.16 sin (90* + (@t+90')) V 8.18 Cos (2t + 90') v Ansi Vo יו 1 this So the final from of vo is - decided Induced voltage always polarity s current direction in both loops. by is Same then cuments If behaviour of voltage induced is the otherwise -ve.