Question

Chapter 5, Problem 5.022 Use superposition to find I, in the circuit in the figure below. 6ko V.=9V 6ko 3 ko | Vb=1V la = 2 mA +Va = 2V 35ko 1, with only Vturned on = Io with only Vy turned on = I. with only ve turned on = I, with only I, turned on =

Answer 1

Given circuit 2KR Pvc-av >6kr ama ۱۷ طV va-ar 35x2 То soft superposition pringle- In any linear active bilateral network, the effect Produced in any element when all the elements sources act at a time is equal to sumof the effects in the same element when each source is considered individually. (1) Io with only va turned on. Encept Va, all other sources suppressed with their internal resistances and circuit is redrawn as follows 36ke За Skr ( to avo VIO - Va tok Io +3K TO + sklo By applying kirchoff's voltage Law 2 - Io (6+3+5)K | Jols to (when wenty To, к А 14K Top= 0.1428 MAJO

Io with only y turned on. all other sources are replaced with their internal resistances circuit can be redrawnas. >6K2 I-TO I Bk2 {6kA lan ska bov incirant-1 Loop-1 =) Sч оро'Я 9 Е By applying kirchoff's voltage law SK Io + GICIO - 31 (I-JO) = 0 I (31) Io (sktok. +36) Io = I x pak Jo -I * - =) By applying krt in Loop-a. -1 + 6k I + 3ic (I - Io) =0 at +6KI + 316 I -31 Io =0 Io:Jog when &b alone considered - - 3) 14 (6k+36) I -3K (IX) = ! I (9K-2) I I = 147 mA Tor – Io = 14 4 3 4 ToR Io = 0.0 256MA Toa - Io = 0.0256 Ma

© To with only ve turned on. Hall other sources are replaced with their internal resistances. y circuit can be redrawn as var hoke IV -av Ssks To By applying KvL in loop- - - 9+ 6K (I+Io) +36 I = 0 9 = qk I +6KIO - > By applying Kve in loop @ tsk. In = 0 ok Io - 3k Io-103 when ve alone Considered. IllIo = 316I Io = 31 y using in eq 9 =qkI +61* I = $k + 12k) I I= ax 11 ma I = 113 MA Li from Eq Io = x | 1 oz i 117 Farma = 0.946mA

@ To with only In turned on Lall other sources are replaced with their internal resistances, circuit can be redrawn as 2+ Soke GIRS 3k2 I a=2MA { skr уто Tato =atio AR=3kalloke - 376 -9K2 6+3 Saka © Tarama I Solar Tasama I к 7) вка {ske уто from In 104 the circuit using current division rule when Is alone 6k+762 considered Joa= Is =-2 mx Joq = - 12 mA Tog; - 0.993 MA) -@ From Equations 0,30,0 Io = Iol + Toa + 103 + 104 usina si g superposition ineple To = 0.1488 +0.02 56+ 0,846 +(-0.923) To = 0.0914 MAI