Question

Q1.Calculate the current I by superposition. ЧА Чл 128 3л 6л. I дох 55L

Answer 1

Superposition Theorem It states that for a leneul bilateral electrical circuit with more than one the gesponse auty element Source, across any due to individual is Gral to Some the individuel responses Sources Given circuit diagram: 4A A w 42 ia 3_2 1987 30ią. 6023 11 212 512 612 Let the current due to 128 V source source through be I Let the current due to 4A source through be be Iz . theorem By superposition I= It Is

Calculating I, and Now we have remove all sounes except 28 V source Heplace them with internal rogistance be, current source (4A) with Then the circuit will be as follows: open circuit. ix Vx 3 42 198V 30i, 6-2 YI, 52 Here ia = 128-Vx 4+2 - 198-VX 6 22 M By applying Kch at Vx node: Vx 128 Vx 6 + V x-Boix + co 4+2 3+5 Vx-128 VU Vx-30ix + + 50 6 8 6 5 Vx-128 6 Vx - 30 vxt šQ ( 13 ) 나 8 Vx-128 VX + Vx - 640+5VX + co 6 8 80 Cho =Vx-198 20 + V + + 6Vx 8 6

Vw [*+ 4+ 1 - 135 - 80 50 64 Vx/13 12 +80 = 64 +80 11 644 840 3 13 X9 = 304 Vx = 4x304 13 1216 13 Vx = 1216 13 from circuit diagram I, vt 1916/13 608 Il 606 tott 13 x16 11 = 6 3439 > I, - 608 39 A Now Calculating Id: we have to seplace all the sources except 4A Scurce witte the internal resistance i.e.) with short circuit, then will be as follows: 125V source the circuit

YA VB 3.2 Vc. Here in VA-VB VA w it 4.2 dlx 4 $6.2 zoia 5.1 2.12 By applying kch at VA node VA 2 VA + ve +4 70 Va[+6] +vo FH --4 [%] + [4] =-4 V 3 By applying Kch at VB node YB - VA 4 + 4 + VB-ve VB 6 20 vo [+3 +4] +46-7) +V(-)=0 Va (-a) + Vo( + Ve C 3)=0 >3 By applying Ich at Ve node: Vc - VB f Vc-30ine 6 =4 3

3 VA-VB Ve-VB + V-30 t 3 2 5 Vc - VB VA-VB Vc + c els = V-ve) 3 2 = 4 5 VEET 3 + + + 5+ V8 (5) 3 IS VA-VB) = 4 (2x8) Ve ( 1 8 15 Vol-12) - 3 VA + 3 VB og + "A(-2) + VB (22 ) + Vc (is) = 4 NA (-32) + Vol 3) + Ve ( )=4 (9 from earation un (A = -4+10( – Va: "[-4+ vect] 4x) + vela) -16 VA AS - Ve 3 VB-16 + Il 3 3 va = V8-16 3 By substituting VA in greation @ & gration &

Substitution en Cariation 3): 1:1) 69 VB + V3 (24) tve ( 32) 20 16 - VB 3x4 + + VB (3) + VC C co 3x4 12-#) + ( VBC +Vc (-1/2) N + 12 0 3 2 + Vel) = -4/3 Substitution in ecreation 6 (wg o + Vo(+6) +(83)=4 + 2 16 + 2. VB (3) + vc ()=4 2 VB [7 - + Ve (is) +8 = 4 > Vo(?) +ve ( ) = 4-8=-4 V8 (213) +Vc (is) =-4 6 By substituting eariation ② from eqruation ®. (2/3) + Ve (-²3) -473 -vecka) - Vc (815) = -(4) ve ( 23 & 4-4/3

Ne (ch 13 15 11 12-4 3 culos Vc = -8x15 13X3 --120 39 Vea -120 39 :-3077 V Vc =-3.0920 By substituting ve cen qreation : Ve +( 안 -120 39 Lula Х av 120 =-4 B t 39 2 VB -120 39 -4 = B 13 VB = .-92 -92 26 13X2 VB = -92 26 = -3,538 V. VB=-3-538 V Va eration ? cen By substituting VB 42 -16 VA -254/13 12-16 26 11 -854 39 3 3 3 -254 VA -6.51 28V 39 VA = 6.5/26V

Ig= VB from circuit diagram: - 3.538 6 Ig=-0.5896 A from circuit diagram: Ig = Ve -92/26 -92 il I! -92 26 X6 = 6 156 Ig - -92 i5 6 from egration 0: I= It - 608 39 92 156 I (608x156) - G2X39) (39x156) 15 91260 I- 3588 94898 6084 Holy I-ISA