Question

Use Loop Analysis to complete the elements of the Amatrix of the equation A*I=S, where A is the nodal matrix, I is the loop currents vector and Sis the sources vector for the circuit below: 13 Z1 212 2/0° A 12/6° v Is Vs 22 Tize 11 73 & 14.01 24 32/2 v 13 Copy the Rxx and paste below then complete. R11= ; R12= ; R13= R21= ; R22= ; R23= R31= ; R32= ; R33=

Answer 1

Iz KVL egn in loop Os 260 4:22 1210 F B If = -2 Lo Zyz Ij = -2 Z2= -23 I 21 Vo KuL in loop o. (FB CD) E C 1240 - 2 (I2+Iz) -4; (I2-1) 20 12-2 Iz - 2 Iz - 4jI2 + 4It — Чј 1 I + 14j+2) In t e Iz 12 2) KuL in loop (AB COE) 2(In+ I) - (-2.3 ( 11+I3)) =0 -213 @j I, + & jIq – 2 Ig - 2 I2 – 213 =0 2ja 2 Iz +(21-4) Iz -3 from es. , , O A 4j+2 2 I2 -45 23 ~2 23-4 Se yo

Matlab Code:

clear all
close all
clc
% variable is define as Nodel_solution = [V1 V2 V3]'
A = [1 0 0;-4i (4i+2) 2;2i -2 (2i-4)]
S = [-2;12;0]
Z4 = 2 ;
I = A\S
I1 = I(1) ;
I2 = I(2) ;
I3 = I(3) ;
V0 = Z4 * (I2+I3) ;
R = abs(V0) ;
theta = phase(V0)*180/pi ;
disp(['V0 = ',num2str(V0)]) ;
disp(['V0 = ',num2str(R),'/_',num2str(theta)]) ;

Result:

MATLAB Command Window A = 1.0000 + 0.0000i 0.0000 4. 0000i 0.0000 + 2.0000i 0.0000 + 0.0000i 2.0000 + 4.0000i -2.0000 + 0.0000i 0.0000 + 0.0000i 2.0000 + 0.0000i -4.0000 + 2.0000i S = -2 12 0 I = -2.0000 + 0.0000i -0.6667 3.3333i -0.0000 + 0.6667i VO -1.3333-5.3333i 5.4975/-104.0362 VO >>