The electrical circuit shown consists of resistors and volta

The electrical circuit shown consists of resistors and voltage sources. Determine i_1, i_2, i_3, i_4 and i_5 using the mesh current method based on Kirchhoff\'s voltage law (see Sample Problem 3-4). V_1 = 40V, V_2 = 30 V, V_3 = 36 V R_1 = 16 ohm, R_2 = 20 ohm, R_3 = 10 ohm R_4 = 14 ohm, R_5 = 8 ohm R_6 = 16 ohm R_7 = 10 ohm, R_8 = 15 ohm, R_9 = 6 ohm, R_10 = 4 ohm

Solution

Equations:

1st loop:

-i5R10 + V1 - i5R4 + i2R4 - i5R8 + i4R8 = 0

i2(-R1) + i4(-R8) + i5(R4+R8+R10) = V1 --- (1)

2nd loop:

-i1R1 -i1R3 + i3R3 - i2R2 + i2R5 - V1 = 0

V1 = i1(-R1-R2-R3) + i3R3 + i2R5

3rd loop:

-i2R2 + i1R2 - i2R5 + i3R5 - i2R6 + i4R6 - i2R4 + i5R4 = 0

i2(-R2-R5-R6-R4) + i1R2 + 13R5 + i5R4 + i4R6 = 0 --(3)

4th loop:

i1R3 + i3(-R3-R7-R5) + i4R7 + i2R5 = V2 --(4)

Overall loop:

i1(-R1) + i4(-R9) + i5(-R10) = V2 - V3

Using these equations, and values from above, using the following matlab code:

%entering r coefficients using above equations

r = [0 -14 0 -15 33;
    -46 8 10 0 0;
    20 -58 8 16 14;
    10 8 -28 10 0;
    -16 0 0 -6 -4];

%constant coefficients

V = [40, 40, 0, 30, -6]\';

% i =inverse(r)*V

i = r\\V;

display(\'Values of currents:\')
I1=i(1)
I2=i(2)
I3=i(3)
I4=i(4)
I5=i(5)