The currents in a circuit can be determined by solving a sys

The currents in a circuit can be determined by solving a system of equations using Kirchhoff\'s law. Determine the currents in the circuit shown below: Establish the governing equations Establish the governing equations solve the system of equations using Gauss-Seidel iteration - use a tolerance of 0.01. How many iterations of converge?

Solution

apply kvl to loop current i1.

3i1+2(i1-i3)+4(i1-i2)=24

9i1-4i2-2i3=24 --------------------------------(1)

apply kvl to loop current i2.

4i2+16+4(i2-i1)+6(i2-i3)+3(i2-i4)=0

-4i1+17i2-6i3-3i4=-16 -------------------------------------(2)

apply kvl to loop current i3.

2(i3-i1)+6(i3-i4)+6(i3-i2)=0

-2i1-6i2+14i3-6i4=0 ------------------------------------(3)

apply kvl to loop current i4.

-18+2i4+3(i4-i2)+6(i4-i3)=0

-3i2-6i3+11i4=18 -----------------------------------(4).

from the above equations (1),(2),(3)&(4).

i1=4.034 amps.

i2=1.6545 amps.

i3=2.845 amps.

i4=3.6395 amps.