For the circuit shown in Figure 2a Derive the mesh equations

For the circuit shown in Figure 2(a): Derive the mesh equations; and Determine the currents i1, i2 and i3.

Solution

apply kvl to loop current i1.

10i1-6+2(i1-i2)=0

12i1-2i2=6 ---------------(1)

apply kvl to loop current i2.

4i2+2(i2-i1)+1(i2-i3)+8=0

-2i1+7i2-i3=-8 ----------------(2)

apply kvl to loop current i3.

+6+5i3-8+1(i3-i2)=0

-i2+6i3=2 ---------------(3)

from equations (1),(2) &(3)

i1=0.329 amps

i2=-1.025 amps

i3=0.1623 amps.