For the network shown below apply mesh analysis to compute m

For the network shown below, apply mesh analysis to compute mesh currents i_a and i_b as well as element voltage v_c. For the network shown below, apply mesh analysis to compute mesh currents i_1 i_2, and i_3, as well as element current i_a and element voltage v_a.

Solution

1)

a) apply kvl to loop current ia.

-2+350ia+4+100(ia-ib)=0

450ia-100ib=-2 ------------------------(1)

apply kvl to loop current ib.

400ib+8+100(ib-ia)-4=0

-100ia+500ib=-4 --------------------------(2)

from equations (1) and (2).

ia=-6.5 mA.

ib=-9.3 mA.

vc=100(ia-ib)=280 mv.

b) apply kvl to loop current i1.

10i1-3va+20ib=0

10i1-3*5(i2-i3)+20*(-i2)=0

10i1-35i2+15i3=0 ---------------------(1).

apply kvl to loop current i2.

20i2-20(-i2)+5(i2-i3)=0

45i2-5i3=0 --------------------(2).

apply kvl to loop current i3.

+10+5(i3-i2)+3va=0

10+5(i3-i2)+3*5(i2-i3)=0

10i2-10i3=-10 -------------------(3).

from equations (1),(2) and (3).

i1=-1.25 A.

i2=0.125 A.

i3=1.125 A.

ia=i3-i2=1.125-0.125=1 A.

va=5(i2-i3)=-5 volts.