Use the mesh-current method to find the branch currents i a, i b, and i c in the

Question

Use the mesh-current method to find the branch currents ia, ib, and ic in the circuit in figure.(Figure 1) And find currents ia, ib, and ic if the polarity of the 79V source is reversed. The values of v1 and v2 are 79V and 30V , respectively.

Solve

A: Find the value of ia.

B: Find the value of ib.

C: Find the value of ic.

D: Find the value of ia  if the polarity of the 79V source is reversed.

E: Find the value of ib if the polarity of the 79V source is reversed.

F: Find the value of ic if the polarity of the 79V source is reversed.

Please answer as soon as possible

Explanation / Answer

we should note that ib=ia+ic

in left mesh:

v1-4*ia-10*(ia+ic)-ia=0

15*ia+10*ic=79...(1)

in right mesh:

v2-2*ic-10*(ia+ic)-3*ic=0

15*ic+10*ia=30..(2)

solving 1 and 2,

ia=7.08 A
ic=-2.72 A

ib=ia+ic=4.36 A

part 2:

now if 79 volt is reversed,
then first equation will be 15*ia+10*ic=-79

solving both the equations,
ia=-11.88 A
ic=9.92 A

ib=-1.96 A

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