Question

find the current through the branch BC in the circuit shown in figure 1 using mesh analysis​

Answer 1

Applying KVL around mesh (loop)-1:(note in mesh-1, 1I is known as local current and

other mesh currents I2 3 &I are known as foreign currents.)

V V I IR I IR a c −− − − − = ( )( ) 1 32 1 24 0

( ) 2 4 1 42 2 3 I 313212111 V V R R I RI R a c −= + − − = − − IRIRIR (4.1)

Applying KVL around mesh (loop)-2:(similarly in mesh-2, 2 I is local current and

I1 3 & I are known as foreign currents)

−− − − − = V I IR I IR b ( )( ) 2 33 2 14 0

− =− + + − V RI R R I R b 41 3 4 2 33 ( ) I 323222121 = − + − IRIRIR (4.2)

Applying KVL around mesh (loop)-3:

V IR I I R I I R c − −− −− = 31 3 2 3 3 1 2 ( )( ) 0

V RI RI R R R c =− − + + + 21 32 1 2 3 3 ( )I 333232131 = − − + IRIRIR (4.3)

** In general, we can write for i

th mesh ( for i N = 1, 2,..... )

11 2 2 , 1 1 ........ .... ∑V RI R I RI R I R I ii i i =− − + − − ii i i i i + + iN N

∑Vii → simply means to take the algebraic sum of all voltage sources around the

mesh.

th i

Rii → means the total self resistance around the mesh. th i

Rij

→ means the mutual resistance between the and th j meshes.

Answer 2

Answer:

Go through the attachment dear...

Hope it help you...