Determine the currents `I_1, I_2, and I_3` for the network shown below

a. `I_1 = ………., b. I_2 = …………. , c. I_3 = …………….`

Explanation

Traversing the upper and lower loops anticlockwise, we get
`2I_1 +6I_2 =24 -27 or 2I_1 + 6I_2 = -3 (i)`
and `4I_3 - 6I_2 = 27 or 4(I_1- I_2)- 6I_2 = 27`
or `4I_1 - 10I_2 = 27 (ii)`

Soling Eqs. (i) and (ii) we get
`I_1 = 3A, I_2 = -1.5A, `
`I_3 = I_1 - I_2 = 3+ 1.5 = 4.5A`