Find currents in different branches of th electric circuit shown in figure.
How to Proceed : In this problem there are three wires `EFAB, BE` and `BCDE`. Therefore, we have three unknown currents `i_1, i_2` and `i_3`. So, we require three equations. One equation will be obtained by applying Kirchhoff's junction law (either at `B` or at `E`) and the remainig two equations, we get from te second law (loop law). We can make three loops `ABEFA, ACDF` and `BCDEB`. But we have to chose any two of them. Initilly, we can choose any arbitrary directions of `i_1, i_2` and `i_3`.

Explanation

Applying Kirchhoff's firt law (junction law) at junction `B`,

Applying Kirhooff's second law in loop `1(ABEFA)` …………….i
`-4i_1+4-2I-+2=0`………..ii
Applying Kirchhoff's second law in loop 2 `(BCDEF)`,
`-2i_3-6-4i+3-4=0` ............iii
solving eqs i, ii, and iii we get
`i_1=1A`
`i_2=8/3A`
`i_3=-5/3A`
Here negative sign of `i_3` implies that current `i_3` is in opposite direction of what we have assumed.