How can I find i0 using the mesh method?
Mesh Method: or nodal method divides the given circuit in different lops or meshes or nodes and they are solved separately. Here we have 3 meshes or nodes: right mesh, left mesh and top mesh.
Let us assume clockwise current, I1 in left mesh and anti-clockwise current, I2 in right mesh. The top mesh current, I0 is already given with clock-wise direction.
Using Kirchhoff's Voltage law:
Top Mesh: 6 I0 + 8 (I0 +I2) + 4 (I0 - I1) = 0
Left Mesh: 4 (I1 - I0) + 2(I1 + I2) +20 =0
Right Mesh: 2 (I1 + I2) + 50 + 8 (I2 + I0) = 0
solving all the equations, we get I0 = 5 A