Calculate the mesh currents i1 and i2 in the circuit.

My problem is... Is V always opposite to I and it comes always from + to - ??

If you could be so kind to write an equation for that, I would apologise that.

Greetings, Adam

 

The way I do it is to always make the voltage drop across a resistor due to the current in the mesh you're working on positive, as you go around the mesh in the direction indicated by the current arrow. If you encounter a resistor that is common to two meshes, then if the other mesh current is going in the same direction to the current in the mesh you're working on, use a positive sign. But if the current in the other mesh is going in the opposite direction, use a negative sign.

As you encounter voltage sources, use the sign you see when you enter the source.

For example, the equation for the i1 loop, starting at top left, would be:

5*i1 + 10*i1 - 10*i2 +10 -15 = 0

And, of course, the branch currents are related to the mesh currents like this: I1 = i1, I2 = i2 and I3 = i1-i2.