Hi.
I want to write the most efficient method's equations.
Can you help me, please?
I heared that this method is Cyclic Currents Methods( i don't know if it's the name in English).
Thanks in advice.

 

I think the method you are referring to is Mesh Current Analysis.

That is certainly one way to solve the problem and, in this case, a very reasonable approach.

How many mesh equations will there be?

Are any of them solvable by inspection? If so, which ones? What is left?

 

I want to write the most efficient method's equations.

Since this problem is complex impedance analysis in the steady-state frequency domain, you must have already studied node & mesh analysis for resistors with DC sources. If this problem were posed with resistance instead of impedance, consider how the node or mesh analysis would be structured. Would it be any different for complex impedance? (Other than simple arithmetic vs complex arithmetic.) Note that for the resistive case there is only one mesh current that is unknown, and there is a single super-node so that only one node voltage is unknown. Can you get more efficient than a single equation?

 

Although it is not the question of the initiator of the discussion,
Does anyone want to apply Kirchhoff laws here?

 

Using mesh current or node voltage analysis IS apply Kirchhoff's laws.