Problem 78-7    Source:    Problem adapted of the Pratical Problem 13-13 - page 525 -    SADIKU, Mathew & ALEXANDER, Charles -    Book: Fundamentos de Circuitos Elétricos - Ed. McGraw Hill - 5ª edição - 2013.

Calculate the current I_o in the circuit shown in Figure 78-07.1 when the circuit is powered by V₁ = 160 cos (4t + 50°).

Solution of the Problem 78-7   

Whenever possible, we chose to place the direction of the current entering the points in the two windings. It doesn't matter where the points are. With that we will obtain a tension whose influence of each current on the other winding will have a positive polarity facing the winding that has no point. Figure 78-07.2 shows how the circuit looked taking into account the influences of each current. Note the direction of the currents.

Once all the circuit parameters are established, we only have to write the equations that solve the problem. We have three meshes. So the equations are:

So, we got a system of three equations to three unknowns that can be solved by any method. Using Octave, we find:

We can also write the result in trigonometric form, or: