Problem 78-8    Source:    Example 13-2 - page 500 -    SADIKU, Mathew & ALEXANDER, Charles -    Book: Fundamentos de Circuitos Elétricos - Ed. McGraw Hill - 5ª edição - 2013.

Determine the mesh currents in the circuit shown in Figure 78-08.1 when the circuit is powered by V = 100∠0°.

Solution of the Problema 78-8   

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 in the other winding will have a positive polarity facing the winding that has no point. Figure 78-08.2 shows how the circuit looked taking into account the influences of each chain. Note the direction of the currents. It is worth mentioning that the coil j6 circulates the currents I₁ and I₂. This is why there are two sources in series with the j8 coil. One due to influence of I₁ and another due to the influence of I₂. As the j8 coil only circulates I₂, so we have a single serial source with j6.

Based on the circuit shown in Figure 78-08.2, we will write the equations for the two loops. The equations are:

Soon, we got a system of two equations with two unknowns. Rearranging the equations, we have:

Solving the system with Octave, we find:

When we choose to consider the current always entering the point, the result obtained obeys the sense of the currents. If in a test or problem, it is established that the chain I₂, for example, is contrary to the one we adopted, so we must multiply the value found by - 1 . If that were the case, then the value of I₂ would be: