Problem 78-1    Source:   Problem developed by the author of the site.

Calculate the currents I₁ and I₂ on the circuit shown in Figure 78-01.1.

Solution of the Problem 78-1   

As we stated at the end of item 2 (in the theory part), whenever possible we will use the technique of the additive configuration. In this sense, Figure 78-01.2 shows the currents I_A and I_B entering the coil points. Through the circuit, we already know that I₁ = I_A and I₂ = - I_B.

With this we will obtain a voltage whose influence of each current in the other winding will have the positive polarity facing the winding that has no point. Figure 78-01.3 shows how the circuit looked, taking into account the influences of each current together with the mutual inductance.

Having established the circuit above, we can determine the equations that will solve the problem. For mesh A we have:

And for the B mesh we have:

So, we got a system of two equations with two unknowns and that can be rearranged, such that:

So, using programs like Octave, Matlab, scientific calculator, etc ..., let's get:

And as we stated at the beginning of solving the problem, we know that I₂ = - I_B. Therefore, the final answer to the problem is: