Problem 78-5    Source:   Problem developed by the author of the site.

Determine the mesh currents and calculate the value of the power supplied by the source for the circuit shown in Figure 78-05.1.

Solution of the Problema 78-5   

As we stated at the end of item 2 (in the theory part), whenever possible we will use the additive configuration technique. In this sense, Figure 78-05.2 shows the currents I₁ and I₂ entering the coil points. With that we will obtain a voltage whose influence of each current in the other winding it will have a positive polarity facing the winding that has no point.

Having established the circuit above, we can determine the equations that will solve the problem. For mesh 1 we have:

And for mesh 2 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 to calculate the power that the source provides we must find the total current, I_T, which comes out of the source. For this, we must add the two currents, that is, I_T = I₁ + I₂. So, we get:

Therefore, the power supplied by the voltage source is: