Problem 78-3
Source: Problem developed by the author of the site.
Write the equations that govern the circuit shown in Figure 78-03.1.
Solution of the Problem 78-3
So, this is the technique, that is, always put 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 78-03.2 shows how the circuit was, taking into
account the influences of each current.
In this circuit we have the two coils magnetically coupled indicated by the mutual inductance M.
In series with the first winding we have an impedance Z1and as a load for the secondary,
the impedance Z2. Note that the two currents,
I1 and I2, enter through the coil points.
In addition, the coils' reactances are represented by jX1 and jX2.
And of course, V is the alternating current source that powers the circuit.
Once all the circuit parameters are established, we only have to write the equations that solve
the problem. We have two meshes: one on the first winding where I1 circulates; and
another in the other winding where it circulates I2. We must not forget to take
into account the mutual inductance M. Soon as equations are::
So, we got a system of two equations with two unknowns that can be solved by any method.
