Problema 15-16    Source:    Problem 13 - page 38 - PERIS, César F. & RIPOLL, M. A. Vicente    Book: 150 Problemas de Teoria de Circuitos - 2004.

Determine the value of V_o in the circuit shown in Figure 15-16.1.

Solution of the Problem 15-16

First, let's determine the Thévenin equivalent of the circuit highlighted by the orange rectangle. Thévenin's voltage is given by:

Thévenin's resistance is given by the parallel of the two resistors, or:

On the other hand, we can calculate the value of I_o as a function of I_x, because the value of V_x = 2k I_x. Therefore, I_o is given by:

In Figure 15-16.2 we see how the circuit looked after the calculations.

Note that the current flowing through the voltage sources is the sum of I_x + (2/7) I_x = (9/7) I_x. Knowing this, we can calculate the value of I_x simply by making the mesh indicated by the arrow brown in Figure 15-16.2. So:

So we have:

As we know that V_x = 2k I_x, then we easily calculate the value of V_o. Just make a voltage divider, that is:

Performing the calculation we find: