Problem 55-19    Source:   Example 10.9 - page 396 -    IRWIN, J. David - Book: Circuit Analysis in Engineering - Ed. Pearson Education do Brasil - 4th edition - 2013.

Determine the voltage V_o in the circuit shown in Figure 55-19.1, using the Thévenin method.

Solution of the problem by Método Kirchhoff   click here!

Solution of the problem 55-19    -    Method of Thévenin

As we know, by Thevenin's theorem it is necessary to determine the Thevenin voltage, V_th, and the Thevenin impedance, Z_th. To apply the method, we must remove from the circuit the impedance where we want to determine the equivalent circuit. Figure 55-19.2 shows how the circuit after the necessary modifications.

Looking at the circuit, we easily determine the value of I_x = 4 ∠0°. This data allows that we directly calculate the value of V_th, making the mesh indicated by the blue arrow in Figure 55-19.2, or:

Now we must find the equivalent Thévenin impedance, Z_th, "viewed" from the points a-b, as shown in Figure 55-19.3. To do so, we must short circuit the independent voltage source, and remove the circuit-independent current source. The dependent current source continues in the circuit.

Conveniently, we introduce a current source of 1 A between the a-b terminals. Note that the arrow on the current source points downwards, so we have I_x = 1 A. Thus, the dependent current source assumes the value 2 A. Therefore, we conclude that through the inductor must pass a current of 1 A. So the voltage V_ab will be:

Now we can calculate Z_th, applying method 3, studied in chapter 15. So:

We have the necessary data to design the Thévenin equivalent circuit, as shown in Figure 55-19.4. Soon:

To find the value of V_o let's apply a voltage divider. Then:

Carrying out the calculation, we get

Note that the value found is the same as that obtained by the other method.