Problem 15-2    Source:    Problem 4.12 - page 96 -    NILSSON & RIEDEL -    Book: Circuitos Elétricos - 8ª edição - Ed. Pearson Education do Brasil - 2010.

In the circuit shown in Figure 15-02.1, calculate:

The voltages in the nodes and the currents i₁ , i₂ , i₃ and i₄.

Solution of the problem using Method of Transforming Sources   Click here!

Solution of the problem using Nodal Voltage   Click here!

Solution of the problem using Superposition Method   Click here!

Solution of the Problem 15-2   -    Thévenin/Norton Method

Calculating i₃, facilitates the calculation of other currents. Thus the 80 ohms resistor will be removed from the circuit. Then, an open circuit appears between two terminals, these terminals where the Thévenin equivalent will be found. See the Figure 15-02.2 for the circuit.

We calculate the value of e₂ using the law of Ohm , that is:

For the calculation of e₁, we use a voltage divider resistive, or:

For the calculation of V_th, just do the mesh equation in the sense anti-clockwise, as shown by the green line in the figure above. Like this:

Solving the equation:

Now it is necessary to find the Thévenin resistance . To do this, simply remove all the independent sources of the circuit. Voltage sources are short circuited and current sources are open circuits , as shown in the Figure 15-02.3. Also, in the figure, the subsequent modifications are shown.

Note that the 4 ohms resistor is in parallel with that of 10 ohms , and the set is in series with that of 5 ohms . Doing the calculation:

As we already know V_th and R_th, we can draw the circuit. See ib the Figure 15-02.4 the circuit, with the inclusion of the 80 ohms resistor where we want to calculate i₃:

For the calculation of i₄, we know that:

We can calculate the values of e₁ e e₂. Applying the Ohm law to e₂, we obtain:

And to calculate e₁:

Finally, to calculate the values of i₁ e i₂, applying the Ohm law , or:

If we want proof that these results are correct, we can take stock circuit power.