Problem 15-1    Source:    Problem elaborated by the author of the site.

In the circuit shown in Figure 15-01.1, calculate:

a) The currents i₁ , i₂ and i₃.

b) The voltage of the node e₁.

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 Kirchhoff Method   Click here!

Solution of the problem using Superposition Method   Click here!

Solution of the Problem 15-1   -    Thévenin/Norton Method

Analyzing the circuit one must decide the best one local to calculate the Thévenin equivalent. In this case, removing the resistor of 2 ohms can calculate the current i₂. With this data, all other variables can be calculated. Thus, the Figure 15-01.2 shows the modified circuit:

Remembering that V_th is the open circuit voltage. We can easily calculate it by making the circuit loop single loop counterclockwise as shows the figure above. Like this:

And therefore:

Therefore, by applying the Ohm law to the 6 ohms resistor and the voltage source of 20 V , we get:

To calculate R_th, all voltage sources must be annulled by short-circuiting them. In the Figure 15-01.3 we see the modified circuit.

Through the circuit it is easy to see that R_th is summarized to the parallel of the 4 ohms and 6 ohms resistors, resulting in:

See the Figure 15-01.4 for the Thévenin equivalent . Note that the resistor of 2 ohms has been replaced in its proper place.

Applying the Ohm law to the circuit, we easily calculate the current i₂, or:

Now that we know the value of i₂ , we can calculate the voltage e₁ by applying the Ohm law again:

And knowing e₁, it is possible to calculate i₁ and i₃.

Thus, we obtained the same results that were found using the other methods of circuit resolution.

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