Problem 12-1    Source:   Problem elaborated by the author of the site.

In the circuit show in Figure 12-01.1, 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 Kirchhoff Method   Click here!

Solution of the problem using Superposition Method   Click here!

Solution of the problem using Thévenin/Norton Method   Click here!

Solution of the Problem 12-1   -    Nodal Voltage Method

Item a

Starting from the node e₁ we can write the equation:

Since we have a unique unknown we can solve the equation by finding the value of e₁, ou:

Item b

With the value of e₁ we can calculate the currents i₁ , i₂ e i₃. First, let's calculate the value of i₁:

As we can see, the current i₃ is negative meaning that its direction is contrary to that established in the circuit shown above.

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 of the circuit's powers.