Problem 12-3    Source:    Example 5.10 - page 188 -    IRWIN, J. David -    Book: Análise de Circuitos em Engenharia - 4ª edição - Ed. Pearson - 2013.

In the circuit show in Figure 12-03.1, calculate:

a) The voltage at the terminals a-b.

b) The currents i_x , i_k.

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

Solution of the problem using Superposition Method   Click here!

Solution of the Problem 12-3   -    Nodal Voltage Method

Item a

Notice that we have three essential nodes and a super-node (e₁ and e₂). So we can write two node equations and one equation for the super-node. Then we have:

For the super-node equation, we have:

Substituting the above equation into the first parcela of the first equation and rearranging the terms, we arrive at:

Once this equality has been established, one can start to obtain the equation of the node e₃, or:

Note that these last two equations involve two unknowns. Therefore, solving the system we find the values of:

And as we know the relationship between e₁ and e₂, through the super-node equation we reach the value of e₁.

Item b

After calculating all the voltages of the nodes, we easily calculate the voltage between the terminals a-b, since we simply apply a resistive voltage divider, or:

Item c

Well, since we know all the voltages of the nodes, it is very easy to calculate the currents requested in the problem statement.